Properties

Label 731.2.e.a.307.9
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 307.9
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.9

$q$-expansion

\(f(q)\) \(=\) \(q-1.65452 q^{2} +(-0.422449 + 0.731703i) q^{3} +0.737422 q^{4} +(0.952877 - 1.65043i) q^{5} +(0.698949 - 1.21061i) q^{6} +(2.62410 + 4.54507i) q^{7} +2.08895 q^{8} +(1.14307 + 1.97986i) q^{9} +O(q^{10})\) \(q-1.65452 q^{2} +(-0.422449 + 0.731703i) q^{3} +0.737422 q^{4} +(0.952877 - 1.65043i) q^{5} +(0.698949 - 1.21061i) q^{6} +(2.62410 + 4.54507i) q^{7} +2.08895 q^{8} +(1.14307 + 1.97986i) q^{9} +(-1.57655 + 2.73067i) q^{10} +5.81812 q^{11} +(-0.311523 + 0.539574i) q^{12} +(-2.92272 - 5.06230i) q^{13} +(-4.34161 - 7.51989i) q^{14} +(0.805084 + 1.39445i) q^{15} -4.93105 q^{16} +(0.500000 + 0.866025i) q^{17} +(-1.89123 - 3.27571i) q^{18} +(1.56761 - 2.71518i) q^{19} +(0.702673 - 1.21706i) q^{20} -4.43419 q^{21} -9.62617 q^{22} +(-2.16761 + 3.75442i) q^{23} +(-0.882477 + 1.52850i) q^{24} +(0.684050 + 1.18481i) q^{25} +(4.83569 + 8.37566i) q^{26} -4.46626 q^{27} +(1.93507 + 3.35163i) q^{28} +(-1.31320 - 2.27452i) q^{29} +(-1.33202 - 2.30713i) q^{30} +(3.13386 - 5.42801i) q^{31} +3.98059 q^{32} +(-2.45786 + 4.25714i) q^{33} +(-0.827258 - 1.43285i) q^{34} +10.0018 q^{35} +(0.842928 + 1.45999i) q^{36} +(-0.267266 + 0.462917i) q^{37} +(-2.59364 + 4.49231i) q^{38} +4.93880 q^{39} +(1.99052 - 3.44768i) q^{40} +3.24274 q^{41} +7.33644 q^{42} +(5.74674 - 3.15832i) q^{43} +4.29041 q^{44} +4.35683 q^{45} +(3.58635 - 6.21174i) q^{46} +1.95647 q^{47} +(2.08312 - 3.60807i) q^{48} +(-10.2718 + 17.7912i) q^{49} +(-1.13177 - 1.96029i) q^{50} -0.844898 q^{51} +(-2.15528 - 3.73305i) q^{52} +(0.175590 - 0.304130i) q^{53} +7.38949 q^{54} +(5.54395 - 9.60241i) q^{55} +(5.48162 + 9.49444i) q^{56} +(1.32447 + 2.29405i) q^{57} +(2.17270 + 3.76323i) q^{58} -0.189298 q^{59} +(0.593687 + 1.02830i) q^{60} +(4.52767 + 7.84215i) q^{61} +(-5.18502 + 8.98072i) q^{62} +(-5.99907 + 10.3907i) q^{63} +3.27615 q^{64} -11.1400 q^{65} +(4.06657 - 7.04350i) q^{66} +(-0.944186 + 1.63538i) q^{67} +(0.368711 + 0.638626i) q^{68} +(-1.83141 - 3.17210i) q^{69} -16.5481 q^{70} +(4.26051 + 7.37941i) q^{71} +(2.38783 + 4.13584i) q^{72} +(-6.92192 - 11.9891i) q^{73} +(0.442195 - 0.765904i) q^{74} -1.15591 q^{75} +(1.15599 - 2.00224i) q^{76} +(15.2673 + 26.4437i) q^{77} -8.17133 q^{78} +(-3.84853 - 6.66585i) q^{79} +(-4.69869 + 8.13837i) q^{80} +(-1.54245 + 2.67161i) q^{81} -5.36517 q^{82} +(-2.39376 + 4.14611i) q^{83} -3.26987 q^{84} +1.90575 q^{85} +(-9.50807 + 5.22548i) q^{86} +2.21903 q^{87} +12.1538 q^{88} +(1.35676 - 2.34997i) q^{89} -7.20845 q^{90} +(15.3390 - 26.5679i) q^{91} +(-1.59845 + 2.76859i) q^{92} +(2.64779 + 4.58611i) q^{93} -3.23701 q^{94} +(-2.98748 - 5.17447i) q^{95} +(-1.68160 + 2.91261i) q^{96} -13.2705 q^{97} +(16.9948 - 29.4359i) q^{98} +(6.65054 + 11.5191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.65452 −1.16992 −0.584960 0.811062i \(-0.698890\pi\)
−0.584960 + 0.811062i \(0.698890\pi\)
\(3\) −0.422449 + 0.731703i −0.243901 + 0.422449i −0.961822 0.273675i \(-0.911761\pi\)
0.717921 + 0.696125i \(0.245094\pi\)
\(4\) 0.737422 0.368711
\(5\) 0.952877 1.65043i 0.426140 0.738096i −0.570386 0.821376i \(-0.693207\pi\)
0.996526 + 0.0832809i \(0.0265399\pi\)
\(6\) 0.698949 1.21061i 0.285345 0.494231i
\(7\) 2.62410 + 4.54507i 0.991815 + 1.71787i 0.606482 + 0.795097i \(0.292580\pi\)
0.385333 + 0.922778i \(0.374087\pi\)
\(8\) 2.08895 0.738557
\(9\) 1.14307 + 1.97986i 0.381024 + 0.659954i
\(10\) −1.57655 + 2.73067i −0.498549 + 0.863512i
\(11\) 5.81812 1.75423 0.877114 0.480282i \(-0.159466\pi\)
0.877114 + 0.480282i \(0.159466\pi\)
\(12\) −0.311523 + 0.539574i −0.0899290 + 0.155762i
\(13\) −2.92272 5.06230i −0.810617 1.40403i −0.912433 0.409227i \(-0.865799\pi\)
0.101816 0.994803i \(-0.467535\pi\)
\(14\) −4.34161 7.51989i −1.16034 2.00977i
\(15\) 0.805084 + 1.39445i 0.207872 + 0.360045i
\(16\) −4.93105 −1.23276
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) −1.89123 3.27571i −0.445768 0.772093i
\(19\) 1.56761 2.71518i 0.359635 0.622906i −0.628265 0.778000i \(-0.716235\pi\)
0.987900 + 0.155094i \(0.0495679\pi\)
\(20\) 0.702673 1.21706i 0.157122 0.272144i
\(21\) −4.43419 −0.967620
\(22\) −9.62617 −2.05231
\(23\) −2.16761 + 3.75442i −0.451979 + 0.782850i −0.998509 0.0545895i \(-0.982615\pi\)
0.546530 + 0.837439i \(0.315948\pi\)
\(24\) −0.882477 + 1.52850i −0.180135 + 0.312003i
\(25\) 0.684050 + 1.18481i 0.136810 + 0.236962i
\(26\) 4.83569 + 8.37566i 0.948357 + 1.64260i
\(27\) −4.46626 −0.859531
\(28\) 1.93507 + 3.35163i 0.365693 + 0.633399i
\(29\) −1.31320 2.27452i −0.243854 0.422368i 0.717954 0.696090i \(-0.245079\pi\)
−0.961809 + 0.273722i \(0.911745\pi\)
\(30\) −1.33202 2.30713i −0.243193 0.421223i
\(31\) 3.13386 5.42801i 0.562858 0.974899i −0.434387 0.900726i \(-0.643035\pi\)
0.997245 0.0741725i \(-0.0236316\pi\)
\(32\) 3.98059 0.703676
\(33\) −2.45786 + 4.25714i −0.427858 + 0.741072i
\(34\) −0.827258 1.43285i −0.141874 0.245732i
\(35\) 10.0018 1.69061
\(36\) 0.842928 + 1.45999i 0.140488 + 0.243332i
\(37\) −0.267266 + 0.462917i −0.0439382 + 0.0761032i −0.887158 0.461466i \(-0.847324\pi\)
0.843220 + 0.537569i \(0.180657\pi\)
\(38\) −2.59364 + 4.49231i −0.420744 + 0.728750i
\(39\) 4.93880 0.790842
\(40\) 1.99052 3.44768i 0.314728 0.545126i
\(41\) 3.24274 0.506431 0.253216 0.967410i \(-0.418512\pi\)
0.253216 + 0.967410i \(0.418512\pi\)
\(42\) 7.33644 1.13204
\(43\) 5.74674 3.15832i 0.876370 0.481639i
\(44\) 4.29041 0.646803
\(45\) 4.35683 0.649479
\(46\) 3.58635 6.21174i 0.528778 0.915871i
\(47\) 1.95647 0.285381 0.142690 0.989767i \(-0.454425\pi\)
0.142690 + 0.989767i \(0.454425\pi\)
\(48\) 2.08312 3.60807i 0.300672 0.520780i
\(49\) −10.2718 + 17.7912i −1.46740 + 2.54160i
\(50\) −1.13177 1.96029i −0.160057 0.277226i
\(51\) −0.844898 −0.118309
\(52\) −2.15528 3.73305i −0.298883 0.517681i
\(53\) 0.175590 0.304130i 0.0241191 0.0417755i −0.853714 0.520742i \(-0.825655\pi\)
0.877833 + 0.478967i \(0.158989\pi\)
\(54\) 7.38949 1.00558
\(55\) 5.54395 9.60241i 0.747546 1.29479i
\(56\) 5.48162 + 9.49444i 0.732512 + 1.26875i
\(57\) 1.32447 + 2.29405i 0.175431 + 0.303855i
\(58\) 2.17270 + 3.76323i 0.285290 + 0.494137i
\(59\) −0.189298 −0.0246445 −0.0123222 0.999924i \(-0.503922\pi\)
−0.0123222 + 0.999924i \(0.503922\pi\)
\(60\) 0.593687 + 1.02830i 0.0766447 + 0.132752i
\(61\) 4.52767 + 7.84215i 0.579709 + 1.00408i 0.995512 + 0.0946304i \(0.0301669\pi\)
−0.415804 + 0.909454i \(0.636500\pi\)
\(62\) −5.18502 + 8.98072i −0.658498 + 1.14055i
\(63\) −5.99907 + 10.3907i −0.755812 + 1.30910i
\(64\) 3.27615 0.409519
\(65\) −11.1400 −1.38174
\(66\) 4.06657 7.04350i 0.500560 0.866995i
\(67\) −0.944186 + 1.63538i −0.115351 + 0.199793i −0.917920 0.396766i \(-0.870133\pi\)
0.802569 + 0.596559i \(0.203466\pi\)
\(68\) 0.368711 + 0.638626i 0.0447128 + 0.0774448i
\(69\) −1.83141 3.17210i −0.220476 0.381876i
\(70\) −16.5481 −1.97787
\(71\) 4.26051 + 7.37941i 0.505629 + 0.875775i 0.999979 + 0.00651210i \(0.00207288\pi\)
−0.494350 + 0.869263i \(0.664594\pi\)
\(72\) 2.38783 + 4.13584i 0.281408 + 0.487414i
\(73\) −6.92192 11.9891i −0.810150 1.40322i −0.912759 0.408499i \(-0.866052\pi\)
0.102609 0.994722i \(-0.467281\pi\)
\(74\) 0.442195 0.765904i 0.0514041 0.0890346i
\(75\) −1.15591 −0.133472
\(76\) 1.15599 2.00224i 0.132601 0.229672i
\(77\) 15.2673 + 26.4437i 1.73987 + 3.01354i
\(78\) −8.17133 −0.925221
\(79\) −3.84853 6.66585i −0.432994 0.749967i 0.564136 0.825682i \(-0.309209\pi\)
−0.997129 + 0.0757150i \(0.975876\pi\)
\(80\) −4.69869 + 8.13837i −0.525329 + 0.909897i
\(81\) −1.54245 + 2.67161i −0.171384 + 0.296845i
\(82\) −5.36517 −0.592484
\(83\) −2.39376 + 4.14611i −0.262749 + 0.455095i −0.966971 0.254885i \(-0.917963\pi\)
0.704222 + 0.709980i \(0.251296\pi\)
\(84\) −3.26987 −0.356772
\(85\) 1.90575 0.206708
\(86\) −9.50807 + 5.22548i −1.02528 + 0.563478i
\(87\) 2.21903 0.237906
\(88\) 12.1538 1.29560
\(89\) 1.35676 2.34997i 0.143816 0.249096i −0.785115 0.619350i \(-0.787396\pi\)
0.928930 + 0.370254i \(0.120729\pi\)
\(90\) −7.20845 −0.759837
\(91\) 15.3390 26.5679i 1.60796 2.78508i
\(92\) −1.59845 + 2.76859i −0.166649 + 0.288645i
\(93\) 2.64779 + 4.58611i 0.274563 + 0.475558i
\(94\) −3.23701 −0.333872
\(95\) −2.98748 5.17447i −0.306509 0.530890i
\(96\) −1.68160 + 2.91261i −0.171627 + 0.297267i
\(97\) −13.2705 −1.34742 −0.673708 0.738998i \(-0.735299\pi\)
−0.673708 + 0.738998i \(0.735299\pi\)
\(98\) 16.9948 29.4359i 1.71673 2.97347i
\(99\) 6.65054 + 11.5191i 0.668404 + 1.15771i
\(100\) 0.504433 + 0.873704i 0.0504433 + 0.0873704i
\(101\) 5.34568 + 9.25898i 0.531915 + 0.921303i 0.999306 + 0.0372526i \(0.0118606\pi\)
−0.467391 + 0.884051i \(0.654806\pi\)
\(102\) 1.39790 0.138412
\(103\) 8.40336 + 14.5550i 0.828007 + 1.43415i 0.899599 + 0.436717i \(0.143859\pi\)
−0.0715915 + 0.997434i \(0.522808\pi\)
\(104\) −6.10543 10.5749i −0.598687 1.03696i
\(105\) −4.22524 + 7.31833i −0.412341 + 0.714196i
\(106\) −0.290516 + 0.503188i −0.0282174 + 0.0488740i
\(107\) −8.08584 −0.781687 −0.390844 0.920457i \(-0.627817\pi\)
−0.390844 + 0.920457i \(0.627817\pi\)
\(108\) −3.29352 −0.316919
\(109\) 4.63758 8.03253i 0.444200 0.769377i −0.553796 0.832652i \(-0.686821\pi\)
0.997996 + 0.0632756i \(0.0201547\pi\)
\(110\) −9.17256 + 15.8873i −0.874569 + 1.51480i
\(111\) −0.225812 0.391118i −0.0214331 0.0371233i
\(112\) −12.9396 22.4120i −1.22267 2.11773i
\(113\) −4.72384 −0.444382 −0.222191 0.975003i \(-0.571321\pi\)
−0.222191 + 0.975003i \(0.571321\pi\)
\(114\) −2.19136 3.79555i −0.205240 0.355486i
\(115\) 4.13094 + 7.15499i 0.385212 + 0.667207i
\(116\) −0.968380 1.67728i −0.0899118 0.155732i
\(117\) 6.68177 11.5732i 0.617730 1.06994i
\(118\) 0.313196 0.0288321
\(119\) −2.62410 + 4.54507i −0.240551 + 0.416646i
\(120\) 1.68178 + 2.91294i 0.153525 + 0.265914i
\(121\) 22.8505 2.07732
\(122\) −7.49110 12.9750i −0.678212 1.17470i
\(123\) −1.36989 + 2.37273i −0.123519 + 0.213941i
\(124\) 2.31098 4.00273i 0.207532 0.359456i
\(125\) 12.1360 1.08548
\(126\) 9.92556 17.1916i 0.884239 1.53155i
\(127\) 7.17014 0.636247 0.318123 0.948049i \(-0.396947\pi\)
0.318123 + 0.948049i \(0.396947\pi\)
\(128\) −13.3816 −1.18278
\(129\) −0.116756 + 5.53914i −0.0102798 + 0.487694i
\(130\) 18.4313 1.61653
\(131\) −2.05816 −0.179822 −0.0899111 0.995950i \(-0.528658\pi\)
−0.0899111 + 0.995950i \(0.528658\pi\)
\(132\) −1.81248 + 3.13931i −0.157756 + 0.273242i
\(133\) 16.4543 1.42677
\(134\) 1.56217 2.70576i 0.134951 0.233742i
\(135\) −4.25579 + 7.37125i −0.366280 + 0.634416i
\(136\) 1.04448 + 1.80909i 0.0895632 + 0.155128i
\(137\) −22.2663 −1.90234 −0.951168 0.308675i \(-0.900114\pi\)
−0.951168 + 0.308675i \(0.900114\pi\)
\(138\) 3.03010 + 5.24829i 0.257939 + 0.446764i
\(139\) 4.09862 7.09901i 0.347640 0.602130i −0.638190 0.769879i \(-0.720316\pi\)
0.985830 + 0.167749i \(0.0536498\pi\)
\(140\) 7.37553 0.623346
\(141\) −0.826510 + 1.43156i −0.0696047 + 0.120559i
\(142\) −7.04907 12.2094i −0.591545 1.02459i
\(143\) −17.0047 29.4531i −1.42201 2.46299i
\(144\) −5.63656 9.76280i −0.469713 0.813567i
\(145\) −5.00526 −0.415664
\(146\) 11.4524 + 19.8362i 0.947810 + 1.64166i
\(147\) −8.67860 15.0318i −0.715799 1.23980i
\(148\) −0.197088 + 0.341366i −0.0162005 + 0.0280601i
\(149\) −0.0840199 + 0.145527i −0.00688318 + 0.0119220i −0.869446 0.494027i \(-0.835524\pi\)
0.862563 + 0.505949i \(0.168858\pi\)
\(150\) 1.91246 0.156152
\(151\) −2.74388 −0.223293 −0.111647 0.993748i \(-0.535612\pi\)
−0.111647 + 0.993748i \(0.535612\pi\)
\(152\) 3.27467 5.67190i 0.265611 0.460052i
\(153\) −1.14307 + 1.97986i −0.0924120 + 0.160062i
\(154\) −25.2600 43.7516i −2.03551 3.52560i
\(155\) −5.97237 10.3444i −0.479712 0.830886i
\(156\) 3.64198 0.291592
\(157\) −2.93011 5.07510i −0.233848 0.405037i 0.725089 0.688655i \(-0.241799\pi\)
−0.958937 + 0.283618i \(0.908465\pi\)
\(158\) 6.36746 + 11.0288i 0.506568 + 0.877401i
\(159\) 0.148355 + 0.256959i 0.0117654 + 0.0203782i
\(160\) 3.79302 6.56970i 0.299864 0.519380i
\(161\) −22.7521 −1.79312
\(162\) 2.55201 4.42022i 0.200505 0.347285i
\(163\) −5.53310 9.58362i −0.433386 0.750647i 0.563776 0.825928i \(-0.309348\pi\)
−0.997162 + 0.0752807i \(0.976015\pi\)
\(164\) 2.39127 0.186727
\(165\) 4.68408 + 8.11306i 0.364655 + 0.631601i
\(166\) 3.96051 6.85981i 0.307395 0.532424i
\(167\) −9.15907 + 15.8640i −0.708750 + 1.22759i 0.256571 + 0.966525i \(0.417407\pi\)
−0.965321 + 0.261066i \(0.915926\pi\)
\(168\) −9.26282 −0.714642
\(169\) −10.5846 + 18.3331i −0.814200 + 1.41024i
\(170\) −3.15310 −0.241832
\(171\) 7.16758 0.548119
\(172\) 4.23777 2.32901i 0.323127 0.177585i
\(173\) 20.7498 1.57758 0.788789 0.614665i \(-0.210709\pi\)
0.788789 + 0.614665i \(0.210709\pi\)
\(174\) −3.67143 −0.278330
\(175\) −3.59003 + 6.21811i −0.271380 + 0.470045i
\(176\) −28.6894 −2.16255
\(177\) 0.0799688 0.138510i 0.00601082 0.0104110i
\(178\) −2.24477 + 3.88806i −0.168253 + 0.291422i
\(179\) 2.33117 + 4.03770i 0.174240 + 0.301792i 0.939898 0.341456i \(-0.110920\pi\)
−0.765658 + 0.643248i \(0.777587\pi\)
\(180\) 3.21283 0.239470
\(181\) −5.74188 9.94522i −0.426790 0.739222i 0.569796 0.821786i \(-0.307022\pi\)
−0.996586 + 0.0825642i \(0.973689\pi\)
\(182\) −25.3786 + 43.9571i −1.88119 + 3.25832i
\(183\) −7.65084 −0.565566
\(184\) −4.52805 + 7.84281i −0.333812 + 0.578179i
\(185\) 0.509342 + 0.882207i 0.0374476 + 0.0648612i
\(186\) −4.38082 7.58780i −0.321217 0.556364i
\(187\) 2.90906 + 5.03864i 0.212731 + 0.368462i
\(188\) 1.44275 0.105223
\(189\) −11.7199 20.2994i −0.852496 1.47657i
\(190\) 4.94284 + 8.56125i 0.358591 + 0.621098i
\(191\) 0.839179 1.45350i 0.0607208 0.105172i −0.834067 0.551663i \(-0.813993\pi\)
0.894788 + 0.446492i \(0.147327\pi\)
\(192\) −1.38401 + 2.39717i −0.0998821 + 0.173001i
\(193\) 1.02661 0.0738971 0.0369486 0.999317i \(-0.488236\pi\)
0.0369486 + 0.999317i \(0.488236\pi\)
\(194\) 21.9563 1.57637
\(195\) 4.70607 8.15116i 0.337009 0.583717i
\(196\) −7.57463 + 13.1196i −0.541045 + 0.937117i
\(197\) 9.74662 + 16.8816i 0.694418 + 1.20277i 0.970376 + 0.241598i \(0.0776715\pi\)
−0.275958 + 0.961170i \(0.588995\pi\)
\(198\) −11.0034 19.0585i −0.781979 1.35443i
\(199\) 14.7304 1.04421 0.522104 0.852882i \(-0.325147\pi\)
0.522104 + 0.852882i \(0.325147\pi\)
\(200\) 1.42895 + 2.47501i 0.101042 + 0.175010i
\(201\) −0.797741 1.38173i −0.0562683 0.0974596i
\(202\) −8.84451 15.3191i −0.622297 1.07785i
\(203\) 6.89191 11.9371i 0.483717 0.837823i
\(204\) −0.623047 −0.0436220
\(205\) 3.08994 5.35193i 0.215810 0.373795i
\(206\) −13.9035 24.0815i −0.968702 1.67784i
\(207\) −9.91096 −0.688860
\(208\) 14.4121 + 24.9625i 0.999299 + 1.73084i
\(209\) 9.12055 15.7973i 0.630882 1.09272i
\(210\) 6.99072 12.1083i 0.482406 0.835551i
\(211\) −23.0570 −1.58731 −0.793654 0.608370i \(-0.791824\pi\)
−0.793654 + 0.608370i \(0.791824\pi\)
\(212\) 0.129484 0.224272i 0.00889298 0.0154031i
\(213\) −7.19939 −0.493294
\(214\) 13.3781 0.914511
\(215\) 0.263354 12.4941i 0.0179606 0.852090i
\(216\) −9.32981 −0.634813
\(217\) 32.8942 2.23300
\(218\) −7.67295 + 13.2899i −0.519678 + 0.900108i
\(219\) 11.6966 0.790386
\(220\) 4.08823 7.08103i 0.275629 0.477403i
\(221\) 2.92272 5.06230i 0.196604 0.340527i
\(222\) 0.373610 + 0.647111i 0.0250750 + 0.0434313i
\(223\) −0.0533378 −0.00357176 −0.00178588 0.999998i \(-0.500568\pi\)
−0.00178588 + 0.999998i \(0.500568\pi\)
\(224\) 10.4455 + 18.0921i 0.697917 + 1.20883i
\(225\) −1.56384 + 2.70865i −0.104256 + 0.180577i
\(226\) 7.81567 0.519891
\(227\) −7.36994 + 12.7651i −0.489160 + 0.847250i −0.999922 0.0124720i \(-0.996030\pi\)
0.510762 + 0.859722i \(0.329363\pi\)
\(228\) 0.976696 + 1.69169i 0.0646832 + 0.112035i
\(229\) 1.21118 + 2.09782i 0.0800370 + 0.138628i 0.903266 0.429082i \(-0.141163\pi\)
−0.823229 + 0.567710i \(0.807829\pi\)
\(230\) −6.83470 11.8381i −0.450667 0.780578i
\(231\) −25.7986 −1.69743
\(232\) −2.74321 4.75138i −0.180100 0.311943i
\(233\) 8.62642 + 14.9414i 0.565135 + 0.978843i 0.997037 + 0.0769226i \(0.0245094\pi\)
−0.431902 + 0.901921i \(0.642157\pi\)
\(234\) −11.0551 + 19.1480i −0.722694 + 1.25174i
\(235\) 1.86428 3.22902i 0.121612 0.210638i
\(236\) −0.139593 −0.00908670
\(237\) 6.50324 0.422431
\(238\) 4.34161 7.51989i 0.281425 0.487442i
\(239\) −0.102695 + 0.177873i −0.00664278 + 0.0115056i −0.869328 0.494236i \(-0.835448\pi\)
0.862685 + 0.505742i \(0.168781\pi\)
\(240\) −3.96991 6.87609i −0.256257 0.443850i
\(241\) −7.23459 12.5307i −0.466021 0.807172i 0.533226 0.845973i \(-0.320979\pi\)
−0.999247 + 0.0388011i \(0.987646\pi\)
\(242\) −37.8065 −2.43029
\(243\) −8.00260 13.8609i −0.513367 0.889178i
\(244\) 3.33880 + 5.78298i 0.213745 + 0.370217i
\(245\) 19.5755 + 33.9057i 1.25063 + 2.16616i
\(246\) 2.26651 3.92571i 0.144507 0.250294i
\(247\) −18.3268 −1.16610
\(248\) 6.54649 11.3389i 0.415703 0.720018i
\(249\) −2.02248 3.50304i −0.128170 0.221996i
\(250\) −20.0793 −1.26992
\(251\) −13.2266 22.9091i −0.834855 1.44601i −0.894148 0.447771i \(-0.852218\pi\)
0.0592934 0.998241i \(-0.481115\pi\)
\(252\) −4.42385 + 7.66233i −0.278676 + 0.482681i
\(253\) −12.6114 + 21.8436i −0.792874 + 1.37330i
\(254\) −11.8631 −0.744357
\(255\) −0.805084 + 1.39445i −0.0504163 + 0.0873237i
\(256\) 15.5878 0.974239
\(257\) 17.2369 1.07521 0.537604 0.843197i \(-0.319329\pi\)
0.537604 + 0.843197i \(0.319329\pi\)
\(258\) 0.193174 9.16459i 0.0120265 0.570563i
\(259\) −2.80532 −0.174314
\(260\) −8.21487 −0.509464
\(261\) 3.00216 5.19989i 0.185829 0.321865i
\(262\) 3.40526 0.210378
\(263\) 4.84903 8.39877i 0.299004 0.517890i −0.676904 0.736071i \(-0.736679\pi\)
0.975908 + 0.218181i \(0.0700122\pi\)
\(264\) −5.13436 + 8.89297i −0.315998 + 0.547324i
\(265\) −0.334631 0.579598i −0.0205562 0.0356044i
\(266\) −27.2238 −1.66920
\(267\) 1.14632 + 1.98548i 0.0701536 + 0.121510i
\(268\) −0.696264 + 1.20596i −0.0425311 + 0.0736660i
\(269\) −10.3908 −0.633536 −0.316768 0.948503i \(-0.602598\pi\)
−0.316768 + 0.948503i \(0.602598\pi\)
\(270\) 7.04128 12.1959i 0.428519 0.742216i
\(271\) −9.35674 16.2064i −0.568382 0.984466i −0.996726 0.0808504i \(-0.974236\pi\)
0.428345 0.903615i \(-0.359097\pi\)
\(272\) −2.46553 4.27042i −0.149494 0.258932i
\(273\) 12.9599 + 22.4472i 0.784369 + 1.35857i
\(274\) 36.8399 2.22558
\(275\) 3.97988 + 6.89336i 0.239996 + 0.415685i
\(276\) −1.35052 2.33918i −0.0812920 0.140802i
\(277\) −9.60160 + 16.6305i −0.576904 + 0.999228i 0.418927 + 0.908020i \(0.362406\pi\)
−0.995832 + 0.0912080i \(0.970927\pi\)
\(278\) −6.78122 + 11.7454i −0.406711 + 0.704444i
\(279\) 14.3289 0.857851
\(280\) 20.8932 1.24861
\(281\) 1.84118 3.18901i 0.109835 0.190240i −0.805868 0.592095i \(-0.798301\pi\)
0.915703 + 0.401855i \(0.131634\pi\)
\(282\) 1.36747 2.36853i 0.0814319 0.141044i
\(283\) −9.45384 16.3745i −0.561973 0.973365i −0.997324 0.0731046i \(-0.976709\pi\)
0.435352 0.900260i \(-0.356624\pi\)
\(284\) 3.14179 + 5.44174i 0.186431 + 0.322908i
\(285\) 5.04824 0.299032
\(286\) 28.1346 + 48.7306i 1.66363 + 2.88150i
\(287\) 8.50927 + 14.7385i 0.502286 + 0.869986i
\(288\) 4.55011 + 7.88102i 0.268118 + 0.464394i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 8.28128 0.486294
\(291\) 5.60612 9.71008i 0.328636 0.569215i
\(292\) −5.10438 8.84105i −0.298711 0.517383i
\(293\) −3.31501 −0.193665 −0.0968324 0.995301i \(-0.530871\pi\)
−0.0968324 + 0.995301i \(0.530871\pi\)
\(294\) 14.3589 + 24.8703i 0.837427 + 1.45047i
\(295\) −0.180378 + 0.312423i −0.0105020 + 0.0181900i
\(296\) −0.558306 + 0.967014i −0.0324509 + 0.0562065i
\(297\) −25.9852 −1.50781
\(298\) 0.139012 0.240776i 0.00805276 0.0139478i
\(299\) 25.3413 1.46553
\(300\) −0.852390 −0.0492128
\(301\) 29.4348 + 17.8316i 1.69659 + 1.02780i
\(302\) 4.53978 0.261235
\(303\) −9.03311 −0.518938
\(304\) −7.72998 + 13.3887i −0.443345 + 0.767896i
\(305\) 17.2573 0.988147
\(306\) 1.89123 3.27571i 0.108115 0.187260i
\(307\) 1.28281 2.22189i 0.0732138 0.126810i −0.827094 0.562063i \(-0.810008\pi\)
0.900308 + 0.435253i \(0.143341\pi\)
\(308\) 11.2584 + 19.5002i 0.641510 + 1.11113i
\(309\) −14.2000 −0.807808
\(310\) 9.88138 + 17.1150i 0.561225 + 0.972070i
\(311\) 14.5361 25.1772i 0.824266 1.42767i −0.0782137 0.996937i \(-0.524922\pi\)
0.902479 0.430733i \(-0.141745\pi\)
\(312\) 10.3169 0.584082
\(313\) 9.34096 16.1790i 0.527982 0.914492i −0.471486 0.881874i \(-0.656282\pi\)
0.999468 0.0326183i \(-0.0103846\pi\)
\(314\) 4.84792 + 8.39684i 0.273584 + 0.473861i
\(315\) 11.4328 + 19.8021i 0.644163 + 1.11572i
\(316\) −2.83799 4.91555i −0.159650 0.276521i
\(317\) 6.70481 0.376579 0.188290 0.982114i \(-0.439706\pi\)
0.188290 + 0.982114i \(0.439706\pi\)
\(318\) −0.245456 0.425143i −0.0137645 0.0238408i
\(319\) −7.64033 13.2334i −0.427776 0.740931i
\(320\) 3.12177 5.40706i 0.174512 0.302264i
\(321\) 3.41585 5.91643i 0.190654 0.330223i
\(322\) 37.6437 2.09780
\(323\) 3.13522 0.174449
\(324\) −1.13744 + 1.97010i −0.0631911 + 0.109450i
\(325\) 3.99857 6.92573i 0.221801 0.384171i
\(326\) 9.15461 + 15.8562i 0.507027 + 0.878196i
\(327\) 3.91828 + 6.78667i 0.216682 + 0.375304i
\(328\) 6.77394 0.374028
\(329\) 5.13397 + 8.89230i 0.283045 + 0.490248i
\(330\) −7.74988 13.4232i −0.426617 0.738922i
\(331\) −9.88908 17.1284i −0.543553 0.941461i −0.998696 0.0510430i \(-0.983745\pi\)
0.455144 0.890418i \(-0.349588\pi\)
\(332\) −1.76521 + 3.05743i −0.0968785 + 0.167799i
\(333\) −1.22202 −0.0669661
\(334\) 15.1538 26.2472i 0.829180 1.43618i
\(335\) 1.79939 + 3.11663i 0.0983110 + 0.170280i
\(336\) 21.8652 1.19285
\(337\) −5.90572 10.2290i −0.321705 0.557209i 0.659135 0.752025i \(-0.270923\pi\)
−0.980840 + 0.194815i \(0.937589\pi\)
\(338\) 17.5124 30.3323i 0.952548 1.64986i
\(339\) 1.99558 3.45645i 0.108385 0.187729i
\(340\) 1.40535 0.0762156
\(341\) 18.2332 31.5808i 0.987381 1.71019i
\(342\) −11.8589 −0.641255
\(343\) −71.0791 −3.83791
\(344\) 12.0047 6.59758i 0.647249 0.355718i
\(345\) −6.98045 −0.375815
\(346\) −34.3309 −1.84564
\(347\) −16.9084 + 29.2862i −0.907691 + 1.57217i −0.0904269 + 0.995903i \(0.528823\pi\)
−0.817264 + 0.576264i \(0.804510\pi\)
\(348\) 1.63637 0.0877184
\(349\) −9.65322 + 16.7199i −0.516725 + 0.894994i 0.483086 + 0.875573i \(0.339516\pi\)
−0.999811 + 0.0194212i \(0.993818\pi\)
\(350\) 5.93975 10.2880i 0.317493 0.549914i
\(351\) 13.0536 + 22.6095i 0.696751 + 1.20681i
\(352\) 23.1596 1.23441
\(353\) −1.02607 1.77721i −0.0546125 0.0945916i 0.837427 0.546550i \(-0.184059\pi\)
−0.892039 + 0.451958i \(0.850726\pi\)
\(354\) −0.132310 + 0.229167i −0.00703218 + 0.0121801i
\(355\) 16.2390 0.861874
\(356\) 1.00050 1.73292i 0.0530265 0.0918445i
\(357\) −2.21709 3.84012i −0.117341 0.203241i
\(358\) −3.85695 6.68044i −0.203846 0.353072i
\(359\) 10.8615 + 18.8127i 0.573248 + 0.992894i 0.996230 + 0.0867559i \(0.0276500\pi\)
−0.422982 + 0.906138i \(0.639017\pi\)
\(360\) 9.10123 0.479677
\(361\) 4.58518 + 7.94177i 0.241325 + 0.417988i
\(362\) 9.50002 + 16.4545i 0.499310 + 0.864830i
\(363\) −9.65317 + 16.7198i −0.506660 + 0.877561i
\(364\) 11.3113 19.5918i 0.592874 1.02689i
\(365\) −26.3830 −1.38095
\(366\) 12.6584 0.661667
\(367\) −2.02142 + 3.50121i −0.105517 + 0.182762i −0.913949 0.405828i \(-0.866983\pi\)
0.808432 + 0.588590i \(0.200317\pi\)
\(368\) 10.6886 18.5132i 0.557183 0.965068i
\(369\) 3.70669 + 6.42018i 0.192963 + 0.334221i
\(370\) −0.842715 1.45963i −0.0438107 0.0758823i
\(371\) 1.84306 0.0956868
\(372\) 1.95254 + 3.38190i 0.101235 + 0.175343i
\(373\) 2.50829 + 4.34448i 0.129874 + 0.224949i 0.923628 0.383291i \(-0.125209\pi\)
−0.793753 + 0.608240i \(0.791876\pi\)
\(374\) −4.81308 8.33650i −0.248879 0.431070i
\(375\) −5.12686 + 8.87998i −0.264750 + 0.458560i
\(376\) 4.08698 0.210770
\(377\) −7.67622 + 13.2956i −0.395345 + 0.684758i
\(378\) 19.3907 + 33.5857i 0.997352 + 1.72746i
\(379\) −17.2726 −0.887234 −0.443617 0.896217i \(-0.646305\pi\)
−0.443617 + 0.896217i \(0.646305\pi\)
\(380\) −2.20304 3.81577i −0.113013 0.195745i
\(381\) −3.02902 + 5.24641i −0.155181 + 0.268782i
\(382\) −1.38843 + 2.40484i −0.0710385 + 0.123042i
\(383\) −7.71229 −0.394080 −0.197040 0.980395i \(-0.563133\pi\)
−0.197040 + 0.980395i \(0.563133\pi\)
\(384\) 5.65306 9.79138i 0.288481 0.499664i
\(385\) 58.1915 2.96571
\(386\) −1.69855 −0.0864537
\(387\) 12.8220 + 7.76756i 0.651778 + 0.394847i
\(388\) −9.78597 −0.496807
\(389\) −14.4313 −0.731698 −0.365849 0.930674i \(-0.619221\pi\)
−0.365849 + 0.930674i \(0.619221\pi\)
\(390\) −7.78627 + 13.4862i −0.394273 + 0.682901i
\(391\) −4.33523 −0.219242
\(392\) −21.4573 + 37.1651i −1.08376 + 1.87712i
\(393\) 0.869468 1.50596i 0.0438589 0.0759658i
\(394\) −16.1259 27.9310i −0.812413 1.40714i
\(395\) −14.6687 −0.738063
\(396\) 4.90425 + 8.49441i 0.246448 + 0.426860i
\(397\) 12.6086 21.8388i 0.632809 1.09606i −0.354166 0.935183i \(-0.615235\pi\)
0.986975 0.160875i \(-0.0514315\pi\)
\(398\) −24.3716 −1.22164
\(399\) −6.95109 + 12.0396i −0.347990 + 0.602736i
\(400\) −3.37309 5.84236i −0.168654 0.292118i
\(401\) −13.8287 23.9521i −0.690574 1.19611i −0.971650 0.236424i \(-0.924025\pi\)
0.281076 0.959685i \(-0.409309\pi\)
\(402\) 1.31988 + 2.28609i 0.0658294 + 0.114020i
\(403\) −36.6376 −1.82505
\(404\) 3.94202 + 6.82778i 0.196123 + 0.339695i
\(405\) 2.93954 + 5.09143i 0.146067 + 0.252995i
\(406\) −11.4028 + 19.7502i −0.565910 + 0.980185i
\(407\) −1.55498 + 2.69331i −0.0770776 + 0.133502i
\(408\) −1.76495 −0.0873783
\(409\) 12.9351 0.639598 0.319799 0.947485i \(-0.396385\pi\)
0.319799 + 0.947485i \(0.396385\pi\)
\(410\) −5.11235 + 8.85485i −0.252481 + 0.437310i
\(411\) 9.40636 16.2923i 0.463982 0.803640i
\(412\) 6.19682 + 10.7332i 0.305296 + 0.528787i
\(413\) −0.496736 0.860372i −0.0244428 0.0423362i
\(414\) 16.3978 0.805910
\(415\) 4.56192 + 7.90147i 0.223936 + 0.387868i
\(416\) −11.6342 20.1510i −0.570412 0.987983i
\(417\) 3.46291 + 5.99794i 0.169580 + 0.293721i
\(418\) −15.0901 + 26.1368i −0.738081 + 1.27839i
\(419\) 11.1168 0.543090 0.271545 0.962426i \(-0.412465\pi\)
0.271545 + 0.962426i \(0.412465\pi\)
\(420\) −3.11578 + 5.39670i −0.152035 + 0.263332i
\(421\) −17.5508 30.3989i −0.855373 1.48155i −0.876298 0.481769i \(-0.839994\pi\)
0.0209247 0.999781i \(-0.493339\pi\)
\(422\) 38.1481 1.85702
\(423\) 2.23639 + 3.87354i 0.108737 + 0.188338i
\(424\) 0.366799 0.635315i 0.0178133 0.0308536i
\(425\) −0.684050 + 1.18481i −0.0331813 + 0.0574717i
\(426\) 11.9115 0.577114
\(427\) −23.7621 + 41.1571i −1.14993 + 1.99173i
\(428\) −5.96267 −0.288217
\(429\) 28.7345 1.38732
\(430\) −0.435724 + 20.6717i −0.0210125 + 0.996877i
\(431\) −3.31824 −0.159834 −0.0799171 0.996802i \(-0.525466\pi\)
−0.0799171 + 0.996802i \(0.525466\pi\)
\(432\) 22.0233 1.05960
\(433\) −12.7897 + 22.1524i −0.614634 + 1.06458i 0.375814 + 0.926695i \(0.377363\pi\)
−0.990449 + 0.137883i \(0.955970\pi\)
\(434\) −54.4240 −2.61244
\(435\) 2.11447 3.66237i 0.101381 0.175597i
\(436\) 3.41986 5.92336i 0.163781 0.283678i
\(437\) 6.79595 + 11.7709i 0.325095 + 0.563080i
\(438\) −19.3523 −0.924688
\(439\) 9.95279 + 17.2387i 0.475021 + 0.822760i 0.999591 0.0286071i \(-0.00910716\pi\)
−0.524570 + 0.851367i \(0.675774\pi\)
\(440\) 11.5811 20.0590i 0.552106 0.956275i
\(441\) −46.9655 −2.23645
\(442\) −4.83569 + 8.37566i −0.230010 + 0.398389i
\(443\) 9.79515 + 16.9657i 0.465382 + 0.806065i 0.999219 0.0395228i \(-0.0125838\pi\)
−0.533837 + 0.845587i \(0.679250\pi\)
\(444\) −0.166519 0.288419i −0.00790264 0.0136878i
\(445\) −2.58564 4.47846i −0.122571 0.212300i
\(446\) 0.0882483 0.00417868
\(447\) −0.0709883 0.122955i −0.00335763 0.00581559i
\(448\) 8.59693 + 14.8903i 0.406167 + 0.703502i
\(449\) −10.4108 + 18.0319i −0.491314 + 0.850980i −0.999950 0.0100012i \(-0.996816\pi\)
0.508636 + 0.860982i \(0.330150\pi\)
\(450\) 2.58740 4.48150i 0.121971 0.211260i
\(451\) 18.8667 0.888396
\(452\) −3.48347 −0.163849
\(453\) 1.15915 2.00770i 0.0544615 0.0943301i
\(454\) 12.1937 21.1201i 0.572278 0.991214i
\(455\) −29.2324 50.6320i −1.37044 2.37366i
\(456\) 2.76676 + 4.79218i 0.129566 + 0.224414i
\(457\) −27.5750 −1.28990 −0.644951 0.764224i \(-0.723122\pi\)
−0.644951 + 0.764224i \(0.723122\pi\)
\(458\) −2.00391 3.47088i −0.0936368 0.162184i
\(459\) −2.23313 3.86789i −0.104233 0.180538i
\(460\) 3.04625 + 5.27625i 0.142032 + 0.246006i
\(461\) 19.9190 34.5007i 0.927720 1.60686i 0.140592 0.990068i \(-0.455099\pi\)
0.787128 0.616790i \(-0.211567\pi\)
\(462\) 42.6842 1.98585
\(463\) −6.23597 + 10.8010i −0.289810 + 0.501966i −0.973764 0.227559i \(-0.926926\pi\)
0.683954 + 0.729525i \(0.260259\pi\)
\(464\) 6.47544 + 11.2158i 0.300615 + 0.520680i
\(465\) 10.0921 0.468009
\(466\) −14.2725 24.7208i −0.661163 1.14517i
\(467\) 9.35949 16.2111i 0.433106 0.750161i −0.564033 0.825752i \(-0.690751\pi\)
0.997139 + 0.0755912i \(0.0240844\pi\)
\(468\) 4.92729 8.53431i 0.227764 0.394499i
\(469\) −9.91055 −0.457626
\(470\) −3.08448 + 5.34247i −0.142276 + 0.246430i
\(471\) 4.95129 0.228144
\(472\) −0.395435 −0.0182014
\(473\) 33.4352 18.3755i 1.53735 0.844904i
\(474\) −10.7597 −0.494210
\(475\) 4.28930 0.196807
\(476\) −1.93507 + 3.35163i −0.0886936 + 0.153622i
\(477\) 0.802848 0.0367599
\(478\) 0.169910 0.294293i 0.00777152 0.0134607i
\(479\) 18.5289 32.0930i 0.846607 1.46637i −0.0376105 0.999292i \(-0.511975\pi\)
0.884218 0.467075i \(-0.154692\pi\)
\(480\) 3.20471 + 5.55073i 0.146275 + 0.253355i
\(481\) 3.12457 0.142468
\(482\) 11.9697 + 20.7322i 0.545207 + 0.944326i
\(483\) 9.61161 16.6478i 0.437343 0.757501i
\(484\) 16.8505 0.765930
\(485\) −12.6452 + 21.9021i −0.574187 + 0.994522i
\(486\) 13.2404 + 22.9331i 0.600598 + 1.04027i
\(487\) −12.1520 21.0478i −0.550657 0.953767i −0.998227 0.0595177i \(-0.981044\pi\)
0.447570 0.894249i \(-0.352290\pi\)
\(488\) 9.45810 + 16.3819i 0.428148 + 0.741574i
\(489\) 9.34982 0.422814
\(490\) −32.3879 56.0975i −1.46314 2.53423i
\(491\) −1.34606 2.33144i −0.0607468 0.105217i 0.834053 0.551685i \(-0.186015\pi\)
−0.894799 + 0.446468i \(0.852682\pi\)
\(492\) −1.01019 + 1.74970i −0.0455429 + 0.0788826i
\(493\) 1.31320 2.27452i 0.0591434 0.102439i
\(494\) 30.3219 1.36425
\(495\) 25.3486 1.13933
\(496\) −15.4532 + 26.7658i −0.693871 + 1.20182i
\(497\) −22.3600 + 38.7286i −1.00298 + 1.73721i
\(498\) 3.34623 + 5.79584i 0.149948 + 0.259718i
\(499\) 0.0477932 + 0.0827802i 0.00213952 + 0.00370575i 0.867093 0.498146i \(-0.165986\pi\)
−0.864954 + 0.501852i \(0.832652\pi\)
\(500\) 8.94938 0.400228
\(501\) −7.73848 13.4034i −0.345730 0.598822i
\(502\) 21.8836 + 37.9035i 0.976713 + 1.69172i
\(503\) 5.21658 + 9.03538i 0.232596 + 0.402868i 0.958571 0.284853i \(-0.0919448\pi\)
−0.725976 + 0.687721i \(0.758611\pi\)
\(504\) −12.5318 + 21.7057i −0.558210 + 0.966848i
\(505\) 20.3751 0.906680
\(506\) 20.8658 36.1406i 0.927598 1.60665i
\(507\) −8.94291 15.4896i −0.397169 0.687916i
\(508\) 5.28742 0.234591
\(509\) −6.81444 11.8029i −0.302045 0.523157i 0.674554 0.738225i \(-0.264336\pi\)
−0.976599 + 0.215069i \(0.931002\pi\)
\(510\) 1.33202 2.30713i 0.0589830 0.102162i
\(511\) 36.3276 62.9212i 1.60704 2.78347i
\(512\) 0.972972 0.0429997
\(513\) −7.00136 + 12.1267i −0.309118 + 0.535407i
\(514\) −28.5187 −1.25791
\(515\) 32.0295 1.41139
\(516\) −0.0860982 + 4.08468i −0.00379026 + 0.179818i
\(517\) 11.3830 0.500623
\(518\) 4.64145 0.203934
\(519\) −8.76573 + 15.1827i −0.384773 + 0.666446i
\(520\) −23.2709 −1.02050
\(521\) −15.3439 + 26.5765i −0.672230 + 1.16434i 0.305041 + 0.952339i \(0.401330\pi\)
−0.977270 + 0.211997i \(0.932003\pi\)
\(522\) −4.96712 + 8.60331i −0.217405 + 0.376556i
\(523\) −12.4883 21.6303i −0.546074 0.945828i −0.998538 0.0540454i \(-0.982788\pi\)
0.452465 0.891782i \(-0.350545\pi\)
\(524\) −1.51773 −0.0663025
\(525\) −3.03321 5.25367i −0.132380 0.229289i
\(526\) −8.02280 + 13.8959i −0.349811 + 0.605890i
\(527\) 6.26772 0.273026
\(528\) 12.1198 20.9922i 0.527448 0.913567i
\(529\) 2.10291 + 3.64234i 0.0914308 + 0.158363i
\(530\) 0.553652 + 0.958954i 0.0240491 + 0.0416543i
\(531\) −0.216381 0.374784i −0.00939016 0.0162642i
\(532\) 12.1337 0.526064
\(533\) −9.47763 16.4157i −0.410522 0.711045i
\(534\) −1.89660 3.28502i −0.0820741 0.142157i
\(535\) −7.70481 + 13.3451i −0.333108 + 0.576960i
\(536\) −1.97236 + 3.41623i −0.0851931 + 0.147559i
\(537\) −3.93920 −0.169989
\(538\) 17.1917 0.741186
\(539\) −59.7623 + 103.511i −2.57415 + 4.45855i
\(540\) −3.13832 + 5.43572i −0.135052 + 0.233916i
\(541\) −19.9237 34.5088i −0.856586 1.48365i −0.875166 0.483823i \(-0.839248\pi\)
0.0185803 0.999827i \(-0.494085\pi\)
\(542\) 15.4809 + 26.8137i 0.664961 + 1.15175i
\(543\) 9.70260 0.416378
\(544\) 1.99030 + 3.44730i 0.0853333 + 0.147802i
\(545\) −8.83809 15.3080i −0.378582 0.655724i
\(546\) −21.4424 37.1393i −0.917648 1.58941i
\(547\) 13.0349 22.5772i 0.557334 0.965330i −0.440384 0.897809i \(-0.645158\pi\)
0.997718 0.0675209i \(-0.0215089\pi\)
\(548\) −16.4196 −0.701412
\(549\) −10.3509 + 17.9283i −0.441766 + 0.765162i
\(550\) −6.58478 11.4052i −0.280776 0.486318i
\(551\) −8.23433 −0.350794
\(552\) −3.82574 6.62637i −0.162834 0.282037i
\(553\) 20.1978 34.9837i 0.858899 1.48766i
\(554\) 15.8860 27.5154i 0.674932 1.16902i
\(555\) −0.860685 −0.0365341
\(556\) 3.02241 5.23497i 0.128179 0.222012i
\(557\) 25.1303 1.06481 0.532403 0.846491i \(-0.321289\pi\)
0.532403 + 0.846491i \(0.321289\pi\)
\(558\) −23.7074 −1.00362
\(559\) −32.7845 19.8609i −1.38664 0.840025i
\(560\) −49.3192 −2.08412
\(561\) −4.91572 −0.207542
\(562\) −3.04625 + 5.27627i −0.128498 + 0.222566i
\(563\) 38.5358 1.62409 0.812045 0.583595i \(-0.198354\pi\)
0.812045 + 0.583595i \(0.198354\pi\)
\(564\) −0.609487 + 1.05566i −0.0256640 + 0.0444514i
\(565\) −4.50124 + 7.79638i −0.189369 + 0.327996i
\(566\) 15.6415 + 27.0919i 0.657463 + 1.13876i
\(567\) −16.1902 −0.679924
\(568\) 8.90000 + 15.4153i 0.373436 + 0.646810i
\(569\) 2.97761 5.15737i 0.124828 0.216208i −0.796838 0.604193i \(-0.793495\pi\)
0.921666 + 0.387985i \(0.126829\pi\)
\(570\) −8.35239 −0.349843
\(571\) 6.59609 11.4248i 0.276038 0.478112i −0.694359 0.719629i \(-0.744312\pi\)
0.970396 + 0.241518i \(0.0776451\pi\)
\(572\) −12.5397 21.7193i −0.524310 0.908131i
\(573\) 0.709021 + 1.22806i 0.0296198 + 0.0513029i
\(574\) −14.0787 24.3851i −0.587634 1.01781i
\(575\) −5.93102 −0.247341
\(576\) 3.74488 + 6.48632i 0.156037 + 0.270263i
\(577\) −3.47084 6.01167i −0.144493 0.250269i 0.784691 0.619888i \(-0.212822\pi\)
−0.929184 + 0.369618i \(0.879488\pi\)
\(578\) 0.827258 1.43285i 0.0344094 0.0595988i
\(579\) −0.433691 + 0.751175i −0.0180236 + 0.0312178i
\(580\) −3.69099 −0.153260
\(581\) −25.1258 −1.04239
\(582\) −9.27541 + 16.0655i −0.384478 + 0.665935i
\(583\) 1.02160 1.76947i 0.0423104 0.0732838i
\(584\) −14.4596 25.0447i −0.598342 1.03636i
\(585\) −12.7338 22.0556i −0.526478 0.911887i
\(586\) 5.48473 0.226572
\(587\) −9.04655 15.6691i −0.373391 0.646732i 0.616694 0.787203i \(-0.288472\pi\)
−0.990085 + 0.140471i \(0.955138\pi\)
\(588\) −6.39979 11.0848i −0.263923 0.457128i
\(589\) −9.82536 17.0180i −0.404847 0.701215i
\(590\) 0.298438 0.516909i 0.0122865 0.0212808i
\(591\) −16.4698 −0.677478
\(592\) 1.31790 2.28267i 0.0541654 0.0938172i
\(593\) −9.22782 15.9831i −0.378941 0.656345i 0.611967 0.790883i \(-0.290378\pi\)
−0.990908 + 0.134538i \(0.957045\pi\)
\(594\) 42.9929 1.76402
\(595\) 5.00088 + 8.66179i 0.205016 + 0.355099i
\(596\) −0.0619581 + 0.107315i −0.00253790 + 0.00439578i
\(597\) −6.22283 + 10.7783i −0.254684 + 0.441125i
\(598\) −41.9276 −1.71455
\(599\) 15.9226 27.5787i 0.650579 1.12684i −0.332404 0.943137i \(-0.607860\pi\)
0.982983 0.183699i \(-0.0588071\pi\)
\(600\) −2.41463 −0.0985770
\(601\) −39.4036 −1.60731 −0.803653 0.595098i \(-0.797113\pi\)
−0.803653 + 0.595098i \(0.797113\pi\)
\(602\) −48.7003 29.5027i −1.98488 1.20244i
\(603\) −4.31710 −0.175806
\(604\) −2.02339 −0.0823307
\(605\) 21.7737 37.7132i 0.885227 1.53326i
\(606\) 14.9454 0.607116
\(607\) 0.841251 1.45709i 0.0341453 0.0591414i −0.848448 0.529279i \(-0.822462\pi\)
0.882593 + 0.470138i \(0.155796\pi\)
\(608\) 6.24003 10.8080i 0.253067 0.438324i
\(609\) 5.82296 + 10.0857i 0.235958 + 0.408692i
\(610\) −28.5524 −1.15605
\(611\) −5.71822 9.90425i −0.231335 0.400683i
\(612\) −0.842928 + 1.45999i −0.0340733 + 0.0590167i
\(613\) 18.0083 0.727348 0.363674 0.931526i \(-0.381522\pi\)
0.363674 + 0.931526i \(0.381522\pi\)
\(614\) −2.12243 + 3.67616i −0.0856543 + 0.148358i
\(615\) 2.61068 + 4.52183i 0.105273 + 0.182338i
\(616\) 31.8927 + 55.2398i 1.28499 + 2.22567i
\(617\) −14.6771 25.4216i −0.590880 1.02343i −0.994114 0.108337i \(-0.965447\pi\)
0.403235 0.915097i \(-0.367886\pi\)
\(618\) 23.4941 0.945070
\(619\) 3.08521 + 5.34375i 0.124005 + 0.214783i 0.921344 0.388749i \(-0.127093\pi\)
−0.797338 + 0.603532i \(0.793759\pi\)
\(620\) −4.40416 7.62822i −0.176875 0.306357i
\(621\) 9.68112 16.7682i 0.388490 0.672884i
\(622\) −24.0502 + 41.6561i −0.964324 + 1.67026i
\(623\) 14.2410 0.570555
\(624\) −24.3535 −0.974921
\(625\) 8.14390 14.1057i 0.325756 0.564226i
\(626\) −15.4548 + 26.7684i −0.617697 + 1.06988i
\(627\) 7.70594 + 13.3471i 0.307746 + 0.533031i
\(628\) −2.16073 3.74249i −0.0862225 0.149342i
\(629\) −0.534531 −0.0213131
\(630\) −18.9157 32.7629i −0.753618 1.30531i
\(631\) −14.4572 25.0406i −0.575532 0.996851i −0.995984 0.0895357i \(-0.971462\pi\)
0.420452 0.907315i \(-0.361872\pi\)
\(632\) −8.03941 13.9247i −0.319790 0.553893i
\(633\) 9.74040 16.8709i 0.387146 0.670557i
\(634\) −11.0932 −0.440568
\(635\) 6.83226 11.8338i 0.271130 0.469611i
\(636\) 0.109401 + 0.189487i 0.00433802 + 0.00751366i
\(637\) 120.086 4.75798
\(638\) 12.6410 + 21.8949i 0.500464 + 0.866829i
\(639\) −9.74014 + 16.8704i −0.385314 + 0.667384i
\(640\) −12.7511 + 22.0855i −0.504030 + 0.873005i
\(641\) −11.0036 −0.434614 −0.217307 0.976103i \(-0.569727\pi\)
−0.217307 + 0.976103i \(0.569727\pi\)
\(642\) −5.65159 + 9.78883i −0.223050 + 0.386334i
\(643\) −40.7776 −1.60811 −0.804055 0.594554i \(-0.797328\pi\)
−0.804055 + 0.594554i \(0.797328\pi\)
\(644\) −16.7779 −0.661142
\(645\) 9.03072 + 5.47082i 0.355584 + 0.215413i
\(646\) −5.18728 −0.204091
\(647\) 19.2904 0.758382 0.379191 0.925318i \(-0.376202\pi\)
0.379191 + 0.925318i \(0.376202\pi\)
\(648\) −3.22212 + 5.58087i −0.126577 + 0.219237i
\(649\) −1.10136 −0.0432321
\(650\) −6.61570 + 11.4587i −0.259489 + 0.449449i
\(651\) −13.8961 + 24.0688i −0.544632 + 0.943331i
\(652\) −4.08023 7.06717i −0.159794 0.276772i
\(653\) 18.5022 0.724046 0.362023 0.932169i \(-0.382086\pi\)
0.362023 + 0.932169i \(0.382086\pi\)
\(654\) −6.48286 11.2286i −0.253500 0.439075i
\(655\) −1.96117 + 3.39685i −0.0766294 + 0.132726i
\(656\) −15.9901 −0.624310
\(657\) 15.8245 27.4089i 0.617374 1.06932i
\(658\) −8.49424 14.7124i −0.331140 0.573551i
\(659\) −5.06189 8.76746i −0.197183 0.341532i 0.750431 0.660949i \(-0.229846\pi\)
−0.947614 + 0.319418i \(0.896513\pi\)
\(660\) 3.45414 + 5.98275i 0.134452 + 0.232878i
\(661\) 27.8467 1.08311 0.541556 0.840665i \(-0.317836\pi\)
0.541556 + 0.840665i \(0.317836\pi\)
\(662\) 16.3616 + 28.3392i 0.635913 + 1.10143i
\(663\) 2.46940 + 4.27713i 0.0959036 + 0.166110i
\(664\) −5.00045 + 8.66104i −0.194055 + 0.336114i
\(665\) 15.6789 27.1566i 0.608001 1.05309i
\(666\) 2.02185 0.0783449
\(667\) 11.3860 0.440868
\(668\) −6.75410 + 11.6984i −0.261324 + 0.452626i
\(669\) 0.0225325 0.0390275i 0.000871157 0.00150889i
\(670\) −2.97711 5.15651i −0.115016 0.199214i
\(671\) 26.3425 + 45.6266i 1.01694 + 1.76139i
\(672\) −17.6507 −0.680891
\(673\) 11.0234 + 19.0931i 0.424922 + 0.735986i 0.996413 0.0846221i \(-0.0269683\pi\)
−0.571491 + 0.820608i \(0.693635\pi\)
\(674\) 9.77110 + 16.9240i 0.376369 + 0.651890i
\(675\) −3.05514 5.29166i −0.117592 0.203676i
\(676\) −7.80532 + 13.5192i −0.300205 + 0.519970i
\(677\) −25.2367 −0.969926 −0.484963 0.874535i \(-0.661167\pi\)
−0.484963 + 0.874535i \(0.661167\pi\)
\(678\) −3.30173 + 5.71876i −0.126802 + 0.219627i
\(679\) −34.8231 60.3154i −1.33639 2.31469i
\(680\) 3.98104 0.152666
\(681\) −6.22685 10.7852i −0.238613 0.413291i
\(682\) −30.1671 + 52.2509i −1.15516 + 2.00079i
\(683\) −8.50876 + 14.7376i −0.325579 + 0.563919i −0.981629 0.190798i \(-0.938892\pi\)
0.656051 + 0.754717i \(0.272226\pi\)
\(684\) 5.28553 0.202097
\(685\) −21.2170 + 36.7489i −0.810660 + 1.40411i
\(686\) 117.601 4.49004
\(687\) −2.04665 −0.0780844
\(688\) −28.3375 + 15.5738i −1.08036 + 0.593746i
\(689\) −2.05280 −0.0782054
\(690\) 11.5493 0.439673
\(691\) 14.4396 25.0101i 0.549308 0.951430i −0.449014 0.893525i \(-0.648225\pi\)
0.998322 0.0579052i \(-0.0184421\pi\)
\(692\) 15.3014 0.581670
\(693\) −34.9033 + 60.4543i −1.32587 + 2.29647i
\(694\) 27.9752 48.4545i 1.06192 1.83931i
\(695\) −7.81096 13.5290i −0.296286 0.513183i
\(696\) 4.63546 0.175707
\(697\) 1.62137 + 2.80830i 0.0614138 + 0.106372i
\(698\) 15.9714 27.6633i 0.604526 1.04707i
\(699\) −14.5769 −0.551349
\(700\) −2.64736 + 4.58537i −0.100061 + 0.173311i
\(701\) 1.11547 + 1.93206i 0.0421309 + 0.0729728i 0.886322 0.463070i \(-0.153252\pi\)
−0.844191 + 0.536042i \(0.819919\pi\)
\(702\) −21.5974 37.4078i −0.815142 1.41187i
\(703\) 0.837937 + 1.45135i 0.0316034 + 0.0547387i
\(704\) 19.0610 0.718389
\(705\) 1.57513 + 2.72820i 0.0593226 + 0.102750i
\(706\) 1.69766 + 2.94043i 0.0638922 + 0.110664i
\(707\) −28.0551 + 48.5929i −1.05512 + 1.82753i
\(708\) 0.0589707 0.102140i 0.00221626 0.00383867i
\(709\) 51.6630 1.94025 0.970123 0.242613i \(-0.0780044\pi\)
0.970123 + 0.242613i \(0.0780044\pi\)
\(710\) −26.8676 −1.00832
\(711\) 8.79831 15.2391i 0.329962 0.571512i
\(712\) 2.83420 4.90898i 0.106216 0.183972i
\(713\) 13.5860 + 23.5316i 0.508799 + 0.881267i
\(714\) 3.66822 + 6.35354i 0.137280 + 0.237775i
\(715\) −64.8137 −2.42390
\(716\) 1.71906 + 2.97749i 0.0642441 + 0.111274i
\(717\) −0.0867668 0.150284i −0.00324036 0.00561248i
\(718\) −17.9705 31.1258i −0.670653 1.16161i
\(719\) 6.50590 11.2685i 0.242629 0.420246i −0.718833 0.695182i \(-0.755324\pi\)
0.961462 + 0.274937i \(0.0886569\pi\)
\(720\) −21.4838 −0.800653
\(721\) −44.1024 + 76.3877i −1.64246 + 2.84483i
\(722\) −7.58626 13.1398i −0.282331 0.489012i
\(723\) 12.2250 0.454652
\(724\) −4.23419 7.33382i −0.157362 0.272559i
\(725\) 1.79658 3.11177i 0.0667234 0.115568i
\(726\) 15.9713 27.6631i 0.592751 1.02668i
\(727\) 13.2381 0.490974 0.245487 0.969400i \(-0.421052\pi\)
0.245487 + 0.969400i \(0.421052\pi\)
\(728\) 32.0425 55.4992i 1.18757 2.05694i
\(729\) 4.26804 0.158076
\(730\) 43.6510 1.61560
\(731\) 5.60855 + 3.39767i 0.207440 + 0.125667i
\(732\) −5.64190 −0.208531
\(733\) −53.0608 −1.95985 −0.979923 0.199375i \(-0.936109\pi\)
−0.979923 + 0.199375i \(0.936109\pi\)
\(734\) 3.34448 5.79280i 0.123447 0.213816i
\(735\) −33.0786 −1.22012
\(736\) −8.62839 + 14.9448i −0.318047 + 0.550873i
\(737\) −5.49339 + 9.51483i −0.202352 + 0.350483i
\(738\) −6.13278 10.6223i −0.225751 0.391012i
\(739\) 13.6787 0.503181 0.251590 0.967834i \(-0.419046\pi\)
0.251590 + 0.967834i \(0.419046\pi\)
\(740\) 0.375600 + 0.650559i 0.0138073 + 0.0239150i
\(741\) 7.74213 13.4098i 0.284414 0.492620i
\(742\) −3.04937 −0.111946
\(743\) 7.22385 12.5121i 0.265017 0.459023i −0.702551 0.711634i \(-0.747956\pi\)
0.967568 + 0.252610i \(0.0812890\pi\)
\(744\) 5.53112 + 9.58018i 0.202781 + 0.351227i
\(745\) 0.160121 + 0.277338i 0.00586639 + 0.0101609i
\(746\) −4.15000 7.18802i −0.151942 0.263172i
\(747\) −10.9450 −0.400455
\(748\) 2.14520 + 3.71560i 0.0784364 + 0.135856i
\(749\) −21.2180 36.7507i −0.775289 1.34284i
\(750\) 8.48247 14.6921i 0.309736 0.536478i
\(751\) −17.5914 + 30.4692i −0.641920 + 1.11184i 0.343084 + 0.939305i \(0.388529\pi\)
−0.985004 + 0.172533i \(0.944805\pi\)
\(752\) −9.64747 −0.351807
\(753\) 22.3502 0.814488
\(754\) 12.7004 21.9978i 0.462522 0.801112i
\(755\) −2.61458 + 4.52858i −0.0951542 + 0.164812i
\(756\) −8.64251 14.9693i −0.314325 0.544427i
\(757\) −14.8539 25.7277i −0.539874 0.935089i −0.998910 0.0466718i \(-0.985139\pi\)
0.459036 0.888418i \(-0.348195\pi\)
\(758\) 28.5778 1.03799
\(759\) −10.6554 18.4556i −0.386766 0.669898i
\(760\) −6.24072 10.8092i −0.226375 0.392092i
\(761\) 21.3523 + 36.9832i 0.774019 + 1.34064i 0.935344 + 0.353739i \(0.115090\pi\)
−0.161326 + 0.986901i \(0.551577\pi\)
\(762\) 5.01156 8.68027i 0.181550 0.314453i
\(763\) 48.6779 1.76226
\(764\) 0.618829 1.07184i 0.0223884 0.0387779i
\(765\) 2.17842 + 3.77313i 0.0787608 + 0.136418i
\(766\) 12.7601 0.461041
\(767\) 0.553265 + 0.958284i 0.0199773 + 0.0346016i
\(768\)