Properties

Label 349.2.e.a.123.1
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.1
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.39209 + 1.38107i) q^{2} +(-0.0982202 + 0.170122i) q^{3} +(2.81473 - 4.87525i) q^{4} +(1.45632 - 2.52242i) q^{5} -0.542597i q^{6} +(-2.31421 + 1.33611i) q^{7} +10.0251i q^{8} +(1.48071 + 2.56466i) q^{9} +O(q^{10})\) \(q+(-2.39209 + 1.38107i) q^{2} +(-0.0982202 + 0.170122i) q^{3} +(2.81473 - 4.87525i) q^{4} +(1.45632 - 2.52242i) q^{5} -0.542597i q^{6} +(-2.31421 + 1.33611i) q^{7} +10.0251i q^{8} +(1.48071 + 2.56466i) q^{9} +8.04515i q^{10} -5.35089i q^{11} +(0.552926 + 0.957695i) q^{12} +(-0.294235 + 0.169876i) q^{13} +(3.69053 - 6.39218i) q^{14} +(0.286081 + 0.495506i) q^{15} +(-8.21590 - 14.2304i) q^{16} +0.0351415 q^{17} +(-7.08396 - 4.08992i) q^{18} +(0.808261 - 1.39995i) q^{19} +(-8.19829 - 14.1999i) q^{20} -0.524931i q^{21} +(7.38997 + 12.7998i) q^{22} +(-3.85967 - 6.68514i) q^{23} +(-1.70549 - 0.984664i) q^{24} +(-1.74175 - 3.01680i) q^{25} +(0.469224 - 0.812719i) q^{26} -1.17106 q^{27} +15.0431i q^{28} +(3.63841 - 6.30191i) q^{29} +(-1.36866 - 0.790196i) q^{30} +4.03069 q^{31} +(21.9424 + 12.6685i) q^{32} +(0.910306 + 0.525565i) q^{33} +(-0.0840616 + 0.0485330i) q^{34} +7.78322i q^{35} +16.6711 q^{36} -1.44509 q^{37} +4.46507i q^{38} -0.0667412i q^{39} +(25.2875 + 14.5997i) q^{40} +2.80612 q^{41} +(0.724968 + 1.25568i) q^{42} +(-3.09513 - 1.78697i) q^{43} +(-26.0869 - 15.0613i) q^{44} +8.62554 q^{45} +(18.4653 + 10.6610i) q^{46} -10.5226i q^{47} +3.22787 q^{48} +(0.0703696 - 0.121884i) q^{49} +(8.33284 + 4.81097i) q^{50} +(-0.00345160 + 0.00597836i) q^{51} +1.91262i q^{52} -0.107518i q^{53} +(2.80128 - 1.61732i) q^{54} +(-13.4972 - 7.79262i) q^{55} +(-13.3946 - 23.2001i) q^{56} +(0.158775 + 0.275006i) q^{57} +20.0996i q^{58} +(-8.10140 - 4.67734i) q^{59} +3.22095 q^{60} +9.48691i q^{61} +(-9.64178 + 5.56668i) q^{62} +(-6.85332 - 3.95677i) q^{63} -37.1206 q^{64} +0.989580i q^{65} -2.90338 q^{66} +14.1458 q^{67} +(0.0989137 - 0.171323i) q^{68} +1.51639 q^{69} +(-10.7492 - 18.6181i) q^{70} +(8.80233 - 5.08203i) q^{71} +(-25.7109 + 14.8442i) q^{72} +(7.39161 - 12.8026i) q^{73} +(3.45679 - 1.99578i) q^{74} +0.684300 q^{75} +(-4.55006 - 7.88094i) q^{76} +(7.14937 + 12.3831i) q^{77} +(0.0921745 + 0.159651i) q^{78} -2.08282i q^{79} -47.8600 q^{80} +(-4.32709 + 7.49475i) q^{81} +(-6.71248 + 3.87545i) q^{82} +(3.57122 + 6.18553i) q^{83} +(-2.55917 - 1.47754i) q^{84} +(0.0511773 - 0.0886418i) q^{85} +9.87176 q^{86} +(0.714730 + 1.23795i) q^{87} +53.6430 q^{88} +(-7.24874 - 4.18506i) q^{89} +(-20.6331 + 11.9125i) q^{90} +(0.453947 - 0.786259i) q^{91} -43.4556 q^{92} +(-0.395895 + 0.685711i) q^{93} +(14.5325 + 25.1710i) q^{94} +(-2.35418 - 4.07755i) q^{95} +(-4.31037 + 2.48860i) q^{96} +(-5.65666 + 3.26587i) q^{97} +0.388742i q^{98} +(13.7232 - 7.92309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39209 + 1.38107i −1.69146 + 0.976566i −0.738122 + 0.674667i \(0.764287\pi\)
−0.953340 + 0.301899i \(0.902380\pi\)
\(3\) −0.0982202 + 0.170122i −0.0567075 + 0.0982202i −0.892986 0.450085i \(-0.851394\pi\)
0.836278 + 0.548306i \(0.184727\pi\)
\(4\) 2.81473 4.87525i 1.40736 2.43762i
\(5\) 1.45632 2.52242i 0.651287 1.12806i −0.331524 0.943447i \(-0.607563\pi\)
0.982811 0.184615i \(-0.0591040\pi\)
\(6\) 0.542597i 0.221514i
\(7\) −2.31421 + 1.33611i −0.874688 + 0.505001i −0.868903 0.494982i \(-0.835175\pi\)
−0.00578476 + 0.999983i \(0.501841\pi\)
\(8\) 10.0251i 3.54440i
\(9\) 1.48071 + 2.56466i 0.493569 + 0.854886i
\(10\) 8.04515i 2.54410i
\(11\) 5.35089i 1.61335i −0.590993 0.806677i \(-0.701264\pi\)
0.590993 0.806677i \(-0.298736\pi\)
\(12\) 0.552926 + 0.957695i 0.159616 + 0.276463i
\(13\) −0.294235 + 0.169876i −0.0816060 + 0.0471153i −0.540248 0.841506i \(-0.681669\pi\)
0.458642 + 0.888621i \(0.348336\pi\)
\(14\) 3.69053 6.39218i 0.986334 1.70838i
\(15\) 0.286081 + 0.495506i 0.0738657 + 0.127939i
\(16\) −8.21590 14.2304i −2.05398 3.55759i
\(17\) 0.0351415 0.00852307 0.00426153 0.999991i \(-0.498644\pi\)
0.00426153 + 0.999991i \(0.498644\pi\)
\(18\) −7.08396 4.08992i −1.66970 0.964005i
\(19\) 0.808261 1.39995i 0.185428 0.321170i −0.758293 0.651914i \(-0.773966\pi\)
0.943721 + 0.330744i \(0.107300\pi\)
\(20\) −8.19829 14.1999i −1.83319 3.17519i
\(21\) 0.524931i 0.114549i
\(22\) 7.38997 + 12.7998i 1.57555 + 2.72893i
\(23\) −3.85967 6.68514i −0.804796 1.39395i −0.916429 0.400198i \(-0.868941\pi\)
0.111632 0.993750i \(-0.464392\pi\)
\(24\) −1.70549 0.984664i −0.348131 0.200994i
\(25\) −1.74175 3.01680i −0.348350 0.603360i
\(26\) 0.469224 0.812719i 0.0920223 0.159387i
\(27\) −1.17106 −0.225371
\(28\) 15.0431i 2.84288i
\(29\) 3.63841 6.30191i 0.675635 1.17023i −0.300648 0.953735i \(-0.597203\pi\)
0.976283 0.216499i \(-0.0694639\pi\)
\(30\) −1.36866 0.790196i −0.249882 0.144269i
\(31\) 4.03069 0.723934 0.361967 0.932191i \(-0.382105\pi\)
0.361967 + 0.932191i \(0.382105\pi\)
\(32\) 21.9424 + 12.6685i 3.87891 + 2.23949i
\(33\) 0.910306 + 0.525565i 0.158464 + 0.0914892i
\(34\) −0.0840616 + 0.0485330i −0.0144164 + 0.00832334i
\(35\) 7.78322i 1.31560i
\(36\) 16.6711 2.77852
\(37\) −1.44509 −0.237572 −0.118786 0.992920i \(-0.537900\pi\)
−0.118786 + 0.992920i \(0.537900\pi\)
\(38\) 4.46507i 0.724330i
\(39\) 0.0667412i 0.0106871i
\(40\) 25.2875 + 14.5997i 3.99830 + 2.30842i
\(41\) 2.80612 0.438242 0.219121 0.975698i \(-0.429681\pi\)
0.219121 + 0.975698i \(0.429681\pi\)
\(42\) 0.724968 + 1.25568i 0.111865 + 0.193756i
\(43\) −3.09513 1.78697i −0.472002 0.272511i 0.245075 0.969504i \(-0.421187\pi\)
−0.717078 + 0.696993i \(0.754521\pi\)
\(44\) −26.0869 15.0613i −3.93275 2.27057i
\(45\) 8.62554 1.28582
\(46\) 18.4653 + 10.6610i 2.72256 + 1.57187i
\(47\) 10.5226i 1.53488i −0.641120 0.767441i \(-0.721530\pi\)
0.641120 0.767441i \(-0.278470\pi\)
\(48\) 3.22787 0.465903
\(49\) 0.0703696 0.121884i 0.0100528 0.0174120i
\(50\) 8.33284 + 4.81097i 1.17844 + 0.680373i
\(51\) −0.00345160 + 0.00597836i −0.000483321 + 0.000837137i
\(52\) 1.91262i 0.265233i
\(53\) 0.107518i 0.0147687i −0.999973 0.00738437i \(-0.997649\pi\)
0.999973 0.00738437i \(-0.00235054\pi\)
\(54\) 2.80128 1.61732i 0.381206 0.220090i
\(55\) −13.4972 7.79262i −1.81996 1.05076i
\(56\) −13.3946 23.2001i −1.78993 3.10024i
\(57\) 0.158775 + 0.275006i 0.0210303 + 0.0364255i
\(58\) 20.0996i 2.63921i
\(59\) −8.10140 4.67734i −1.05471 0.608938i −0.130747 0.991416i \(-0.541738\pi\)
−0.923965 + 0.382477i \(0.875071\pi\)
\(60\) 3.22095 0.415823
\(61\) 9.48691i 1.21467i 0.794444 + 0.607337i \(0.207762\pi\)
−0.794444 + 0.607337i \(0.792238\pi\)
\(62\) −9.64178 + 5.56668i −1.22451 + 0.706969i
\(63\) −6.85332 3.95677i −0.863437 0.498506i
\(64\) −37.1206 −4.64008
\(65\) 0.989580i 0.122742i
\(66\) −2.90338 −0.357381
\(67\) 14.1458 1.72818 0.864090 0.503337i \(-0.167894\pi\)
0.864090 + 0.503337i \(0.167894\pi\)
\(68\) 0.0989137 0.171323i 0.0119950 0.0207760i
\(69\) 1.51639 0.182552
\(70\) −10.7492 18.6181i −1.28477 2.22529i
\(71\) 8.80233 5.08203i 1.04464 0.603126i 0.123499 0.992345i \(-0.460588\pi\)
0.921145 + 0.389219i \(0.127255\pi\)
\(72\) −25.7109 + 14.8442i −3.03006 + 1.74940i
\(73\) 7.39161 12.8026i 0.865122 1.49844i −0.00180318 0.999998i \(-0.500574\pi\)
0.866926 0.498438i \(-0.166093\pi\)
\(74\) 3.45679 1.99578i 0.401843 0.232004i
\(75\) 0.684300 0.0790161
\(76\) −4.55006 7.88094i −0.521928 0.904006i
\(77\) 7.14937 + 12.3831i 0.814746 + 1.41118i
\(78\) 0.0921745 + 0.159651i 0.0104367 + 0.0180769i
\(79\) 2.08282i 0.234336i −0.993112 0.117168i \(-0.962618\pi\)
0.993112 0.117168i \(-0.0373816\pi\)
\(80\) −47.8600 −5.35091
\(81\) −4.32709 + 7.49475i −0.480788 + 0.832750i
\(82\) −6.71248 + 3.87545i −0.741270 + 0.427972i
\(83\) 3.57122 + 6.18553i 0.391992 + 0.678951i 0.992712 0.120509i \(-0.0384526\pi\)
−0.600720 + 0.799460i \(0.705119\pi\)
\(84\) −2.55917 1.47754i −0.279228 0.161212i
\(85\) 0.0511773 0.0886418i 0.00555096 0.00961455i
\(86\) 9.87176 1.06450
\(87\) 0.714730 + 1.23795i 0.0766271 + 0.132722i
\(88\) 53.6430 5.71837
\(89\) −7.24874 4.18506i −0.768365 0.443616i 0.0639259 0.997955i \(-0.479638\pi\)
−0.832291 + 0.554339i \(0.812971\pi\)
\(90\) −20.6331 + 11.9125i −2.17491 + 1.25569i
\(91\) 0.453947 0.786259i 0.0475865 0.0824223i
\(92\) −43.4556 −4.53056
\(93\) −0.395895 + 0.685711i −0.0410524 + 0.0711049i
\(94\) 14.5325 + 25.1710i 1.49891 + 2.59619i
\(95\) −2.35418 4.07755i −0.241533 0.418348i
\(96\) −4.31037 + 2.48860i −0.439926 + 0.253991i
\(97\) −5.65666 + 3.26587i −0.574347 + 0.331599i −0.758884 0.651226i \(-0.774255\pi\)
0.184537 + 0.982826i \(0.440922\pi\)
\(98\) 0.388742i 0.0392689i
\(99\) 13.7232 7.92309i 1.37923 0.796301i
\(100\) −19.6102 −1.96102
\(101\) 16.8964i 1.68125i 0.541616 + 0.840626i \(0.317813\pi\)
−0.541616 + 0.840626i \(0.682187\pi\)
\(102\) 0.0190677i 0.00188798i
\(103\) 11.8362i 1.16626i −0.812380 0.583129i \(-0.801828\pi\)
0.812380 0.583129i \(-0.198172\pi\)
\(104\) −1.70302 2.94972i −0.166995 0.289244i
\(105\) −1.32410 0.764469i −0.129219 0.0746045i
\(106\) 0.148490 + 0.257193i 0.0144227 + 0.0249808i
\(107\) 0.133523 0.0770895i 0.0129081 0.00745252i −0.493532 0.869728i \(-0.664294\pi\)
0.506440 + 0.862275i \(0.330961\pi\)
\(108\) −3.29622 + 5.70922i −0.317179 + 0.549370i
\(109\) −0.821524 + 1.42292i −0.0786877 + 0.136291i −0.902684 0.430304i \(-0.858406\pi\)
0.823996 + 0.566595i \(0.191740\pi\)
\(110\) 43.0487 4.10453
\(111\) 0.141937 0.245842i 0.0134721 0.0233343i
\(112\) 38.0266 + 21.9547i 3.59318 + 2.07452i
\(113\) −5.52494 + 3.18982i −0.519742 + 0.300073i −0.736829 0.676079i \(-0.763678\pi\)
0.217087 + 0.976152i \(0.430344\pi\)
\(114\) −0.759608 0.438560i −0.0711438 0.0410749i
\(115\) −22.4837 −2.09661
\(116\) −20.4822 35.4763i −1.90173 3.29389i
\(117\) −0.871350 0.503074i −0.0805563 0.0465092i
\(118\) 25.8390 2.37867
\(119\) −0.0813247 + 0.0469528i −0.00745502 + 0.00430416i
\(120\) −4.96748 + 2.86798i −0.453467 + 0.261809i
\(121\) −17.6320 −1.60291
\(122\) −13.1021 22.6935i −1.18621 2.05458i
\(123\) −0.275617 + 0.477383i −0.0248516 + 0.0430442i
\(124\) 11.3453 19.6506i 1.01884 1.76468i
\(125\) 4.41703 0.395071
\(126\) 21.8583 1.94729
\(127\) 3.59361i 0.318881i 0.987208 + 0.159441i \(0.0509691\pi\)
−0.987208 + 0.159441i \(0.949031\pi\)
\(128\) 44.9110 25.9294i 3.96961 2.29186i
\(129\) 0.608008 0.351034i 0.0535321 0.0309068i
\(130\) −1.36668 2.36716i −0.119866 0.207614i
\(131\) 7.57106i 0.661486i 0.943721 + 0.330743i \(0.107299\pi\)
−0.943721 + 0.330743i \(0.892701\pi\)
\(132\) 5.12452 2.95864i 0.446032 0.257517i
\(133\) 4.31969i 0.374565i
\(134\) −33.8379 + 19.5363i −2.92315 + 1.68768i
\(135\) −1.70544 + 2.95391i −0.146781 + 0.254233i
\(136\) 0.352296i 0.0302091i
\(137\) 7.44782 + 4.30000i 0.636310 + 0.367374i 0.783192 0.621780i \(-0.213590\pi\)
−0.146882 + 0.989154i \(0.546924\pi\)
\(138\) −3.62734 + 2.09424i −0.308779 + 0.178274i
\(139\) −20.3259 −1.72402 −0.862011 0.506890i \(-0.830795\pi\)
−0.862011 + 0.506890i \(0.830795\pi\)
\(140\) 37.9451 + 21.9076i 3.20695 + 1.85153i
\(141\) 1.79013 + 1.03353i 0.150756 + 0.0870392i
\(142\) −14.0373 + 24.3133i −1.17798 + 2.04033i
\(143\) 0.908990 + 1.57442i 0.0760136 + 0.131659i
\(144\) 24.3307 42.1420i 2.02756 3.51183i
\(145\) −10.5974 18.3552i −0.880065 1.52432i
\(146\) 40.8334i 3.37940i
\(147\) 0.0138234 + 0.0239429i 0.00114014 + 0.00197478i
\(148\) −4.06753 + 7.04518i −0.334349 + 0.579110i
\(149\) 11.3275 6.53996i 0.927988 0.535774i 0.0418135 0.999125i \(-0.486686\pi\)
0.886175 + 0.463351i \(0.153353\pi\)
\(150\) −1.63691 + 0.945068i −0.133653 + 0.0771645i
\(151\) −5.33900 + 9.24742i −0.434482 + 0.752545i −0.997253 0.0740680i \(-0.976402\pi\)
0.562771 + 0.826613i \(0.309735\pi\)
\(152\) 14.0346 + 8.10287i 1.13836 + 0.657230i
\(153\) 0.0520342 + 0.0901259i 0.00420672 + 0.00728625i
\(154\) −34.2038 19.7476i −2.75622 1.59131i
\(155\) 5.86999 10.1671i 0.471489 0.816643i
\(156\) −0.325380 0.187858i −0.0260512 0.0150407i
\(157\) 0.679906 1.17763i 0.0542624 0.0939853i −0.837618 0.546256i \(-0.816053\pi\)
0.891881 + 0.452271i \(0.149386\pi\)
\(158\) 2.87653 + 4.98229i 0.228844 + 0.396370i
\(159\) 0.0182912 + 0.0105605i 0.00145059 + 0.000837498i
\(160\) 63.9104 36.8987i 5.05256 2.91710i
\(161\) 17.8641 + 10.3139i 1.40789 + 0.812846i
\(162\) 23.9041i 1.87809i
\(163\) 19.3336i 1.51433i 0.653226 + 0.757163i \(0.273415\pi\)
−0.653226 + 0.757163i \(0.726585\pi\)
\(164\) 7.89845 13.6805i 0.616765 1.06827i
\(165\) 2.65140 1.53079i 0.206411 0.119171i
\(166\) −17.0853 9.86423i −1.32608 0.765613i
\(167\) 20.3762i 1.57676i 0.615192 + 0.788378i \(0.289079\pi\)
−0.615192 + 0.788378i \(0.710921\pi\)
\(168\) 5.26247 0.406009
\(169\) −6.44228 + 11.1584i −0.495560 + 0.858336i
\(170\) 0.282719i 0.0216835i
\(171\) 4.78718 0.366085
\(172\) −17.4239 + 10.0597i −1.32856 + 0.767043i
\(173\) 5.42400 3.13155i 0.412379 0.238087i −0.279432 0.960165i \(-0.590146\pi\)
0.691812 + 0.722078i \(0.256813\pi\)
\(174\) −3.41940 1.97419i −0.259224 0.149663i
\(175\) 8.06154 + 4.65433i 0.609395 + 0.351834i
\(176\) −76.1451 + 43.9624i −5.73965 + 3.31379i
\(177\) 1.59144 0.918819i 0.119620 0.0690627i
\(178\) 23.1195 1.73288
\(179\) 21.1663i 1.58204i 0.611788 + 0.791022i \(0.290451\pi\)
−0.611788 + 0.791022i \(0.709549\pi\)
\(180\) 24.2785 42.0516i 1.80961 3.13434i
\(181\) 14.3589 1.06728 0.533642 0.845710i \(-0.320823\pi\)
0.533642 + 0.845710i \(0.320823\pi\)
\(182\) 2.50773i 0.185886i
\(183\) −1.61394 0.931806i −0.119306 0.0688811i
\(184\) 67.0190 38.6934i 4.94071 2.85252i
\(185\) −2.10452 + 3.64513i −0.154727 + 0.267995i
\(186\) 2.18704i 0.160362i
\(187\) 0.188038i 0.0137507i
\(188\) −51.3004 29.6183i −3.74146 2.16013i
\(189\) 2.71008 1.56467i 0.197129 0.113813i
\(190\) 11.2628 + 6.50258i 0.817089 + 0.471747i
\(191\) −12.3588 21.4061i −0.894253 1.54889i −0.834726 0.550665i \(-0.814374\pi\)
−0.0595272 0.998227i \(-0.518959\pi\)
\(192\) 3.64599 6.31505i 0.263127 0.455749i
\(193\) 1.94519 + 1.12306i 0.140018 + 0.0808393i 0.568372 0.822771i \(-0.307573\pi\)
−0.428355 + 0.903611i \(0.640907\pi\)
\(194\) 9.02082 15.6245i 0.647657 1.12178i
\(195\) −0.168350 0.0971967i −0.0120558 0.00696040i
\(196\) −0.396142 0.686138i −0.0282959 0.0490099i
\(197\) −6.70596 3.87169i −0.477780 0.275846i 0.241711 0.970348i \(-0.422291\pi\)
−0.719491 + 0.694502i \(0.755625\pi\)
\(198\) −21.8847 + 37.9055i −1.55528 + 2.69382i
\(199\) 4.34931 2.51108i 0.308315 0.178005i −0.337857 0.941197i \(-0.609702\pi\)
0.646172 + 0.763192i \(0.276369\pi\)
\(200\) 30.2436 17.4612i 2.13855 1.23469i
\(201\) −1.38940 + 2.40651i −0.0980007 + 0.169742i
\(202\) −23.3351 40.4176i −1.64185 2.84377i
\(203\) 19.4452i 1.36479i
\(204\) 0.0194306 + 0.0336549i 0.00136042 + 0.00235631i
\(205\) 4.08661 7.07822i 0.285421 0.494364i
\(206\) 16.3467 + 28.3133i 1.13893 + 1.97268i
\(207\) 11.4301 19.7974i 0.794444 1.37602i
\(208\) 4.83481 + 2.79138i 0.335234 + 0.193547i
\(209\) −7.49097 4.32491i −0.518161 0.299161i
\(210\) 4.22315 0.291425
\(211\) 11.7601 6.78971i 0.809600 0.467423i −0.0372172 0.999307i \(-0.511849\pi\)
0.846817 + 0.531885i \(0.178516\pi\)
\(212\) −0.524177 0.302634i −0.0360006 0.0207850i
\(213\) 1.99663i 0.136807i
\(214\) −0.212932 + 0.368810i −0.0145558 + 0.0252113i
\(215\) −9.01501 + 5.20482i −0.614818 + 0.354965i
\(216\) 11.7400i 0.798804i
\(217\) −9.32786 + 5.38544i −0.633216 + 0.365588i
\(218\) 4.53834i 0.307375i
\(219\) 1.45201 + 2.51496i 0.0981178 + 0.169945i
\(220\) −75.9819 + 43.8682i −5.12270 + 2.95759i
\(221\) −0.0103398 + 0.00596971i −0.000695534 + 0.000401566i
\(222\) 0.784102i 0.0526255i
\(223\) −2.47102 −0.165472 −0.0827360 0.996571i \(-0.526366\pi\)
−0.0827360 + 0.996571i \(0.526366\pi\)
\(224\) −67.7057 −4.52378
\(225\) 5.15804 8.93398i 0.343869 0.595599i
\(226\) 8.81076 15.2607i 0.586083 1.01513i
\(227\) 6.13283 + 10.6224i 0.407050 + 0.705032i 0.994558 0.104187i \(-0.0332241\pi\)
−0.587508 + 0.809219i \(0.699891\pi\)
\(228\) 1.78763 0.118389
\(229\) −2.79397 + 1.61310i −0.184631 + 0.106597i −0.589467 0.807793i \(-0.700662\pi\)
0.404836 + 0.914389i \(0.367329\pi\)
\(230\) 53.7829 31.0516i 3.54634 2.04748i
\(231\) −2.80885 −0.184809
\(232\) 63.1770 + 36.4753i 4.14778 + 2.39472i
\(233\) −4.34800 7.53096i −0.284847 0.493370i 0.687725 0.725971i \(-0.258610\pi\)
−0.972572 + 0.232602i \(0.925276\pi\)
\(234\) 2.77913 0.181677
\(235\) −26.5425 15.3243i −1.73144 0.999649i
\(236\) −45.6064 + 26.3309i −2.96872 + 1.71399i
\(237\) 0.354335 + 0.204575i 0.0230165 + 0.0132886i
\(238\) 0.129691 0.224631i 0.00840659 0.0145606i
\(239\) 7.24990 0.468957 0.234478 0.972121i \(-0.424662\pi\)
0.234478 + 0.972121i \(0.424662\pi\)
\(240\) 4.70082 8.14206i 0.303437 0.525568i
\(241\) 7.76119 13.4428i 0.499942 0.865926i −0.500058 0.865992i \(-0.666688\pi\)
1.00000 6.65409e-5i \(2.11806e-5\pi\)
\(242\) 42.1774 24.3511i 2.71126 1.56535i
\(243\) −2.60661 4.51478i −0.167214 0.289623i
\(244\) 46.2510 + 26.7030i 2.96092 + 1.70949i
\(245\) −0.204962 0.355004i −0.0130945 0.0226804i
\(246\) 1.52259i 0.0970769i
\(247\) 0.549218i 0.0349459i
\(248\) 40.4080i 2.56591i
\(249\) −1.40306 −0.0889155
\(250\) −10.5659 + 6.10024i −0.668248 + 0.385813i
\(251\) 20.6764i 1.30508i 0.757753 + 0.652542i \(0.226297\pi\)
−0.757753 + 0.652542i \(0.773703\pi\)
\(252\) −38.5804 + 22.2744i −2.43034 + 1.40316i
\(253\) −35.7714 + 20.6527i −2.24893 + 1.29842i
\(254\) −4.96304 8.59624i −0.311409 0.539376i
\(255\) 0.0100533 + 0.0174128i 0.000629562 + 0.00109043i
\(256\) −34.5001 + 59.7559i −2.15626 + 3.73475i
\(257\) 23.9827 1.49600 0.748001 0.663698i \(-0.231014\pi\)
0.748001 + 0.663698i \(0.231014\pi\)
\(258\) −0.969606 + 1.67941i −0.0603650 + 0.104555i
\(259\) 3.34424 1.93080i 0.207801 0.119974i
\(260\) 4.82445 + 2.78539i 0.299199 + 0.172743i
\(261\) 21.5496 1.33389
\(262\) −10.4562 18.1106i −0.645985 1.11888i
\(263\) −17.8223 −1.09897 −0.549484 0.835504i \(-0.685176\pi\)
−0.549484 + 0.835504i \(0.685176\pi\)
\(264\) −5.26883 + 9.12588i −0.324274 + 0.561659i
\(265\) −0.271206 0.156581i −0.0166601 0.00961870i
\(266\) −5.96581 10.3331i −0.365787 0.633563i
\(267\) 1.42395 0.822116i 0.0871441 0.0503127i
\(268\) 39.8165 68.9641i 2.43218 4.21265i
\(269\) −8.13958 −0.496279 −0.248140 0.968724i \(-0.579819\pi\)
−0.248140 + 0.968724i \(0.579819\pi\)
\(270\) 9.42137i 0.573366i
\(271\) 11.0480 + 19.1357i 0.671120 + 1.16241i 0.977587 + 0.210532i \(0.0675197\pi\)
−0.306467 + 0.951881i \(0.599147\pi\)
\(272\) −0.288719 0.500076i −0.0175062 0.0303216i
\(273\) 0.0891735 + 0.154453i 0.00539702 + 0.00934792i
\(274\) −23.7545 −1.43506
\(275\) −16.1426 + 9.31991i −0.973433 + 0.562012i
\(276\) 4.26822 7.39277i 0.256917 0.444993i
\(277\) −0.868236 + 0.501277i −0.0521673 + 0.0301188i −0.525857 0.850573i \(-0.676255\pi\)
0.473690 + 0.880692i \(0.342922\pi\)
\(278\) 48.6214 28.0716i 2.91612 1.68362i
\(279\) 5.96827 + 10.3373i 0.357311 + 0.618881i
\(280\) −78.0273 −4.66302
\(281\) 0.394144 0.682677i 0.0235126 0.0407251i −0.854030 0.520224i \(-0.825848\pi\)
0.877542 + 0.479499i \(0.159182\pi\)
\(282\) −5.70954 −0.339998
\(283\) −2.05156 −0.121952 −0.0609762 0.998139i \(-0.519421\pi\)
−0.0609762 + 0.998139i \(0.519421\pi\)
\(284\) 57.2180i 3.39527i
\(285\) 0.924911 0.0547870
\(286\) −4.34877 2.51076i −0.257148 0.148465i
\(287\) −6.49394 + 3.74928i −0.383325 + 0.221313i
\(288\) 75.0330i 4.42136i
\(289\) −16.9988 −0.999927
\(290\) 50.6998 + 29.2715i 2.97719 + 1.71888i
\(291\) 1.28310i 0.0752166i
\(292\) −41.6107 72.0718i −2.43508 4.21769i
\(293\) −5.78761 10.0244i −0.338116 0.585634i 0.645962 0.763369i \(-0.276456\pi\)
−0.984078 + 0.177735i \(0.943123\pi\)
\(294\) −0.0661338 0.0381823i −0.00385700 0.00222684i
\(295\) −23.5965 + 13.6234i −1.37384 + 0.793187i
\(296\) 14.4871i 0.842048i
\(297\) 6.26622i 0.363603i
\(298\) −18.0643 + 31.2883i −1.04644 + 1.81248i
\(299\) 2.27130 + 1.31133i 0.131352 + 0.0758364i
\(300\) 1.92612 3.33613i 0.111204 0.192612i
\(301\) 9.55035 0.550473
\(302\) 29.4942i 1.69720i
\(303\) −2.87445 1.65957i −0.165133 0.0953395i
\(304\) −26.5624 −1.52346
\(305\) 23.9300 + 13.8160i 1.37023 + 0.791102i
\(306\) −0.248941 0.143726i −0.0142310 0.00821627i
\(307\) 7.76635 + 13.4517i 0.443249 + 0.767730i 0.997928 0.0643343i \(-0.0204924\pi\)
−0.554679 + 0.832064i \(0.687159\pi\)
\(308\) 80.4940 4.58657
\(309\) 2.01361 + 1.16256i 0.114550 + 0.0661355i
\(310\) 32.4275i 1.84176i
\(311\) 1.80144i 0.102150i −0.998695 0.0510751i \(-0.983735\pi\)
0.998695 0.0510751i \(-0.0162648\pi\)
\(312\) 0.669085 0.0378795
\(313\) 34.1766 1.93178 0.965889 0.258956i \(-0.0833786\pi\)
0.965889 + 0.258956i \(0.0833786\pi\)
\(314\) 3.75600i 0.211963i
\(315\) −19.9613 + 11.5247i −1.12469 + 0.649341i
\(316\) −10.1543 5.86257i −0.571222 0.329795i
\(317\) −5.48213 3.16511i −0.307907 0.177770i 0.338083 0.941116i \(-0.390222\pi\)
−0.645990 + 0.763346i \(0.723555\pi\)
\(318\) −0.0583390 −0.00327149
\(319\) −33.7208 19.4687i −1.88800 1.09004i
\(320\) −54.0596 + 93.6340i −3.02202 + 5.23430i
\(321\) 0.0302870i 0.00169045i
\(322\) −56.9768 −3.17519
\(323\) 0.0284035 0.0491963i 0.00158041 0.00273735i
\(324\) 24.3592 + 42.1913i 1.35329 + 2.34396i
\(325\) 1.02497 + 0.591764i 0.0568549 + 0.0328252i
\(326\) −26.7011 46.2477i −1.47884 2.56143i
\(327\) −0.161381 0.279519i −0.00892436 0.0154574i
\(328\) 28.1315i 1.55330i
\(329\) 14.0594 + 24.3515i 0.775117 + 1.34254i
\(330\) −4.22825 + 7.32355i −0.232758 + 0.403148i
\(331\) 13.9623 + 8.06114i 0.767438 + 0.443080i 0.831960 0.554836i \(-0.187219\pi\)
−0.0645220 + 0.997916i \(0.520552\pi\)
\(332\) 40.2080 2.20670
\(333\) −2.13975 3.70616i −0.117258 0.203097i
\(334\) −28.1410 48.7416i −1.53981 2.66702i
\(335\) 20.6008 35.6816i 1.12554 1.94950i
\(336\) −7.46996 + 4.31278i −0.407520 + 0.235282i
\(337\) −2.95327 5.11522i −0.160875 0.278644i 0.774308 0.632809i \(-0.218098\pi\)
−0.935183 + 0.354166i \(0.884765\pi\)
\(338\) 35.5891i 1.93579i
\(339\) 1.25322i 0.0680656i
\(340\) −0.288100 0.499004i −0.0156244 0.0270623i
\(341\) 21.5678i 1.16796i
\(342\) −11.4514 + 6.61145i −0.619219 + 0.357506i
\(343\) 18.3294i 0.989696i
\(344\) 17.9145 31.0289i 0.965886 1.67296i
\(345\) 2.20835 3.82498i 0.118894 0.205930i
\(346\) −8.64980 + 14.9819i −0.465016 + 0.805431i
\(347\) −4.39995 + 2.54031i −0.236202 + 0.136371i −0.613430 0.789749i \(-0.710211\pi\)
0.377228 + 0.926120i \(0.376877\pi\)
\(348\) 8.04707 0.431368
\(349\) 16.0822 9.50595i 0.860860 0.508842i
\(350\) −25.7119 −1.37436
\(351\) 0.344567 0.198936i 0.0183916 0.0106184i
\(352\) 67.7875 117.411i 3.61309 6.25805i
\(353\) 8.22288 14.2424i 0.437660 0.758049i −0.559849 0.828595i \(-0.689141\pi\)
0.997509 + 0.0705461i \(0.0224742\pi\)
\(354\) −2.53791 + 4.39579i −0.134889 + 0.233634i
\(355\) 29.6043i 1.57123i
\(356\) −40.8064 + 23.5596i −2.16274 + 1.24866i
\(357\) 0.0184469i 0.000976312i
\(358\) −29.2322 50.6317i −1.54497 2.67597i
\(359\) 11.6802i 0.616456i 0.951313 + 0.308228i \(0.0997359\pi\)
−0.951313 + 0.308228i \(0.900264\pi\)
\(360\) 86.4716i 4.55745i
\(361\) 8.19343 + 14.1914i 0.431233 + 0.746918i
\(362\) −34.3476 + 19.8306i −1.80527 + 1.04227i
\(363\) 1.73182 2.99960i 0.0908970 0.157438i
\(364\) −2.55547 4.42620i −0.133943 0.231996i
\(365\) −21.5291 37.2895i −1.12689 1.95182i
\(366\) 5.14757 0.269068
\(367\) −1.51426 0.874258i −0.0790437 0.0456359i 0.459957 0.887941i \(-0.347865\pi\)
−0.539001 + 0.842305i \(0.681198\pi\)
\(368\) −63.4213 + 109.849i −3.30606 + 5.72627i
\(369\) 4.15503 + 7.19673i 0.216302 + 0.374647i
\(370\) 11.6260i 0.604406i
\(371\) 0.143656 + 0.248819i 0.00745824 + 0.0129180i
\(372\) 2.22867 + 3.86018i 0.115551 + 0.200141i
\(373\) 9.97244 + 5.75759i 0.516354 + 0.298117i 0.735441 0.677588i \(-0.236975\pi\)
−0.219088 + 0.975705i \(0.570308\pi\)
\(374\) 0.259695 + 0.449804i 0.0134285 + 0.0232588i
\(375\) −0.433842 + 0.751436i −0.0224035 + 0.0388040i
\(376\) 105.490 5.44023
\(377\) 2.47232i 0.127331i
\(378\) −4.32183 + 7.48564i −0.222291 + 0.385020i
\(379\) 14.5004 + 8.37181i 0.744835 + 0.430031i 0.823825 0.566845i \(-0.191836\pi\)
−0.0789894 + 0.996875i \(0.525169\pi\)
\(380\) −26.5054 −1.35970
\(381\) −0.611354 0.352965i −0.0313206 0.0180830i
\(382\) 59.1268 + 34.1369i 3.02519 + 1.74659i
\(383\) −10.6927 + 6.17345i −0.546373 + 0.315449i −0.747658 0.664084i \(-0.768822\pi\)
0.201285 + 0.979533i \(0.435488\pi\)
\(384\) 10.1872i 0.519861i
\(385\) 41.6471 2.12253
\(386\) −6.20409 −0.315780
\(387\) 10.5839i 0.538011i
\(388\) 36.7701i 1.86672i
\(389\) 3.18983 + 1.84165i 0.161731 + 0.0933754i 0.578681 0.815554i \(-0.303568\pi\)
−0.416950 + 0.908929i \(0.636901\pi\)
\(390\) 0.536943 0.0271892
\(391\) −0.135634 0.234926i −0.00685933 0.0118807i
\(392\) 1.22189 + 0.705460i 0.0617149 + 0.0356311i
\(393\) −1.28801 0.743631i −0.0649713 0.0375112i
\(394\) 21.3883 1.07753
\(395\) −5.25376 3.03326i −0.264345 0.152620i
\(396\) 89.2053i 4.48274i
\(397\) 14.2477 0.715073 0.357536 0.933899i \(-0.383617\pi\)
0.357536 + 0.933899i \(0.383617\pi\)
\(398\) −6.93596 + 12.0134i −0.347668 + 0.602179i
\(399\) −0.734877 0.424281i −0.0367898 0.0212406i
\(400\) −28.6201 + 49.5714i −1.43100 + 2.47857i
\(401\) 19.4375i 0.970663i −0.874330 0.485332i \(-0.838699\pi\)
0.874330 0.485332i \(-0.161301\pi\)
\(402\) 7.67545i 0.382817i
\(403\) −1.18597 + 0.684720i −0.0590774 + 0.0341083i
\(404\) 82.3740 + 47.5587i 4.09826 + 2.36613i
\(405\) 12.6033 + 21.8295i 0.626262 + 1.08472i
\(406\) −26.8553 46.5147i −1.33280 2.30849i
\(407\) 7.73252i 0.383287i
\(408\) −0.0599334 0.0346026i −0.00296715 0.00171308i
\(409\) −23.1487 −1.14463 −0.572314 0.820034i \(-0.693954\pi\)
−0.572314 + 0.820034i \(0.693954\pi\)
\(410\) 22.5756i 1.11493i
\(411\) −1.46305 + 0.844694i −0.0721671 + 0.0416657i
\(412\) −57.7045 33.3157i −2.84290 1.64135i
\(413\) 24.9977 1.23006
\(414\) 63.1430i 3.10331i
\(415\) 20.8034 1.02120
\(416\) −8.60829 −0.422056
\(417\) 1.99642 3.45789i 0.0977649 0.169334i
\(418\) 23.8921 1.16860
\(419\) 3.01164 + 5.21632i 0.147128 + 0.254834i 0.930165 0.367142i \(-0.119664\pi\)
−0.783037 + 0.621976i \(0.786330\pi\)
\(420\) −7.45395 + 4.30354i −0.363716 + 0.209991i
\(421\) 15.0567 8.69300i 0.733819 0.423671i −0.0859986 0.996295i \(-0.527408\pi\)
0.819818 + 0.572625i \(0.194075\pi\)
\(422\) −18.7542 + 32.4832i −0.912938 + 1.58126i
\(423\) 26.9869 15.5809i 1.31215 0.757569i
\(424\) 1.07788 0.0523463
\(425\) −0.0612077 0.106015i −0.00296901 0.00514247i
\(426\) −2.75749 4.77612i −0.133601 0.231404i
\(427\) −12.6755 21.9547i −0.613412 1.06246i
\(428\) 0.867943i 0.0419536i
\(429\) −0.357125 −0.0172422
\(430\) 14.3765 24.9008i 0.693294 1.20082i
\(431\) 4.56967 2.63830i 0.220113 0.127082i −0.385889 0.922545i \(-0.626105\pi\)
0.606003 + 0.795463i \(0.292772\pi\)
\(432\) 9.62133 + 16.6646i 0.462907 + 0.801778i
\(433\) 16.3268 + 9.42626i 0.784614 + 0.452997i 0.838063 0.545573i \(-0.183688\pi\)
−0.0534488 + 0.998571i \(0.517021\pi\)
\(434\) 14.8754 25.7649i 0.714041 1.23676i
\(435\) 4.16351 0.199625
\(436\) 4.62473 + 8.01027i 0.221484 + 0.383622i
\(437\) −12.4785 −0.596926
\(438\) −6.94668 4.01067i −0.331925 0.191637i
\(439\) 19.9462 11.5159i 0.951981 0.549626i 0.0582850 0.998300i \(-0.481437\pi\)
0.893696 + 0.448674i \(0.148103\pi\)
\(440\) 78.1216 135.311i 3.72430 6.45068i
\(441\) 0.416787 0.0198470
\(442\) 0.0164892 0.0285602i 0.000784312 0.00135847i
\(443\) −4.19028 7.25778i −0.199086 0.344827i 0.749146 0.662405i \(-0.230464\pi\)
−0.948232 + 0.317577i \(0.897131\pi\)
\(444\) −0.799028 1.38396i −0.0379202 0.0656797i
\(445\) −21.1130 + 12.1896i −1.00085 + 0.577843i
\(446\) 5.91091 3.41266i 0.279890 0.161594i
\(447\) 2.56942i 0.121530i
\(448\) 85.9048 49.5972i 4.05862 2.34325i
\(449\) −4.01620 −0.189536 −0.0947681 0.995499i \(-0.530211\pi\)
−0.0947681 + 0.995499i \(0.530211\pi\)
\(450\) 28.4945i 1.34324i
\(451\) 15.0152i 0.707040i
\(452\) 35.9139i 1.68925i
\(453\) −1.04880 1.81657i −0.0492767 0.0853498i
\(454\) −29.3405 16.9398i −1.37702 0.795023i
\(455\) −1.32219 2.29009i −0.0619850 0.107361i
\(456\) −2.75696 + 1.59173i −0.129106 + 0.0745396i
\(457\) 1.66443 2.88288i 0.0778589 0.134855i −0.824467 0.565910i \(-0.808525\pi\)
0.902326 + 0.431054i \(0.141858\pi\)
\(458\) 4.45562 7.71736i 0.208198 0.360609i
\(459\) −0.0411529 −0.00192085
\(460\) −63.2854 + 109.613i −2.95070 + 5.11075i
\(461\) −1.69157 0.976631i −0.0787845 0.0454862i 0.460090 0.887872i \(-0.347817\pi\)
−0.538875 + 0.842386i \(0.681150\pi\)
\(462\) 6.71902 3.87923i 0.312597 0.180478i
\(463\) −1.72203 0.994212i −0.0800293 0.0462050i 0.459451 0.888203i \(-0.348046\pi\)
−0.539481 + 0.841998i \(0.681379\pi\)
\(464\) −119.571 −5.55095
\(465\) 1.15310 + 1.99723i 0.0534739 + 0.0926194i
\(466\) 20.8016 + 12.0098i 0.963617 + 0.556344i
\(467\) −7.84717 −0.363123 −0.181562 0.983380i \(-0.558115\pi\)
−0.181562 + 0.983380i \(0.558115\pi\)
\(468\) −4.90522 + 2.83203i −0.226744 + 0.130911i
\(469\) −32.7362 + 18.9003i −1.51162 + 0.872734i
\(470\) 84.6560 3.90489
\(471\) 0.133561 + 0.231335i 0.00615417 + 0.0106593i
\(472\) 46.8907 81.2171i 2.15832 3.73832i
\(473\) −9.56189 + 16.5617i −0.439656 + 0.761507i
\(474\) −1.13013 −0.0519087
\(475\) −5.63115 −0.258375
\(476\) 0.528637i 0.0242301i
\(477\) 0.275747 0.159203i 0.0126256 0.00728939i
\(478\) −17.3424 + 10.0126i −0.793223 + 0.457967i
\(479\) −2.26532 3.92365i −0.103505 0.179276i 0.809621 0.586952i \(-0.199672\pi\)
−0.913126 + 0.407676i \(0.866339\pi\)
\(480\) 14.4968i 0.661685i
\(481\) 0.425196 0.245487i 0.0193873 0.0111932i
\(482\) 42.8751i 1.95291i
\(483\) −3.50924 + 2.02606i −0.159676 + 0.0921889i
\(484\) −49.6293 + 85.9605i −2.25588 + 3.90729i
\(485\) 19.0247i 0.863865i
\(486\) 12.4705 + 7.19983i 0.565672 + 0.326591i
\(487\) 0.703125 0.405949i 0.0318616 0.0183953i −0.483985 0.875077i \(-0.660811\pi\)
0.515846 + 0.856681i \(0.327478\pi\)
\(488\) −95.1069 −4.30529
\(489\) −3.28908 1.89895i −0.148737 0.0858736i
\(490\) 0.980573 + 0.566134i 0.0442978 + 0.0255753i
\(491\) −2.93041 + 5.07562i −0.132247 + 0.229059i −0.924543 0.381079i \(-0.875553\pi\)
0.792295 + 0.610138i \(0.208886\pi\)
\(492\) 1.55157 + 2.68741i 0.0699504 + 0.121158i
\(493\) 0.127859 0.221458i 0.00575848 0.00997399i
\(494\) −0.758510 1.31378i −0.0341270 0.0591097i
\(495\) 46.1543i 2.07448i
\(496\) −33.1158 57.3582i −1.48694 2.57546i
\(497\) −13.5803 + 23.5217i −0.609159 + 1.05509i
\(498\) 3.35625 1.93773i 0.150397 0.0868319i
\(499\) 7.27105 4.19794i 0.325497 0.187926i −0.328343 0.944558i \(-0.606490\pi\)
0.653840 + 0.756633i \(0.273157\pi\)
\(500\) 12.4327 21.5341i 0.556008 0.963035i
\(501\) −3.46644 2.00135i −0.154869 0.0894138i
\(502\) −28.5556 49.4598i −1.27450 2.20750i
\(503\) 12.0625 + 6.96431i 0.537842 + 0.310523i 0.744204 0.667953i \(-0.232829\pi\)
−0.206362 + 0.978476i \(0.566162\pi\)
\(504\) 39.6669 68.7050i 1.76690 3.06036i
\(505\) 42.6198 + 24.6066i 1.89656 + 1.09498i
\(506\) 57.0456 98.8060i 2.53599 4.39246i
\(507\) −1.26552 2.19195i −0.0562039 0.0973481i
\(508\) 17.5197 + 10.1150i 0.777313 + 0.448782i
\(509\) 24.0920 13.9095i 1.06786 0.616528i 0.140262 0.990114i \(-0.455206\pi\)
0.927595 + 0.373587i \(0.121872\pi\)
\(510\) −0.0480968 0.0277687i −0.00212976 0.00122962i
\(511\) 39.5040i 1.74755i
\(512\) 86.8711i 3.83920i
\(513\) −0.946523 + 1.63943i −0.0417900 + 0.0723824i
\(514\) −57.3688 + 33.1219i −2.53043 + 1.46094i
\(515\) −29.8560 17.2374i −1.31561 0.759568i
\(516\) 3.95225i 0.173988i
\(517\) −56.3054 −2.47631
\(518\) −5.33315 + 9.23728i −0.234325 + 0.405863i
\(519\) 1.23033i 0.0540053i
\(520\) −9.92061 −0.435047
\(521\) −26.4320 + 15.2605i −1.15801 + 0.668576i −0.950826 0.309727i \(-0.899762\pi\)
−0.207181 + 0.978303i \(0.566429\pi\)
\(522\) −51.5486 + 29.7616i −2.25622 + 1.30263i
\(523\) −24.8019 14.3194i −1.08451 0.626144i −0.152403 0.988318i \(-0.548701\pi\)
−0.932110 + 0.362175i \(0.882034\pi\)
\(524\) 36.9108 + 21.3104i 1.61245 + 0.930951i
\(525\) −1.58361 + 0.914298i −0.0691145 + 0.0399033i
\(526\) 42.6324 24.6139i 1.85886 1.07321i
\(527\) 0.141645 0.00617014
\(528\) 17.2720i 0.751666i
\(529\) −18.2941 + 31.6862i −0.795394 + 1.37766i
\(530\) 0.864999 0.0375732
\(531\) 27.7031i 1.20221i
\(532\) 21.0596 + 12.1588i 0.913048 + 0.527149i
\(533\) −0.825657 + 0.476694i −0.0357632 + 0.0206479i
\(534\) −2.27080 + 3.93315i −0.0982673 + 0.170204i
\(535\) 0.449069i 0.0194149i
\(536\) 141.812i 6.12536i
\(537\) −3.60086 2.07896i −0.155389 0.0897137i
\(538\) 19.4706 11.2414i 0.839437 0.484649i
\(539\) −0.652186 0.376540i −0.0280917 0.0162187i
\(540\) 9.60071 + 16.6289i 0.413149 + 0.715595i
\(541\) 11.5271 19.9655i 0.495589 0.858385i −0.504398 0.863471i \(-0.668286\pi\)
0.999987 + 0.00508632i \(0.00161903\pi\)
\(542\) −52.8557 30.5163i −2.27035 1.31079i
\(543\) −1.41033 + 2.44276i −0.0605230 + 0.104829i
\(544\) 0.771089 + 0.445188i 0.0330602 + 0.0190873i
\(545\) 2.39281 + 4.14446i 0.102497 + 0.177529i
\(546\) −0.426622 0.246310i −0.0182577 0.0105411i
\(547\) −2.21491 + 3.83634i −0.0947028 + 0.164030i −0.909485 0.415738i \(-0.863523\pi\)
0.814782 + 0.579768i \(0.196857\pi\)
\(548\) 41.9271 24.2066i 1.79104 1.03406i
\(549\) −24.3307 + 14.0473i −1.03841 + 0.599525i
\(550\) 25.7429 44.5881i 1.09768 1.90124i
\(551\) −5.88156 10.1872i −0.250563 0.433988i
\(552\) 15.2019i 0.647036i
\(553\) 2.78287 + 4.82008i 0.118340 + 0.204971i
\(554\) 1.38460 2.39820i 0.0588260 0.101890i
\(555\) −0.413412 0.716051i −0.0175484 0.0303947i
\(556\) −57.2119 + 99.0938i −2.42632 + 4.20252i
\(557\) −17.4902 10.0980i −0.741084 0.427865i 0.0813791 0.996683i \(-0.474068\pi\)
−0.822463 + 0.568818i \(0.807401\pi\)
\(558\) −28.5533 16.4852i −1.20876 0.697876i
\(559\) 1.21426 0.0513577
\(560\) 110.758 63.9462i 4.68038 2.70222i
\(561\) 0.0319895 + 0.0184692i 0.00135060 + 0.000779768i
\(562\) 2.17736i 0.0918466i
\(563\) −18.9314 + 32.7901i −0.797861 + 1.38194i 0.123145 + 0.992389i \(0.460702\pi\)
−0.921006 + 0.389548i \(0.872631\pi\)
\(564\) 10.0775 5.81823i 0.424338 0.244991i
\(565\) 18.5816i 0.781736i
\(566\) 4.90751 2.83335i 0.206278 0.119095i
\(567\) 23.1259i 0.971195i
\(568\) 50.9477 + 88.2440i 2.13772 + 3.70263i
\(569\) −35.2539 + 20.3539i −1.47792 + 0.853279i −0.999689 0.0249538i \(-0.992056\pi\)
−0.478234 + 0.878233i \(0.658723\pi\)
\(570\) −2.21247 + 1.27737i −0.0926701 + 0.0535031i
\(571\) 10.0552i 0.420797i −0.977616 0.210398i \(-0.932524\pi\)
0.977616 0.210398i \(-0.0674761\pi\)
\(572\) 10.2342 0.427915
\(573\) 4.85555 0.202843
\(574\) 10.3561 17.9372i 0.432253 0.748685i
\(575\) −13.4451 + 23.2877i −0.560701 + 0.971163i
\(576\) −54.9647 95.2017i −2.29020 3.96674i
\(577\) 24.9219 1.03751 0.518756 0.854922i \(-0.326395\pi\)
0.518756 + 0.854922i \(0.326395\pi\)
\(578\) 40.6626 23.4765i 1.69134 0.976495i
\(579\) −0.382114 + 0.220614i −0.0158801 + 0.00916838i
\(580\) −119.315 −4.95428
\(581\) −16.5291 9.54307i −0.685742 0.395913i
\(582\) 1.77205 + 3.06929i 0.0734540 + 0.127226i
\(583\) −0.575318 −0.0238272
\(584\) 128.347 + 74.1014i 5.31105 + 3.06634i
\(585\) −2.53793 + 1.46528i −0.104931 + 0.0605817i
\(586\) 27.6890 + 15.9862i 1.14382 + 0.660385i
\(587\) 13.8072 23.9148i 0.569886 0.987071i −0.426691 0.904397i \(-0.640321\pi\)
0.996577 0.0826735i \(-0.0263459\pi\)
\(588\) 0.155637 0.00641835
\(589\) 3.25785 5.64276i 0.134237 0.232506i
\(590\) 37.6299 65.1769i 1.54920 2.68329i
\(591\) 1.31732 0.760556i 0.0541874 0.0312851i
\(592\) 11.8727 + 20.5642i 0.487966 + 0.845182i
\(593\) −28.9737 16.7280i −1.18981 0.686936i −0.231545 0.972824i \(-0.574378\pi\)
−0.958263 + 0.285888i \(0.907711\pi\)
\(594\) −8.65411 14.9894i −0.355083 0.615021i
\(595\) 0.273514i 0.0112130i
\(596\) 73.6327i 3.01611i
\(597\) 0.986554i 0.0403770i
\(598\) −7.24419 −0.296237
\(599\) 1.21040 0.698827i 0.0494558 0.0285533i −0.475068 0.879949i \(-0.657577\pi\)
0.524524 + 0.851396i \(0.324243\pi\)
\(600\) 6.86015i 0.280065i
\(601\) 6.41172 3.70181i 0.261539 0.151000i −0.363497 0.931595i \(-0.618417\pi\)
0.625037 + 0.780595i \(0.285084\pi\)
\(602\) −22.8453 + 13.1897i −0.931105 + 0.537573i
\(603\) 20.9457 + 36.2791i 0.852976 + 1.47740i
\(604\) 30.0556 + 52.0579i 1.22295 + 2.11821i
\(605\) −25.6779 + 44.4754i −1.04396 + 1.80818i
\(606\) 9.16792 0.372421
\(607\) −2.21700 + 3.83995i −0.0899852 + 0.155859i −0.907505 0.420042i \(-0.862015\pi\)
0.817519 + 0.575901i \(0.195349\pi\)
\(608\) 35.4704 20.4788i 1.43851 0.830526i
\(609\) −3.30807 1.90991i −0.134050 0.0773936i
\(610\) −76.3236 −3.09025
\(611\) 1.78755 + 3.09612i 0.0723163 + 0.125256i
\(612\) 0.585848 0.0236815
\(613\) 15.9766 27.6724i 0.645291 1.11768i −0.338944 0.940807i \(-0.610070\pi\)
0.984234 0.176870i \(-0.0565971\pi\)
\(614\) −37.1556 21.4518i −1.49948 0.865724i
\(615\) 0.802776 + 1.39045i 0.0323710 + 0.0560683i
\(616\) −124.141 + 71.6729i −5.00179 + 2.88778i
\(617\) −2.74924 + 4.76183i −0.110680 + 0.191704i −0.916045 0.401076i \(-0.868636\pi\)
0.805364 + 0.592780i \(0.201970\pi\)
\(618\) −6.42230 −0.258343
\(619\) 22.1024i 0.888372i −0.895935 0.444186i \(-0.853493\pi\)
0.895935 0.444186i \(-0.146507\pi\)
\(620\) −33.0448 57.2353i −1.32711 2.29862i
\(621\) 4.51991 + 7.82871i 0.181378 + 0.314155i
\(622\) 2.48792 + 4.30920i 0.0997563 + 0.172783i
\(623\) 22.3668 0.896107
\(624\) −0.949752 + 0.548339i −0.0380205 + 0.0219511i
\(625\) 15.1414 26.2256i 0.605655 1.04902i
\(626\) −81.7536 + 47.2004i −3.26753 + 1.88651i
\(627\) 1.47153 0.849588i 0.0587672 0.0339293i
\(628\) −3.82750 6.62942i −0.152734 0.264543i
\(629\) −0.0507827 −0.00202484
\(630\) 31.8328 55.1360i 1.26825 2.19667i
\(631\) 3.43953 0.136925 0.0684627 0.997654i \(-0.478191\pi\)
0.0684627 + 0.997654i \(0.478191\pi\)
\(632\) 20.8804 0.830579
\(633\) 2.66754i 0.106025i
\(634\) 17.4850 0.694417
\(635\) 9.06461 + 5.23346i 0.359718 + 0.207683i
\(636\) 0.102970 0.0594495i 0.00408301 0.00235733i
\(637\) 0.0478166i 0.00189456i
\(638\) 107.551 4.25798
\(639\) 26.0673 + 15.0500i 1.03121 + 0.595368i
\(640\) 151.046i 5.97062i
\(641\) −9.48636 16.4309i −0.374689 0.648980i 0.615592 0.788065i \(-0.288917\pi\)
−0.990280 + 0.139085i \(0.955584\pi\)
\(642\) −0.0418285 0.0724491i −0.00165084 0.00285934i
\(643\) −0.726100 0.419214i −0.0286346 0.0165322i 0.485614 0.874173i \(-0.338596\pi\)
−0.514249 + 0.857641i \(0.671929\pi\)
\(644\) 100.565 58.0614i 3.96283 2.28794i
\(645\) 2.04487i 0.0805168i
\(646\) 0.156909i 0.00617351i
\(647\) 15.8390 27.4340i 0.622697 1.07854i −0.366284 0.930503i \(-0.619370\pi\)
0.988981 0.148040i \(-0.0472964\pi\)
\(648\) −75.1354 43.3794i −2.95160 1.70410i
\(649\) −25.0279 + 43.3497i −0.982433 + 1.70162i
\(650\) −3.26908 −0.128224
\(651\) 2.11584i 0.0829262i
\(652\) 94.2562 + 54.4188i 3.69136 + 2.13121i
\(653\) 37.2415 1.45737 0.728686 0.684848i \(-0.240131\pi\)
0.728686 + 0.684848i \(0.240131\pi\)
\(654\) 0.772073 + 0.445757i 0.0301904 + 0.0174305i
\(655\) 19.0974 + 11.0259i 0.746198 + 0.430817i
\(656\) −23.0548 39.9321i −0.900139 1.55909i
\(657\) 43.7792 1.70799
\(658\) −67.2624 38.8340i −2.62216 1.51391i
\(659\) 34.2785i 1.33530i 0.744475 + 0.667651i \(0.232700\pi\)
−0.744475 + 0.667651i \(0.767300\pi\)
\(660\) 17.2350i 0.670870i
\(661\) 27.4661 1.06831 0.534153 0.845388i \(-0.320630\pi\)
0.534153 + 0.845388i \(0.320630\pi\)
\(662\) −44.5321 −1.73079
\(663\) 0.00234539i 9.10873e-5i
\(664\) −62.0104 + 35.8017i −2.40647 + 1.38938i
\(665\) 10.8961 + 6.29087i 0.422533 + 0.243949i
\(666\) 10.2370 + 5.91031i 0.396674 + 0.229020i
\(667\) −56.1722 −2.17499
\(668\) 99.3388 + 57.3533i 3.84354 + 2.21907i
\(669\) 0.242704 0.420377i 0.00938350 0.0162527i
\(670\) 113.805i 4.39666i
\(671\) 50.7634 1.95970
\(672\) 6.65007 11.5183i 0.256532 0.444326i
\(673\) 13.7683 + 23.8473i 0.530728 + 0.919248i 0.999357 + 0.0358527i \(0.0114147\pi\)
−0.468629 + 0.883395i \(0.655252\pi\)
\(674\) 14.1290 + 8.15737i 0.544228 + 0.314210i
\(675\) 2.03970 + 3.53286i 0.0785079 + 0.135980i
\(676\) 36.2665 + 62.8154i 1.39487 + 2.41598i
\(677\) 23.9968i 0.922273i −0.887329 0.461136i \(-0.847442\pi\)
0.887329 0.461136i \(-0.152558\pi\)
\(678\) 1.73079 + 2.99781i 0.0664705 + 0.115130i
\(679\) 8.72712 15.1158i 0.334916 0.580092i
\(680\) 0.888640 + 0.513057i 0.0340778 + 0.0196748i
\(681\) −2.40947 −0.0923311
\(682\) 29.7867 + 51.5921i 1.14059 + 1.97556i
\(683\) 6.26767 + 10.8559i 0.239826 + 0.415391i 0.960664 0.277713i \(-0.0895763\pi\)
−0.720838 + 0.693103i \(0.756243\pi\)
\(684\) 13.4746 23.3387i 0.515215 0.892378i
\(685\) 21.6929 12.5244i 0.828841 0.478532i
\(686\) 25.3143 + 43.8456i 0.966504 + 1.67403i
\(687\) 0.633757i 0.0241793i
\(688\) 58.7264i 2.23892i
\(689\) 0.0182648 + 0.0316356i 0.000695833 + 0.00120522i
\(690\) 12.1996i 0.464430i
\(691\) −16.7691 + 9.68164i −0.637926 + 0.368307i −0.783815 0.620994i \(-0.786729\pi\)
0.145889 + 0.989301i \(0.453396\pi\)
\(692\) 35.2578i 1.34030i
\(693\) −21.1722 + 36.6714i −0.804266 + 1.39303i
\(694\) 7.01671 12.1533i 0.266351 0.461333i
\(695\) −29.6011 + 51.2706i −1.12283 + 1.94480i
\(696\) −12.4105 + 7.16522i −0.470420 + 0.271597i
\(697\) 0.0986112 0.00373517
\(698\) −25.3416 + 44.9497i −0.959195 + 1.70137i
\(699\) 1.70825 0.0646118
\(700\) 45.3820 26.2013i 1.71528 0.990317i
\(701\) 2.47099 4.27987i 0.0933279 0.161649i −0.815582 0.578642i \(-0.803583\pi\)
0.908910 + 0.416993i \(0.136916\pi\)
\(702\) −0.549490 + 0.951745i −0.0207392 + 0.0359213i
\(703\) −1.16801 + 2.02305i −0.0440523 + 0.0763009i
\(704\) 198.628i 7.48609i
\(705\) 5.21402 3.01032i 0.196371 0.113375i
\(706\) 45.4256i 1.70961i
\(707\) −22.5754 39.1017i −0.849035 1.47057i
\(708\) 10.3449i 0.388785i
\(709\) 3.49149i 0.131126i 0.997848 + 0.0655629i \(0.0208843\pi\)
−0.997848 + 0.0655629i \(0.979116\pi\)
\(710\) 40.8857 + 70.8160i 1.53441 + 2.65768i
\(711\) 5.34172 3.08405i 0.200330 0.115661i
\(712\) 41.9556 72.6692i 1.57235 2.72339i
\(713\) −15.5571 26.9457i −0.582619 1.00913i
\(714\) 0.0254765 + 0.0441265i 0.000953433 + 0.00165139i
\(715\) 5.29513 0.198027
\(716\) 103.191 + 59.5773i 3.85643 + 2.22651i
\(717\) −0.712086 + 1.23337i −0.0265934 + 0.0460610i
\(718\) −16.1312 27.9400i −0.602010 1.04271i
\(719\) 22.2679i 0.830453i −0.909718 0.415227i \(-0.863702\pi\)
0.909718 0.415227i \(-0.136298\pi\)
\(720\) −70.8666 122.745i −2.64104 4.57442i
\(721\) 15.8145 + 27.3915i 0.588962 + 1.02011i
\(722\) −39.1988 22.6314i −1.45883 0.842255i
\(723\) 1.52461 + 2.64071i 0.0567009 + 0.0982089i
\(724\) 40.4162 70.0029i 1.50206 2.60164i
\(725\) −25.3488 −0.941430
\(726\) 9.56708i 0.355068i
\(727\) −11.2124 + 19.4205i −0.415846 + 0.720266i −0.995517 0.0945843i \(-0.969848\pi\)
0.579671 + 0.814851i \(0.303181\pi\)
\(728\) 7.88230 + 4.55085i 0.292137 + 0.168666i
\(729\) −24.9385 −0.923647
\(730\) 102.999 + 59.4666i 3.81217 + 2.20096i
\(731\) −0.108767 0.0627969i −0.00402291 0.00232263i
\(732\) −9.08557 + 5.24556i −0.335812 + 0.193881i
\(733\) 9.26501i 0.342211i −0.985253 0.171106i \(-0.945266\pi\)
0.985253 0.171106i \(-0.0547339\pi\)
\(734\) 4.82966 0.178266
\(735\) 0.0805255 0.00297023
\(736\) 195.584i 7.20932i
\(737\) 75.6925i 2.78817i
\(738\) −19.8784 11.4768i −0.731735 0.422467i
\(739\) −43.6677 −1.60634 −0.803171 0.595748i \(-0.796856\pi\)
−0.803171 + 0.595748i \(0.796856\pi\)
\(740\) 11.8473 + 20.5201i 0.435515 + 0.754334i
\(741\) −0.0934343 0.0539443i −0.00343239 0.00198169i
\(742\) −0.687275 0.396798i −0.0252307 0.0145669i
\(743\) −23.6138 −0.866306 −0.433153 0.901320i \(-0.642599\pi\)
−0.433153 + 0.901320i \(0.642599\pi\)
\(744\) −6.87430 3.96888i −0.252024 0.145506i
\(745\) 38.0972i 1.39577i
\(746\) −31.8066 −1.16452
\(747\) −10.5759 + 18.3179i −0.386950 + 0.670217i
\(748\) −0.916733 0.529276i −0.0335191 0.0193522i
\(749\) −0.206000 + 0.356802i −0.00752707 + 0.0130373i
\(750\) 2.39667i 0.0875139i
\(751\) 11.1479i 0.406794i 0.979096 + 0.203397i \(0.0651982\pi\)
−0.979096 + 0.203397i \(0.934802\pi\)
\(752\) −149.741 + 86.4528i −5.46048 + 3.15261i
\(753\) −3.51752 2.03084i −0.128186 0.0740079i
\(754\) −3.41445 5.91401i −0.124347 0.215375i
\(755\) 15.5506 + 26.9345i 0.565945 + 0.980245i
\(756\) 17.6164i 0.640703i
\(757\) −11.8133 6.82039i −0.429360 0.247891i 0.269714 0.962941i \(-0.413071\pi\)
−0.699074 + 0.715049i \(0.746404\pi\)
\(758\) −46.2483 −1.67981
\(759\) 8.11403i 0.294521i
\(760\) 40.8778 23.6008i 1.48279 0.856090i
\(761\) −19.7291 11.3906i −0.715181 0.412910i 0.0977954 0.995207i \(-0.468821\pi\)
−0.812976 + 0.582297i \(0.802154\pi\)
\(762\) 1.94988 0.0706368
\(763\) 4.39058i 0.158950i
\(764\) −139.147 −5.03415
\(765\) 0.303114 0.0109591
\(766\) 17.0520 29.5349i 0.616113 1.06714i