Properties

Label 125.2.e.a.24.1
Level $125$
Weight $2$
Character 125.24
Analytic conductor $0.998$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 125 = 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 125.e (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.998130025266\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 24.1
Root \(0.587785 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 125.24
Dual form 125.2.e.a.99.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.53884 - 0.500000i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(1.30902 - 0.951057i) q^{6} +0.618034i q^{7} +(1.31433 + 1.80902i) q^{8} +(0.618034 + 1.90211i) q^{9} +O(q^{10})\) \(q+(-1.53884 - 0.500000i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(1.30902 - 0.951057i) q^{6} +0.618034i q^{7} +(1.31433 + 1.80902i) q^{8} +(0.618034 + 1.90211i) q^{9} +(-1.61803 + 4.97980i) q^{11} +(-0.587785 + 0.190983i) q^{12} +(1.76336 - 0.572949i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-1.50000 - 4.61653i) q^{16} +(3.07768 + 4.23607i) q^{17} -3.23607i q^{18} +(0.690983 - 0.502029i) q^{19} +(-0.500000 - 0.363271i) q^{21} +(4.97980 - 6.85410i) q^{22} +(-3.57971 - 1.16312i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(-4.75528 - 1.54508i) q^{27} +(-0.224514 + 0.309017i) q^{28} +(-2.92705 - 2.12663i) q^{29} +(2.42705 - 1.76336i) q^{31} +3.38197i q^{32} +(-3.07768 - 4.23607i) q^{33} +(-2.61803 - 8.05748i) q^{34} +(-0.381966 + 1.17557i) q^{36} +(0.224514 - 0.0729490i) q^{37} +(-1.31433 + 0.427051i) q^{38} +(-0.572949 + 1.76336i) q^{39} +(-0.236068 - 0.726543i) q^{41} +(0.587785 + 0.809017i) q^{42} +4.85410i q^{43} +(-2.61803 + 1.90211i) q^{44} +(4.92705 + 3.57971i) q^{46} +(0.363271 - 0.500000i) q^{47} +(4.61653 + 1.50000i) q^{48} +6.61803 q^{49} -5.23607 q^{51} +(1.08981 + 0.354102i) q^{52} +(2.04087 - 2.80902i) q^{53} +(6.54508 + 4.75528i) q^{54} +(-1.11803 + 0.812299i) q^{56} +0.854102i q^{57} +(3.44095 + 4.73607i) q^{58} +(3.35410 + 10.3229i) q^{59} +(2.69098 - 8.28199i) q^{61} +(-4.61653 + 1.50000i) q^{62} +(-1.17557 + 0.381966i) q^{63} +(-1.30902 + 4.02874i) q^{64} +(2.61803 + 8.05748i) q^{66} +(-2.80017 - 3.85410i) q^{67} +3.23607i q^{68} +(3.04508 - 2.21238i) q^{69} +(5.35410 + 3.88998i) q^{71} +(-2.62866 + 3.61803i) q^{72} +(8.55951 + 2.78115i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(-3.07768 - 1.00000i) q^{77} +(1.76336 - 2.42705i) q^{78} +(-6.54508 - 4.75528i) q^{79} +(-0.809017 + 0.587785i) q^{81} +1.23607i q^{82} +(-3.66547 - 5.04508i) q^{83} +(-0.118034 - 0.363271i) q^{84} +(2.42705 - 7.46969i) q^{86} +(3.44095 - 1.11803i) q^{87} +(-11.1352 + 3.61803i) q^{88} +(2.76393 - 8.50651i) q^{89} +(0.354102 + 1.08981i) q^{91} +(-1.36733 - 1.88197i) q^{92} +3.00000i q^{93} +(-0.809017 + 0.587785i) q^{94} +(-2.73607 - 1.98787i) q^{96} +(-2.26538 + 3.11803i) q^{97} +(-10.1841 - 3.30902i) q^{98} -10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{11} - 2 q^{14} - 12 q^{16} + 10 q^{19} - 4 q^{21} - 24 q^{26} - 10 q^{29} + 6 q^{31} - 12 q^{34} - 12 q^{36} - 18 q^{39} + 16 q^{41} - 12 q^{44} + 26 q^{46} + 44 q^{49} - 24 q^{51} + 30 q^{54} + 26 q^{61} - 6 q^{64} + 12 q^{66} + 2 q^{69} + 16 q^{71} - 12 q^{74} + 40 q^{76} - 30 q^{79} - 2 q^{81} + 8 q^{84} + 6 q^{86} + 40 q^{89} - 24 q^{91} - 2 q^{94} - 4 q^{96} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.53884 0.500000i −1.08813 0.353553i −0.290604 0.956844i \(-0.593856\pi\)
−0.797522 + 0.603290i \(0.793856\pi\)
\(3\) −0.587785 + 0.809017i −0.339358 + 0.467086i −0.944254 0.329218i \(-0.893215\pi\)
0.604896 + 0.796305i \(0.293215\pi\)
\(4\) 0.500000 + 0.363271i 0.250000 + 0.181636i
\(5\) 0 0
\(6\) 1.30902 0.951057i 0.534404 0.388267i
\(7\) 0.618034i 0.233595i 0.993156 + 0.116797i \(0.0372628\pi\)
−0.993156 + 0.116797i \(0.962737\pi\)
\(8\) 1.31433 + 1.80902i 0.464685 + 0.639584i
\(9\) 0.618034 + 1.90211i 0.206011 + 0.634038i
\(10\) 0 0
\(11\) −1.61803 + 4.97980i −0.487856 + 1.50147i 0.339946 + 0.940445i \(0.389591\pi\)
−0.827802 + 0.561020i \(0.810409\pi\)
\(12\) −0.587785 + 0.190983i −0.169679 + 0.0551320i
\(13\) 1.76336 0.572949i 0.489067 0.158907i −0.0540944 0.998536i \(-0.517227\pi\)
0.543161 + 0.839628i \(0.317227\pi\)
\(14\) 0.309017 0.951057i 0.0825883 0.254181i
\(15\) 0 0
\(16\) −1.50000 4.61653i −0.375000 1.15413i
\(17\) 3.07768 + 4.23607i 0.746448 + 1.02740i 0.998222 + 0.0596113i \(0.0189861\pi\)
−0.251774 + 0.967786i \(0.581014\pi\)
\(18\) 3.23607i 0.762749i
\(19\) 0.690983 0.502029i 0.158522 0.115173i −0.505696 0.862712i \(-0.668764\pi\)
0.664219 + 0.747538i \(0.268764\pi\)
\(20\) 0 0
\(21\) −0.500000 0.363271i −0.109109 0.0792723i
\(22\) 4.97980 6.85410i 1.06170 1.46130i
\(23\) −3.57971 1.16312i −0.746422 0.242527i −0.0889808 0.996033i \(-0.528361\pi\)
−0.657441 + 0.753506i \(0.728361\pi\)
\(24\) −2.23607 −0.456435
\(25\) 0 0
\(26\) −3.00000 −0.588348
\(27\) −4.75528 1.54508i −0.915155 0.297352i
\(28\) −0.224514 + 0.309017i −0.0424292 + 0.0583987i
\(29\) −2.92705 2.12663i −0.543540 0.394905i 0.281858 0.959456i \(-0.409049\pi\)
−0.825398 + 0.564551i \(0.809049\pi\)
\(30\) 0 0
\(31\) 2.42705 1.76336i 0.435911 0.316708i −0.348097 0.937459i \(-0.613172\pi\)
0.784008 + 0.620750i \(0.213172\pi\)
\(32\) 3.38197i 0.597853i
\(33\) −3.07768 4.23607i −0.535756 0.737405i
\(34\) −2.61803 8.05748i −0.448989 1.38185i
\(35\) 0 0
\(36\) −0.381966 + 1.17557i −0.0636610 + 0.195928i
\(37\) 0.224514 0.0729490i 0.0369099 0.0119927i −0.290504 0.956874i \(-0.593823\pi\)
0.327414 + 0.944881i \(0.393823\pi\)
\(38\) −1.31433 + 0.427051i −0.213212 + 0.0692768i
\(39\) −0.572949 + 1.76336i −0.0917453 + 0.282363i
\(40\) 0 0
\(41\) −0.236068 0.726543i −0.0368676 0.113467i 0.930929 0.365200i \(-0.118999\pi\)
−0.967797 + 0.251733i \(0.918999\pi\)
\(42\) 0.587785 + 0.809017i 0.0906972 + 0.124834i
\(43\) 4.85410i 0.740244i 0.928983 + 0.370122i \(0.120684\pi\)
−0.928983 + 0.370122i \(0.879316\pi\)
\(44\) −2.61803 + 1.90211i −0.394683 + 0.286754i
\(45\) 0 0
\(46\) 4.92705 + 3.57971i 0.726454 + 0.527800i
\(47\) 0.363271 0.500000i 0.0529886 0.0729325i −0.781700 0.623654i \(-0.785647\pi\)
0.834689 + 0.550722i \(0.185647\pi\)
\(48\) 4.61653 + 1.50000i 0.666338 + 0.216506i
\(49\) 6.61803 0.945433
\(50\) 0 0
\(51\) −5.23607 −0.733196
\(52\) 1.08981 + 0.354102i 0.151130 + 0.0491051i
\(53\) 2.04087 2.80902i 0.280335 0.385848i −0.645510 0.763752i \(-0.723355\pi\)
0.925845 + 0.377904i \(0.123355\pi\)
\(54\) 6.54508 + 4.75528i 0.890673 + 0.647112i
\(55\) 0 0
\(56\) −1.11803 + 0.812299i −0.149404 + 0.108548i
\(57\) 0.854102i 0.113129i
\(58\) 3.44095 + 4.73607i 0.451820 + 0.621876i
\(59\) 3.35410 + 10.3229i 0.436667 + 1.34392i 0.891369 + 0.453279i \(0.149746\pi\)
−0.454702 + 0.890644i \(0.650254\pi\)
\(60\) 0 0
\(61\) 2.69098 8.28199i 0.344545 1.06040i −0.617282 0.786742i \(-0.711766\pi\)
0.961827 0.273659i \(-0.0882338\pi\)
\(62\) −4.61653 + 1.50000i −0.586299 + 0.190500i
\(63\) −1.17557 + 0.381966i −0.148108 + 0.0481232i
\(64\) −1.30902 + 4.02874i −0.163627 + 0.503593i
\(65\) 0 0
\(66\) 2.61803 + 8.05748i 0.322258 + 0.991807i
\(67\) −2.80017 3.85410i −0.342095 0.470853i 0.602957 0.797774i \(-0.293989\pi\)
−0.945052 + 0.326920i \(0.893989\pi\)
\(68\) 3.23607i 0.392431i
\(69\) 3.04508 2.21238i 0.366585 0.266340i
\(70\) 0 0
\(71\) 5.35410 + 3.88998i 0.635415 + 0.461656i 0.858272 0.513195i \(-0.171538\pi\)
−0.222857 + 0.974851i \(0.571538\pi\)
\(72\) −2.62866 + 3.61803i −0.309790 + 0.426389i
\(73\) 8.55951 + 2.78115i 1.00181 + 0.325509i 0.763590 0.645701i \(-0.223435\pi\)
0.238224 + 0.971210i \(0.423435\pi\)
\(74\) −0.381966 −0.0444026
\(75\) 0 0
\(76\) 0.527864 0.0605502
\(77\) −3.07768 1.00000i −0.350735 0.113961i
\(78\) 1.76336 2.42705i 0.199661 0.274809i
\(79\) −6.54508 4.75528i −0.736380 0.535011i 0.155196 0.987884i \(-0.450399\pi\)
−0.891575 + 0.452873i \(0.850399\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 1.23607i 0.136501i
\(83\) −3.66547 5.04508i −0.402337 0.553770i 0.558991 0.829174i \(-0.311189\pi\)
−0.961329 + 0.275404i \(0.911189\pi\)
\(84\) −0.118034 0.363271i −0.0128786 0.0396361i
\(85\) 0 0
\(86\) 2.42705 7.46969i 0.261716 0.805478i
\(87\) 3.44095 1.11803i 0.368909 0.119866i
\(88\) −11.1352 + 3.61803i −1.18701 + 0.385684i
\(89\) 2.76393 8.50651i 0.292976 0.901688i −0.690918 0.722934i \(-0.742793\pi\)
0.983894 0.178754i \(-0.0572068\pi\)
\(90\) 0 0
\(91\) 0.354102 + 1.08981i 0.0371200 + 0.114244i
\(92\) −1.36733 1.88197i −0.142554 0.196209i
\(93\) 3.00000i 0.311086i
\(94\) −0.809017 + 0.587785i −0.0834437 + 0.0606254i
\(95\) 0 0
\(96\) −2.73607 1.98787i −0.279249 0.202886i
\(97\) −2.26538 + 3.11803i −0.230015 + 0.316588i −0.908387 0.418130i \(-0.862686\pi\)
0.678372 + 0.734718i \(0.262686\pi\)
\(98\) −10.1841 3.30902i −1.02875 0.334261i
\(99\) −10.4721 −1.05249
\(100\) 0 0
\(101\) 1.47214 0.146483 0.0732415 0.997314i \(-0.476666\pi\)
0.0732415 + 0.997314i \(0.476666\pi\)
\(102\) 8.05748 + 2.61803i 0.797809 + 0.259224i
\(103\) −5.03280 + 6.92705i −0.495896 + 0.682543i −0.981462 0.191658i \(-0.938614\pi\)
0.485566 + 0.874200i \(0.338614\pi\)
\(104\) 3.35410 + 2.43690i 0.328897 + 0.238957i
\(105\) 0 0
\(106\) −4.54508 + 3.30220i −0.441458 + 0.320738i
\(107\) 16.4164i 1.58703i −0.608548 0.793517i \(-0.708248\pi\)
0.608548 0.793517i \(-0.291752\pi\)
\(108\) −1.81636 2.50000i −0.174779 0.240563i
\(109\) −3.09017 9.51057i −0.295985 0.910947i −0.982889 0.184199i \(-0.941031\pi\)
0.686904 0.726748i \(-0.258969\pi\)
\(110\) 0 0
\(111\) −0.0729490 + 0.224514i −0.00692401 + 0.0213099i
\(112\) 2.85317 0.927051i 0.269599 0.0875981i
\(113\) 16.0292 5.20820i 1.50790 0.489947i 0.565590 0.824687i \(-0.308648\pi\)
0.942311 + 0.334740i \(0.108648\pi\)
\(114\) 0.427051 1.31433i 0.0399970 0.123098i
\(115\) 0 0
\(116\) −0.690983 2.12663i −0.0641562 0.197452i
\(117\) 2.17963 + 3.00000i 0.201507 + 0.277350i
\(118\) 17.5623i 1.61674i
\(119\) −2.61803 + 1.90211i −0.239995 + 0.174366i
\(120\) 0 0
\(121\) −13.2812 9.64932i −1.20738 0.877211i
\(122\) −8.28199 + 11.3992i −0.749817 + 1.03203i
\(123\) 0.726543 + 0.236068i 0.0655101 + 0.0212855i
\(124\) 1.85410 0.166503
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) 18.9151 + 6.14590i 1.67845 + 0.545360i 0.984609 0.174772i \(-0.0559187\pi\)
0.693837 + 0.720132i \(0.255919\pi\)
\(128\) 8.00448 11.0172i 0.707503 0.973794i
\(129\) −3.92705 2.85317i −0.345758 0.251208i
\(130\) 0 0
\(131\) −5.50000 + 3.99598i −0.480537 + 0.349131i −0.801534 0.597950i \(-0.795982\pi\)
0.320996 + 0.947080i \(0.395982\pi\)
\(132\) 3.23607i 0.281664i
\(133\) 0.310271 + 0.427051i 0.0269039 + 0.0370300i
\(134\) 2.38197 + 7.33094i 0.205771 + 0.633297i
\(135\) 0 0
\(136\) −3.61803 + 11.1352i −0.310244 + 0.954832i
\(137\) 11.3597 3.69098i 0.970523 0.315342i 0.219496 0.975613i \(-0.429559\pi\)
0.751027 + 0.660271i \(0.229559\pi\)
\(138\) −5.79210 + 1.88197i −0.493056 + 0.160204i
\(139\) −1.54508 + 4.75528i −0.131052 + 0.403338i −0.994955 0.100321i \(-0.968013\pi\)
0.863903 + 0.503659i \(0.168013\pi\)
\(140\) 0 0
\(141\) 0.190983 + 0.587785i 0.0160837 + 0.0495004i
\(142\) −6.29412 8.66312i −0.528191 0.726993i
\(143\) 9.70820i 0.811841i
\(144\) 7.85410 5.70634i 0.654508 0.475528i
\(145\) 0 0
\(146\) −11.7812 8.55951i −0.975015 0.708390i
\(147\) −3.88998 + 5.35410i −0.320840 + 0.441599i
\(148\) 0.138757 + 0.0450850i 0.0114058 + 0.00370596i
\(149\) 3.94427 0.323127 0.161564 0.986862i \(-0.448346\pi\)
0.161564 + 0.986862i \(0.448346\pi\)
\(150\) 0 0
\(151\) 14.5623 1.18506 0.592532 0.805547i \(-0.298128\pi\)
0.592532 + 0.805547i \(0.298128\pi\)
\(152\) 1.81636 + 0.590170i 0.147326 + 0.0478691i
\(153\) −6.15537 + 8.47214i −0.497632 + 0.684932i
\(154\) 4.23607 + 3.07768i 0.341352 + 0.248007i
\(155\) 0 0
\(156\) −0.927051 + 0.673542i −0.0742235 + 0.0539265i
\(157\) 13.1803i 1.05191i 0.850514 + 0.525953i \(0.176291\pi\)
−0.850514 + 0.525953i \(0.823709\pi\)
\(158\) 7.69421 + 10.5902i 0.612118 + 0.842509i
\(159\) 1.07295 + 3.30220i 0.0850904 + 0.261881i
\(160\) 0 0
\(161\) 0.718847 2.21238i 0.0566531 0.174360i
\(162\) 1.53884 0.500000i 0.120903 0.0392837i
\(163\) 10.4616 3.39919i 0.819417 0.266245i 0.130836 0.991404i \(-0.458234\pi\)
0.688581 + 0.725159i \(0.258234\pi\)
\(164\) 0.145898 0.449028i 0.0113927 0.0350632i
\(165\) 0 0
\(166\) 3.11803 + 9.59632i 0.242006 + 0.744819i
\(167\) −8.55951 11.7812i −0.662355 0.911653i 0.337202 0.941432i \(-0.390520\pi\)
−0.999556 + 0.0297794i \(0.990520\pi\)
\(168\) 1.38197i 0.106621i
\(169\) −7.73607 + 5.62058i −0.595082 + 0.432352i
\(170\) 0 0
\(171\) 1.38197 + 1.00406i 0.105682 + 0.0767822i
\(172\) −1.76336 + 2.42705i −0.134455 + 0.185061i
\(173\) −17.9641 5.83688i −1.36578 0.443770i −0.467813 0.883827i \(-0.654958\pi\)
−0.897970 + 0.440057i \(0.854958\pi\)
\(174\) −5.85410 −0.443798
\(175\) 0 0
\(176\) 25.4164 1.91583
\(177\) −10.3229 3.35410i −0.775914 0.252110i
\(178\) −8.50651 + 11.7082i −0.637590 + 0.877567i
\(179\) −0.427051 0.310271i −0.0319193 0.0231907i 0.571711 0.820455i \(-0.306280\pi\)
−0.603631 + 0.797264i \(0.706280\pi\)
\(180\) 0 0
\(181\) −0.236068 + 0.171513i −0.0175468 + 0.0127485i −0.596524 0.802595i \(-0.703452\pi\)
0.578977 + 0.815344i \(0.303452\pi\)
\(182\) 1.85410i 0.137435i
\(183\) 5.11855 + 7.04508i 0.378374 + 0.520788i
\(184\) −2.60081 8.00448i −0.191734 0.590098i
\(185\) 0 0
\(186\) 1.50000 4.61653i 0.109985 0.338500i
\(187\) −26.0746 + 8.47214i −1.90676 + 0.619544i
\(188\) 0.363271 0.118034i 0.0264943 0.00860851i
\(189\) 0.954915 2.93893i 0.0694598 0.213775i
\(190\) 0 0
\(191\) −0.562306 1.73060i −0.0406870 0.125222i 0.928650 0.370958i \(-0.120970\pi\)
−0.969337 + 0.245736i \(0.920970\pi\)
\(192\) −2.48990 3.42705i −0.179693 0.247326i
\(193\) 7.70820i 0.554849i −0.960747 0.277424i \(-0.910519\pi\)
0.960747 0.277424i \(-0.0894808\pi\)
\(194\) 5.04508 3.66547i 0.362216 0.263165i
\(195\) 0 0
\(196\) 3.30902 + 2.40414i 0.236358 + 0.171724i
\(197\) 2.17963 3.00000i 0.155292 0.213741i −0.724281 0.689505i \(-0.757828\pi\)
0.879573 + 0.475764i \(0.157828\pi\)
\(198\) 16.1150 + 5.23607i 1.14524 + 0.372111i
\(199\) 17.5623 1.24496 0.622479 0.782636i \(-0.286125\pi\)
0.622479 + 0.782636i \(0.286125\pi\)
\(200\) 0 0
\(201\) 4.76393 0.336022
\(202\) −2.26538 0.736068i −0.159392 0.0517896i
\(203\) 1.31433 1.80902i 0.0922477 0.126968i
\(204\) −2.61803 1.90211i −0.183299 0.133175i
\(205\) 0 0
\(206\) 11.2082 8.14324i 0.780913 0.567366i
\(207\) 7.52786i 0.523223i
\(208\) −5.29007 7.28115i −0.366800 0.504857i
\(209\) 1.38197 + 4.25325i 0.0955926 + 0.294204i
\(210\) 0 0
\(211\) −2.83688 + 8.73102i −0.195299 + 0.601068i 0.804674 + 0.593717i \(0.202340\pi\)
−0.999973 + 0.00735149i \(0.997660\pi\)
\(212\) 2.04087 0.663119i 0.140168 0.0455432i
\(213\) −6.29412 + 2.04508i −0.431266 + 0.140127i
\(214\) −8.20820 + 25.2623i −0.561101 + 1.72689i
\(215\) 0 0
\(216\) −3.45492 10.6331i −0.235077 0.723493i
\(217\) 1.08981 + 1.50000i 0.0739814 + 0.101827i
\(218\) 16.1803i 1.09587i
\(219\) −7.28115 + 5.29007i −0.492015 + 0.357470i
\(220\) 0 0
\(221\) 7.85410 + 5.70634i 0.528324 + 0.383850i
\(222\) 0.224514 0.309017i 0.0150684 0.0207399i
\(223\) 0.171513 + 0.0557281i 0.0114854 + 0.00373183i 0.314754 0.949173i \(-0.398078\pi\)
−0.303269 + 0.952905i \(0.598078\pi\)
\(224\) −2.09017 −0.139655
\(225\) 0 0
\(226\) −27.2705 −1.81401
\(227\) 14.0413 + 4.56231i 0.931956 + 0.302811i 0.735362 0.677674i \(-0.237012\pi\)
0.196594 + 0.980485i \(0.437012\pi\)
\(228\) −0.310271 + 0.427051i −0.0205482 + 0.0282821i
\(229\) 17.5623 + 12.7598i 1.16055 + 0.843189i 0.989847 0.142134i \(-0.0453963\pi\)
0.170702 + 0.985323i \(0.445396\pi\)
\(230\) 0 0
\(231\) 2.61803 1.90211i 0.172254 0.125150i
\(232\) 8.09017i 0.531146i
\(233\) −1.73060 2.38197i −0.113375 0.156048i 0.748558 0.663069i \(-0.230746\pi\)
−0.861933 + 0.507021i \(0.830746\pi\)
\(234\) −1.85410 5.70634i −0.121206 0.373035i
\(235\) 0 0
\(236\) −2.07295 + 6.37988i −0.134937 + 0.415295i
\(237\) 7.69421 2.50000i 0.499793 0.162392i
\(238\) 4.97980 1.61803i 0.322792 0.104882i
\(239\) 6.34346 19.5232i 0.410324 1.26285i −0.506043 0.862508i \(-0.668892\pi\)
0.916367 0.400340i \(-0.131108\pi\)
\(240\) 0 0
\(241\) 0.781153 + 2.40414i 0.0503185 + 0.154864i 0.973058 0.230559i \(-0.0740554\pi\)
−0.922740 + 0.385423i \(0.874055\pi\)
\(242\) 15.6129 + 21.4894i 1.00364 + 1.38139i
\(243\) 16.0000i 1.02640i
\(244\) 4.35410 3.16344i 0.278743 0.202519i
\(245\) 0 0
\(246\) −1.00000 0.726543i −0.0637577 0.0463227i
\(247\) 0.930812 1.28115i 0.0592262 0.0815178i
\(248\) 6.37988 + 2.07295i 0.405123 + 0.131632i
\(249\) 6.23607 0.395195
\(250\) 0 0
\(251\) −29.1803 −1.84185 −0.920923 0.389744i \(-0.872564\pi\)
−0.920923 + 0.389744i \(0.872564\pi\)
\(252\) −0.726543 0.236068i −0.0457679 0.0148709i
\(253\) 11.5842 15.9443i 0.728292 1.00241i
\(254\) −26.0344 18.9151i −1.63355 1.18684i
\(255\) 0 0
\(256\) −10.9721 + 7.97172i −0.685758 + 0.498233i
\(257\) 22.8541i 1.42560i 0.701367 + 0.712800i \(0.252573\pi\)
−0.701367 + 0.712800i \(0.747427\pi\)
\(258\) 4.61653 + 6.35410i 0.287412 + 0.395589i
\(259\) 0.0450850 + 0.138757i 0.00280144 + 0.00862196i
\(260\) 0 0
\(261\) 2.23607 6.88191i 0.138409 0.425980i
\(262\) 10.4616 3.39919i 0.646321 0.210002i
\(263\) −10.3759 + 3.37132i −0.639803 + 0.207885i −0.610913 0.791698i \(-0.709197\pi\)
−0.0288905 + 0.999583i \(0.509197\pi\)
\(264\) 3.61803 11.1352i 0.222675 0.685322i
\(265\) 0 0
\(266\) −0.263932 0.812299i −0.0161827 0.0498053i
\(267\) 5.25731 + 7.23607i 0.321742 + 0.442840i
\(268\) 2.94427i 0.179850i
\(269\) −10.3262 + 7.50245i −0.629602 + 0.457433i −0.856262 0.516541i \(-0.827219\pi\)
0.226660 + 0.973974i \(0.427219\pi\)
\(270\) 0 0
\(271\) 6.47214 + 4.70228i 0.393154 + 0.285643i 0.766747 0.641950i \(-0.221874\pi\)
−0.373593 + 0.927593i \(0.621874\pi\)
\(272\) 14.9394 20.5623i 0.905834 1.24677i
\(273\) −1.08981 0.354102i −0.0659585 0.0214312i
\(274\) −19.3262 −1.16754
\(275\) 0 0
\(276\) 2.32624 0.140023
\(277\) −23.4989 7.63525i −1.41191 0.458758i −0.498889 0.866666i \(-0.666258\pi\)
−0.913023 + 0.407908i \(0.866258\pi\)
\(278\) 4.75528 6.54508i 0.285203 0.392548i
\(279\) 4.85410 + 3.52671i 0.290607 + 0.211139i
\(280\) 0 0
\(281\) −8.16312 + 5.93085i −0.486971 + 0.353805i −0.804018 0.594605i \(-0.797309\pi\)
0.317047 + 0.948410i \(0.397309\pi\)
\(282\) 1.00000i 0.0595491i
\(283\) −17.5478 24.1525i −1.04311 1.43572i −0.894634 0.446799i \(-0.852564\pi\)
−0.148474 0.988916i \(-0.547436\pi\)
\(284\) 1.26393 + 3.88998i 0.0750006 + 0.230828i
\(285\) 0 0
\(286\) 4.85410 14.9394i 0.287029 0.883385i
\(287\) 0.449028 0.145898i 0.0265053 0.00861209i
\(288\) −6.43288 + 2.09017i −0.379061 + 0.123164i
\(289\) −3.21885 + 9.90659i −0.189344 + 0.582741i
\(290\) 0 0
\(291\) −1.19098 3.66547i −0.0698167 0.214874i
\(292\) 3.26944 + 4.50000i 0.191330 + 0.263343i
\(293\) 19.5279i 1.14083i 0.821357 + 0.570415i \(0.193218\pi\)
−0.821357 + 0.570415i \(0.806782\pi\)
\(294\) 8.66312 6.29412i 0.505243 0.367081i
\(295\) 0 0
\(296\) 0.427051 + 0.310271i 0.0248218 + 0.0180341i
\(297\) 15.3884 21.1803i 0.892927 1.22901i
\(298\) −6.06961 1.97214i −0.351603 0.114243i
\(299\) −6.97871 −0.403589
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) −22.4091 7.28115i −1.28950 0.418983i
\(303\) −0.865300 + 1.19098i −0.0497102 + 0.0684202i
\(304\) −3.35410 2.43690i −0.192371 0.139766i
\(305\) 0 0
\(306\) 13.7082 9.95959i 0.783646 0.569352i
\(307\) 9.23607i 0.527130i 0.964642 + 0.263565i \(0.0848984\pi\)
−0.964642 + 0.263565i \(0.915102\pi\)
\(308\) −1.17557 1.61803i −0.0669843 0.0921960i
\(309\) −2.64590 8.14324i −0.150520 0.463253i
\(310\) 0 0
\(311\) 2.62868 8.09024i 0.149059 0.458755i −0.848452 0.529272i \(-0.822465\pi\)
0.997511 + 0.0705172i \(0.0224650\pi\)
\(312\) −3.94298 + 1.28115i −0.223227 + 0.0725310i
\(313\) −15.9434 + 5.18034i −0.901177 + 0.292810i −0.722723 0.691138i \(-0.757110\pi\)
−0.178454 + 0.983948i \(0.557110\pi\)
\(314\) 6.59017 20.2825i 0.371905 1.14461i
\(315\) 0 0
\(316\) −1.54508 4.75528i −0.0869178 0.267506i
\(317\) −4.49801 6.19098i −0.252634 0.347720i 0.663798 0.747912i \(-0.268944\pi\)
−0.916431 + 0.400192i \(0.868944\pi\)
\(318\) 5.61803i 0.315044i
\(319\) 15.3262 11.1352i 0.858105 0.623449i
\(320\) 0 0
\(321\) 13.2812 + 9.64932i 0.741282 + 0.538573i
\(322\) −2.21238 + 3.04508i −0.123291 + 0.169696i
\(323\) 4.25325 + 1.38197i 0.236657 + 0.0768946i
\(324\) −0.618034 −0.0343352
\(325\) 0 0
\(326\) −17.7984 −0.985761
\(327\) 9.51057 + 3.09017i 0.525935 + 0.170887i
\(328\) 1.00406 1.38197i 0.0554398 0.0763063i
\(329\) 0.309017 + 0.224514i 0.0170367 + 0.0123779i
\(330\) 0 0
\(331\) 18.7082 13.5923i 1.02830 0.747101i 0.0603290 0.998179i \(-0.480785\pi\)
0.967967 + 0.251078i \(0.0807850\pi\)
\(332\) 3.85410i 0.211521i
\(333\) 0.277515 + 0.381966i 0.0152077 + 0.0209316i
\(334\) 7.28115 + 22.4091i 0.398407 + 1.22617i
\(335\) 0 0
\(336\) −0.927051 + 2.85317i −0.0505748 + 0.155653i
\(337\) −7.46969 + 2.42705i −0.406900 + 0.132210i −0.505314 0.862936i \(-0.668623\pi\)
0.0984135 + 0.995146i \(0.468623\pi\)
\(338\) 14.7149 4.78115i 0.800384 0.260060i
\(339\) −5.20820 + 16.0292i −0.282871 + 0.870587i
\(340\) 0 0
\(341\) 4.85410 + 14.9394i 0.262864 + 0.809013i
\(342\) −1.62460 2.23607i −0.0878482 0.120913i
\(343\) 8.41641i 0.454443i
\(344\) −8.78115 + 6.37988i −0.473448 + 0.343980i
\(345\) 0 0
\(346\) 24.7254 + 17.9641i 1.32925 + 0.965755i
\(347\) −11.7027 + 16.1074i −0.628234 + 0.864690i −0.997920 0.0644668i \(-0.979465\pi\)
0.369686 + 0.929157i \(0.379465\pi\)
\(348\) 2.12663 + 0.690983i 0.113999 + 0.0370406i
\(349\) −21.7082 −1.16201 −0.581007 0.813899i \(-0.697341\pi\)
−0.581007 + 0.813899i \(0.697341\pi\)
\(350\) 0 0
\(351\) −9.27051 −0.494823
\(352\) −16.8415 5.47214i −0.897655 0.291666i
\(353\) −7.58821 + 10.4443i −0.403880 + 0.555893i −0.961712 0.274061i \(-0.911633\pi\)
0.557833 + 0.829953i \(0.311633\pi\)
\(354\) 14.2082 + 10.3229i 0.755158 + 0.548654i
\(355\) 0 0
\(356\) 4.47214 3.24920i 0.237023 0.172207i
\(357\) 3.23607i 0.171271i
\(358\) 0.502029 + 0.690983i 0.0265330 + 0.0365196i
\(359\) −4.24671 13.0700i −0.224133 0.689810i −0.998378 0.0569247i \(-0.981870\pi\)
0.774246 0.632885i \(-0.218130\pi\)
\(360\) 0 0
\(361\) −5.64590 + 17.3763i −0.297153 + 0.914541i
\(362\) 0.449028 0.145898i 0.0236004 0.00766823i
\(363\) 15.6129 5.07295i 0.819466 0.266261i
\(364\) −0.218847 + 0.673542i −0.0114707 + 0.0353032i
\(365\) 0 0
\(366\) −4.35410 13.4005i −0.227593 0.700458i
\(367\) 15.0251 + 20.6803i 0.784306 + 1.07950i 0.994794 + 0.101908i \(0.0324949\pi\)
−0.210488 + 0.977597i \(0.567505\pi\)
\(368\) 18.2705i 0.952416i
\(369\) 1.23607 0.898056i 0.0643471 0.0467509i
\(370\) 0 0
\(371\) 1.73607 + 1.26133i 0.0901322 + 0.0654848i
\(372\) −1.08981 + 1.50000i −0.0565042 + 0.0777714i
\(373\) 26.8869 + 8.73607i 1.39215 + 0.452336i 0.906644 0.421897i \(-0.138636\pi\)
0.485505 + 0.874234i \(0.338636\pi\)
\(374\) 44.3607 2.29384
\(375\) 0 0
\(376\) 1.38197 0.0712695
\(377\) −6.37988 2.07295i −0.328581 0.106762i
\(378\) −2.93893 + 4.04508i −0.151162 + 0.208057i
\(379\) 11.8090 + 8.57975i 0.606588 + 0.440712i 0.848211 0.529658i \(-0.177680\pi\)
−0.241623 + 0.970370i \(0.577680\pi\)
\(380\) 0 0
\(381\) −16.0902 + 11.6902i −0.824324 + 0.598907i
\(382\) 2.94427i 0.150642i
\(383\) 19.6089 + 26.9894i 1.00197 + 1.37909i 0.924110 + 0.382127i \(0.124808\pi\)
0.0778591 + 0.996964i \(0.475192\pi\)
\(384\) 4.20820 + 12.9515i 0.214749 + 0.660929i
\(385\) 0 0
\(386\) −3.85410 + 11.8617i −0.196169 + 0.603745i
\(387\) −9.23305 + 3.00000i −0.469342 + 0.152499i
\(388\) −2.26538 + 0.736068i −0.115007 + 0.0373682i
\(389\) −4.63525 + 14.2658i −0.235017 + 0.723307i 0.762102 + 0.647456i \(0.224167\pi\)
−0.997119 + 0.0758507i \(0.975833\pi\)
\(390\) 0 0
\(391\) −6.09017 18.7436i −0.307993 0.947905i
\(392\) 8.69827 + 11.9721i 0.439329 + 0.604684i
\(393\) 6.79837i 0.342933i
\(394\) −4.85410 + 3.52671i −0.244546 + 0.177673i
\(395\) 0 0
\(396\) −5.23607 3.80423i −0.263122 0.191170i
\(397\) 17.0660 23.4894i 0.856519 1.17890i −0.125870 0.992047i \(-0.540172\pi\)
0.982388 0.186850i \(-0.0598279\pi\)
\(398\) −27.0256 8.78115i −1.35467 0.440159i
\(399\) −0.527864 −0.0264263
\(400\) 0 0
\(401\) 26.5967 1.32818 0.664089 0.747653i \(-0.268820\pi\)
0.664089 + 0.747653i \(0.268820\pi\)
\(402\) −7.33094 2.38197i −0.365634 0.118802i
\(403\) 3.26944 4.50000i 0.162862 0.224161i
\(404\) 0.736068 + 0.534785i 0.0366208 + 0.0266065i
\(405\) 0 0
\(406\) −2.92705 + 2.12663i −0.145267 + 0.105543i
\(407\) 1.23607i 0.0612696i
\(408\) −6.88191 9.47214i −0.340705 0.468941i
\(409\) −0.489357 1.50609i −0.0241971 0.0744711i 0.938229 0.346016i \(-0.112466\pi\)
−0.962426 + 0.271544i \(0.912466\pi\)
\(410\) 0 0
\(411\) −3.69098 + 11.3597i −0.182063 + 0.560332i
\(412\) −5.03280 + 1.63525i −0.247948 + 0.0805632i
\(413\) −6.37988 + 2.07295i −0.313933 + 0.102003i
\(414\) −3.76393 + 11.5842i −0.184987 + 0.569332i
\(415\) 0 0
\(416\) 1.93769 + 5.96361i 0.0950033 + 0.292390i
\(417\) −2.93893 4.04508i −0.143920 0.198089i
\(418\) 7.23607i 0.353928i
\(419\) −7.66312 + 5.56758i −0.374368 + 0.271994i −0.759020 0.651068i \(-0.774321\pi\)
0.384652 + 0.923062i \(0.374321\pi\)
\(420\) 0 0
\(421\) −25.8885 18.8091i −1.26173 0.916701i −0.262889 0.964826i \(-0.584675\pi\)
−0.998841 + 0.0481252i \(0.984675\pi\)
\(422\) 8.73102 12.0172i 0.425020 0.584989i
\(423\) 1.17557 + 0.381966i 0.0571582 + 0.0185718i
\(424\) 7.76393 0.377050
\(425\) 0 0
\(426\) 10.7082 0.518814
\(427\) 5.11855 + 1.66312i 0.247704 + 0.0804840i
\(428\) 5.96361 8.20820i 0.288262 0.396759i
\(429\) −7.85410 5.70634i −0.379200 0.275505i
\(430\) 0 0
\(431\) 24.1353 17.5353i 1.16255 0.844645i 0.172456 0.985017i \(-0.444830\pi\)
0.990099 + 0.140372i \(0.0448299\pi\)
\(432\) 24.2705i 1.16772i
\(433\) 15.7844 + 21.7254i 0.758552 + 1.04406i 0.997333 + 0.0729839i \(0.0232522\pi\)
−0.238781 + 0.971073i \(0.576748\pi\)
\(434\) −0.927051 2.85317i −0.0444999 0.136957i
\(435\) 0 0
\(436\) 1.90983 5.87785i 0.0914643 0.281498i
\(437\) −3.05744 + 0.993422i −0.146257 + 0.0475218i
\(438\) 13.8496 4.50000i 0.661758 0.215018i
\(439\) 12.6631 38.9731i 0.604378 1.86008i 0.103365 0.994644i \(-0.467039\pi\)
0.501013 0.865440i \(-0.332961\pi\)
\(440\) 0 0
\(441\) 4.09017 + 12.5882i 0.194770 + 0.599440i
\(442\) −9.23305 12.7082i −0.439171 0.604468i
\(443\) 29.9443i 1.42270i −0.702840 0.711348i \(-0.748085\pi\)
0.702840 0.711348i \(-0.251915\pi\)
\(444\) −0.118034 + 0.0857567i −0.00560165 + 0.00406983i
\(445\) 0 0
\(446\) −0.236068 0.171513i −0.0111781 0.00812140i
\(447\) −2.31838 + 3.19098i −0.109656 + 0.150928i
\(448\) −2.48990 0.809017i −0.117637 0.0382225i
\(449\) −4.67376 −0.220568 −0.110284 0.993900i \(-0.535176\pi\)
−0.110284 + 0.993900i \(0.535176\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) 9.90659 + 3.21885i 0.465967 + 0.151402i
\(453\) −8.55951 + 11.7812i −0.402161 + 0.553527i
\(454\) −19.3262 14.0413i −0.907025 0.658992i
\(455\) 0 0
\(456\) −1.54508 + 1.12257i −0.0723552 + 0.0525692i
\(457\) 21.4164i 1.00182i −0.865500 0.500909i \(-0.832999\pi\)
0.865500 0.500909i \(-0.167001\pi\)
\(458\) −20.6457 28.4164i −0.964712 1.32781i
\(459\) −8.09017 24.8990i −0.377617 1.16218i
\(460\) 0 0
\(461\) 0.253289 0.779543i 0.0117968 0.0363069i −0.944985 0.327114i \(-0.893924\pi\)
0.956782 + 0.290807i \(0.0939238\pi\)
\(462\) −4.97980 + 1.61803i −0.231681 + 0.0752778i
\(463\) −22.9439 + 7.45492i −1.06629 + 0.346459i −0.789042 0.614339i \(-0.789423\pi\)
−0.277250 + 0.960798i \(0.589423\pi\)
\(464\) −5.42705 + 16.7027i −0.251945 + 0.775405i
\(465\) 0 0
\(466\) 1.47214 + 4.53077i 0.0681954 + 0.209884i
\(467\) −16.1352 22.2082i −0.746648 1.02767i −0.998208 0.0598315i \(-0.980944\pi\)
0.251560 0.967842i \(-0.419056\pi\)
\(468\) 2.29180i 0.105938i
\(469\) 2.38197 1.73060i 0.109989 0.0799117i
\(470\) 0 0
\(471\) −10.6631 7.74721i −0.491331 0.356973i
\(472\) −14.2658 + 19.6353i −0.656639 + 0.903786i
\(473\) −24.1724 7.85410i −1.11145 0.361132i
\(474\) −13.0902 −0.601251
\(475\) 0 0
\(476\) −2.00000 −0.0916698
\(477\) 6.60440 + 2.14590i 0.302394 + 0.0982539i
\(478\) −19.5232 + 26.8713i −0.892969 + 1.22907i
\(479\) −8.78115 6.37988i −0.401221 0.291504i 0.368817 0.929502i \(-0.379763\pi\)
−0.770038 + 0.637998i \(0.779763\pi\)
\(480\) 0 0
\(481\) 0.354102 0.257270i 0.0161457 0.0117305i
\(482\) 4.09017i 0.186302i
\(483\) 1.36733 + 1.88197i 0.0622156 + 0.0856324i
\(484\) −3.13525 9.64932i −0.142512 0.438606i
\(485\) 0 0
\(486\) −8.00000 + 24.6215i −0.362887 + 1.11685i
\(487\) 34.6341 11.2533i 1.56942 0.509935i 0.610116 0.792312i \(-0.291123\pi\)
0.959303 + 0.282377i \(0.0911230\pi\)
\(488\) 18.5191 6.01722i 0.838320 0.272387i
\(489\) −3.39919 + 10.4616i −0.153717 + 0.473091i
\(490\) 0 0
\(491\) −13.3647 41.1325i −0.603143 1.85628i −0.509088 0.860715i \(-0.670017\pi\)
−0.0940550 0.995567i \(-0.529983\pi\)
\(492\) 0.277515 + 0.381966i 0.0125113 + 0.0172204i
\(493\) 18.9443i 0.853207i
\(494\) −2.07295 + 1.50609i −0.0932664 + 0.0677620i
\(495\) 0 0
\(496\) −11.7812 8.55951i −0.528989 0.384333i
\(497\) −2.40414 + 3.30902i −0.107840 + 0.148430i
\(498\) −9.59632 3.11803i −0.430021 0.139722i
\(499\) −7.56231 −0.338535 −0.169268 0.985570i \(-0.554140\pi\)
−0.169268 + 0.985570i \(0.554140\pi\)
\(500\) 0 0
\(501\) 14.5623 0.650596
\(502\) 44.9039 + 14.5902i 2.00416 + 0.651191i
\(503\) 21.9928 30.2705i 0.980611 1.34970i 0.0441115 0.999027i \(-0.485954\pi\)
0.936500 0.350669i \(-0.114046\pi\)
\(504\) −2.23607 1.62460i −0.0996024 0.0723654i
\(505\) 0 0
\(506\) −25.7984 + 18.7436i −1.14688 + 0.833255i
\(507\) 9.56231i 0.424677i
\(508\) 7.22494 + 9.94427i 0.320555 + 0.441206i
\(509\) 6.28115 + 19.3314i 0.278407 + 0.856849i 0.988298 + 0.152537i \(0.0487444\pi\)
−0.709891 + 0.704312i \(0.751256\pi\)
\(510\) 0 0
\(511\) −1.71885 + 5.29007i −0.0760373 + 0.234019i
\(512\) −5.03280 + 1.63525i −0.222420 + 0.0722687i
\(513\) −4.06150 + 1.31966i −0.179319 + 0.0582644i
\(514\) 11.4271 35.1688i 0.504026 1.55123i
\(515\) 0 0
\(516\) −0.927051 2.85317i −0.0408111 0.125604i
\(517\) 1.90211 + 2.61803i 0.0836548 + 0.115141i
\(518\) 0.236068i 0.0103722i
\(519\) 15.2812 11.1024i 0.670768 0.487342i
\(520\) 0 0
\(521\) −23.7533 17.2578i −1.04065 0.756077i −0.0702381 0.997530i \(-0.522376\pi\)
−0.970412 + 0.241453i \(0.922376\pi\)
\(522\) −6.88191 + 9.47214i −0.301213 + 0.414584i
\(523\) 12.5025 + 4.06231i 0.546696 + 0.177632i 0.569326 0.822112i \(-0.307204\pi\)
−0.0226305 + 0.999744i \(0.507204\pi\)
\(524\) −4.20163 −0.183549
\(525\) 0 0
\(526\) 17.6525 0.769685
\(527\) 14.9394 + 4.85410i 0.650770 + 0.211448i
\(528\) −14.9394 + 20.5623i −0.650153 + 0.894860i
\(529\) −7.14590 5.19180i −0.310691 0.225730i
\(530\) 0 0
\(531\) −17.5623 + 12.7598i −0.762139 + 0.553727i
\(532\) 0.326238i 0.0141442i
\(533\) −0.832544 1.14590i −0.0360615 0.0496344i
\(534\) −4.47214 13.7638i −0.193528 0.595619i
\(535\) 0 0
\(536\) 3.29180 10.1311i 0.142184 0.437597i
\(537\) 0.502029 0.163119i 0.0216641 0.00703910i
\(538\) 19.6417 6.38197i 0.846813 0.275146i
\(539\) −10.7082 + 32.9565i −0.461235 + 1.41954i
\(540\) 0 0
\(541\) 8.38197 + 25.7970i 0.360369 + 1.10910i 0.952831 + 0.303503i \(0.0981561\pi\)
−0.592462 + 0.805599i \(0.701844\pi\)
\(542\) −7.60845 10.4721i −0.326811 0.449817i
\(543\) 0.291796i 0.0125222i
\(544\) −14.3262 + 10.4086i −0.614232 + 0.446266i
\(545\) 0 0
\(546\) 1.50000 + 1.08981i 0.0641941 + 0.0466397i
\(547\) −12.5150 + 17.2254i −0.535103 + 0.736506i −0.987897 0.155109i \(-0.950427\pi\)
0.452794 + 0.891615i \(0.350427\pi\)
\(548\) 7.02067 + 2.28115i 0.299908 + 0.0974460i
\(549\) 17.4164 0.743314
\(550\) 0 0
\(551\) −3.09017 −0.131646
\(552\) 8.00448 + 2.60081i 0.340693 + 0.110698i
\(553\) 2.93893 4.04508i 0.124976 0.172015i
\(554\) 32.3435 + 23.4989i 1.37414 + 0.998373i
\(555\) 0 0
\(556\) −2.50000 + 1.81636i −0.106024 + 0.0770307i
\(557\) 4.76393i 0.201854i 0.994894 + 0.100927i \(0.0321809\pi\)
−0.994894 + 0.100927i \(0.967819\pi\)
\(558\) −5.70634 7.85410i −0.241569 0.332491i
\(559\) 2.78115 + 8.55951i 0.117630 + 0.362029i
\(560\) 0 0
\(561\) 8.47214 26.0746i 0.357694 1.10087i
\(562\) 15.5272 5.04508i 0.654974 0.212814i
\(563\) 7.02067 2.28115i 0.295886 0.0961391i −0.157312 0.987549i \(-0.550283\pi\)
0.453198 + 0.891410i \(0.350283\pi\)
\(564\) −0.118034 + 0.363271i −0.00497013 + 0.0152965i
\(565\) 0 0
\(566\) 14.9271 + 45.9407i 0.627431 + 1.93103i
\(567\) −0.363271 0.500000i −0.0152560 0.0209980i
\(568\) 14.7984i 0.620926i
\(569\) 16.6074 12.0660i 0.696218 0.505832i −0.182480 0.983210i \(-0.558413\pi\)
0.878698 + 0.477377i \(0.158413\pi\)
\(570\) 0 0
\(571\) 6.57295 + 4.77553i 0.275069 + 0.199850i 0.716764 0.697316i \(-0.245623\pi\)
−0.441695 + 0.897165i \(0.645623\pi\)
\(572\) −3.52671 + 4.85410i −0.147459 + 0.202960i
\(573\) 1.73060 + 0.562306i 0.0722968 + 0.0234907i
\(574\) −0.763932 −0.0318859
\(575\) 0 0
\(576\) −8.47214 −0.353006
\(577\) −32.1239 10.4377i −1.33734 0.434527i −0.448923 0.893571i \(-0.648192\pi\)
−0.888414 + 0.459044i \(0.848192\pi\)
\(578\) 9.90659 13.6353i 0.412060 0.567152i
\(579\) 6.23607 + 4.53077i 0.259162 + 0.188292i
\(580\) 0 0
\(581\) 3.11803 2.26538i 0.129358 0.0939840i
\(582\) 6.23607i 0.258493i
\(583\) 10.6861 + 14.7082i 0.442575 + 0.609152i
\(584\) 6.21885 + 19.1396i 0.257338 + 0.792004i
\(585\) 0 0
\(586\) 9.76393 30.0503i 0.403344 1.24137i
\(587\) −5.03280 + 1.63525i −0.207726 + 0.0674942i −0.411032 0.911621i \(-0.634831\pi\)
0.203306 + 0.979115i \(0.434831\pi\)
\(588\) −3.88998 + 1.26393i −0.160420 + 0.0521237i
\(589\) 0.791796 2.43690i 0.0326254 0.100411i
\(590\) 0 0
\(591\) 1.14590 + 3.52671i 0.0471359 + 0.145070i
\(592\) −0.673542 0.927051i −0.0276824 0.0381016i
\(593\) 10.9098i 0.448013i 0.974588 + 0.224007i \(0.0719137\pi\)
−0.974588 + 0.224007i \(0.928086\pi\)
\(594\) −34.2705 + 24.8990i −1.40614 + 1.02162i
\(595\) 0 0
\(596\) 1.97214 + 1.43284i 0.0807818 + 0.0586914i
\(597\) −10.3229 + 14.2082i −0.422487 + 0.581503i
\(598\) 10.7391 + 3.48936i 0.439156 + 0.142690i
\(599\) 9.47214 0.387021 0.193510 0.981098i \(-0.438013\pi\)
0.193510 + 0.981098i \(0.438013\pi\)
\(600\) 0 0
\(601\) 2.72949 0.111338 0.0556691 0.998449i \(-0.482271\pi\)
0.0556691 + 0.998449i \(0.482271\pi\)
\(602\) 4.61653 + 1.50000i 0.188156 + 0.0611354i
\(603\) 5.60034 7.70820i 0.228063 0.313902i
\(604\) 7.28115 + 5.29007i 0.296266 + 0.215250i
\(605\) 0 0
\(606\) 1.92705 1.40008i 0.0782811 0.0568745i
\(607\) 35.5623i 1.44343i −0.692191 0.721715i \(-0.743354\pi\)
0.692191 0.721715i \(-0.256646\pi\)
\(608\) 1.69784 + 2.33688i 0.0688566 + 0.0947730i
\(609\) 0.690983 + 2.12663i 0.0280000 + 0.0861753i
\(610\) 0 0
\(611\) 0.354102 1.08981i 0.0143254 0.0440891i
\(612\) −6.15537 + 2.00000i −0.248816 + 0.0808452i
\(613\) −14.2456 + 4.62868i −0.575374 + 0.186951i −0.582227 0.813026i \(-0.697819\pi\)
0.00685287 + 0.999977i \(0.497819\pi\)
\(614\) 4.61803 14.2128i 0.186369 0.573584i
\(615\) 0 0
\(616\) −2.23607 6.88191i −0.0900937 0.277280i
\(617\) −8.36775 11.5172i −0.336873 0.463666i 0.606652 0.794968i \(-0.292512\pi\)
−0.943525 + 0.331302i \(0.892512\pi\)
\(618\) 13.8541i 0.557294i
\(619\) 24.6976 17.9438i 0.992679 0.721223i 0.0321727 0.999482i \(-0.489757\pi\)
0.960506 + 0.278259i \(0.0897573\pi\)
\(620\) 0 0
\(621\) 15.2254 + 11.0619i 0.610975 + 0.443900i
\(622\) −8.09024 + 11.1353i −0.324389 + 0.446483i
\(623\) 5.25731 + 1.70820i 0.210630 + 0.0684377i
\(624\) 9.00000 0.360288
\(625\) 0 0
\(626\) 27.1246 1.08412
\(627\) −4.25325 1.38197i −0.169859 0.0551904i
\(628\) −4.78804 + 6.59017i −0.191064 + 0.262976i
\(629\) 1.00000 + 0.726543i 0.0398726 + 0.0289691i
\(630\) 0 0
\(631\) 8.28115 6.01661i 0.329667 0.239517i −0.410622 0.911806i \(-0.634688\pi\)
0.740290 + 0.672288i \(0.234688\pi\)
\(632\) 18.0902i 0.719588i
\(633\) −5.39607 7.42705i −0.214474 0.295199i
\(634\) 3.82624 + 11.7759i 0.151959 + 0.467683i
\(635\) 0 0
\(636\) −0.663119 + 2.04087i −0.0262944 + 0.0809258i
\(637\) 11.6699 3.79180i 0.462380 0.150236i
\(638\) −29.1522 + 9.47214i −1.15415 + 0.375005i
\(639\) −4.09017 + 12.5882i −0.161805 + 0.497983i
\(640\) 0 0
\(641\) −0.336881 1.03681i −0.0133060 0.0409517i 0.944183 0.329421i \(-0.106854\pi\)
−0.957489 + 0.288470i \(0.906854\pi\)
\(642\) −15.6129 21.4894i −0.616193 0.848117i
\(643\) 30.8328i 1.21593i 0.793965 + 0.607964i \(0.208013\pi\)
−0.793965 + 0.607964i \(0.791987\pi\)
\(644\) 1.16312 0.845055i 0.0458333 0.0332998i
\(645\) 0 0
\(646\) −5.85410 4.25325i −0.230327 0.167342i
\(647\) −21.4783 + 29.5623i −0.844398 + 1.16221i 0.140671 + 0.990056i \(0.455074\pi\)
−0.985069 + 0.172158i \(0.944926\pi\)
\(648\) −2.12663 0.690983i −0.0835418 0.0271444i
\(649\) −56.8328 −2.23088
\(650\) 0 0
\(651\) −1.85410 −0.0726680
\(652\) 6.46564 + 2.10081i 0.253214 + 0.0822742i
\(653\) −11.2209 + 15.4443i −0.439109 + 0.604381i −0.970014 0.243050i \(-0.921852\pi\)
0.530905 + 0.847431i \(0.321852\pi\)
\(654\) −13.0902 9.51057i −0.511866 0.371893i
\(655\) 0 0
\(656\) −3.00000 + 2.17963i −0.117130 + 0.0851002i
\(657\) 18.0000i 0.702247i
\(658\) −0.363271 0.500000i −0.0141618 0.0194920i
\(659\) −4.79837 14.7679i −0.186918 0.575275i 0.813058 0.582183i \(-0.197801\pi\)
−0.999976 + 0.00690786i \(0.997801\pi\)
\(660\) 0 0
\(661\) 6.08359 18.7234i 0.236624 0.728255i −0.760277 0.649598i \(-0.774937\pi\)
0.996902 0.0786563i \(-0.0250630\pi\)
\(662\) −35.5851 + 11.5623i −1.38305 + 0.449382i
\(663\) −9.23305 + 3.00000i −0.358582 + 0.116510i
\(664\) 4.30902 13.2618i 0.167222 0.514657i
\(665\) 0 0
\(666\) −0.236068 0.726543i −0.00914745 0.0281530i
\(667\) 8.00448 + 11.0172i 0.309935 + 0.426588i
\(668\) 9.00000i 0.348220i
\(669\) −0.145898 + 0.106001i −0.00564074 + 0.00409824i
\(670\) 0 0
\(671\) 36.8885 + 26.8011i 1.42407 + 1.03464i
\(672\) 1.22857 1.69098i 0.0473932 0.0652311i
\(673\) −11.5842 3.76393i −0.446538 0.145089i 0.0771122 0.997022i \(-0.475430\pi\)
−0.523650 + 0.851934i \(0.675430\pi\)
\(674\) 12.7082 0.489502
\(675\) 0 0
\(676\) −5.90983 −0.227301
\(677\) 10.0984 + 3.28115i 0.388111 + 0.126105i 0.496571 0.867996i \(-0.334592\pi\)
−0.108460 + 0.994101i \(0.534592\pi\)
\(678\) 16.0292 22.0623i 0.615598 0.847298i
\(679\) −1.92705 1.40008i −0.0739534 0.0537303i
\(680\) 0 0
\(681\) −11.9443 + 8.67802i −0.457705 + 0.332543i
\(682\) 25.4164i 0.973245i
\(683\) −7.91872 10.8992i −0.303002 0.417046i 0.630181 0.776448i \(-0.282981\pi\)
−0.933183 + 0.359402i \(0.882981\pi\)
\(684\) 0.326238 + 1.00406i 0.0124740 + 0.0383911i
\(685\) 0 0
\(686\) 4.20820 12.9515i 0.160670 0.494491i
\(687\) −20.6457 + 6.70820i −0.787684 + 0.255934i
\(688\) 22.4091 7.28115i 0.854338 0.277591i
\(689\) 1.98936 6.12261i 0.0757885 0.233253i
\(690\) 0 0
\(691\) 11.2082 + 34.4953i 0.426380 + 1.31226i 0.901667 + 0.432432i \(0.142344\pi\)
−0.475286 + 0.879831i \(0.657656\pi\)
\(692\) −6.86167 9.44427i −0.260841 0.359017i
\(693\) 6.47214i 0.245856i
\(694\) 26.0623 18.9354i 0.989312 0.718777i
\(695\) 0 0
\(696\) 6.54508 + 4.75528i 0.248091 + 0.180249i
\(697\) 2.35114 3.23607i 0.0890558 0.122575i
\(698\) 33.4055 + 10.8541i 1.26442 + 0.410834i
\(699\) 2.94427 0.111363
\(700\) 0 0
\(701\) −41.0132 −1.54905 −0.774523 0.632546i \(-0.782010\pi\)
−0.774523 + 0.632546i \(0.782010\pi\)
\(702\) 14.2658 + 4.63525i 0.538430 + 0.174946i
\(703\) 0.118513 0.163119i 0.00446980 0.00615215i
\(704\) −17.9443 13.0373i −0.676300 0.491361i
\(705\) 0 0
\(706\) 16.8992 12.2780i 0.636009 0.462088i
\(707\) 0.909830i 0.0342177i
\(708\) −3.94298 5.42705i −0.148186 0.203961i
\(709\) 10.3647 + 31.8994i 0.389256 + 1.19801i 0.933345 + 0.358980i \(0.116875\pi\)
−0.544089 + 0.839027i \(0.683125\pi\)
\(710\) 0 0
\(711\) 5.00000 15.3884i 0.187515 0.577111i
\(712\) 19.0211 6.18034i 0.712847 0.231618i
\(713\) −10.7391 + 3.48936i −0.402184 + 0.130677i
\(714\) −1.61803 + 4.97980i −0.0605534 + 0.186364i
\(715\) 0 0
\(716\) −0.100813 0.310271i −0.00376756 0.0115954i
\(717\) 12.0660 + 16.6074i 0.450612 + 0.620214i
\(718\) 22.2361i 0.829843i
\(719\) −18.8435 + 13.6906i −0.702742 + 0.510572i −0.880824 0.473443i \(-0.843011\pi\)
0.178082 + 0.984016i \(0.443011\pi\)
\(720\) 0 0
\(721\) −4.28115 3.11044i −0.159438 0.115839i
\(722\) 17.3763 23.9164i 0.646678 0.890077i
\(723\) −2.40414 0.781153i −0.0894110 0.0290514i
\(724\) −0.180340 −0.00670228
\(725\) 0 0
\(726\) −26.5623 −0.985820
\(727\) 23.3601 + 7.59017i 0.866380 + 0.281504i 0.708291 0.705921i \(-0.249467\pi\)
0.158089 + 0.987425i \(0.449467\pi\)
\(728\) −1.50609 + 2.07295i −0.0558192 + 0.0768286i
\(729\) 10.5172 + 7.64121i 0.389527 + 0.283008i
\(730\) 0 0
\(731\) −20.5623 + 14.9394i −0.760524 + 0.552553i
\(732\) 5.38197i 0.198923i
\(733\) −11.7432 16.1631i −0.433745 0.596998i 0.535063 0.844812i \(-0.320288\pi\)
−0.968808 + 0.247814i \(0.920288\pi\)
\(734\) −12.7812 39.3363i −0.471761 1.45193i
\(735\) 0 0
\(736\) 3.93363 12.1065i 0.144995 0.446250i
\(737\) 23.7234 7.70820i 0.873863 0.283935i
\(738\) −2.35114 + 0.763932i −0.0865467 + 0.0281207i
\(739\) −4.93769 + 15.1967i −0.181636 + 0.559018i −0.999874 0.0158612i \(-0.994951\pi\)
0.818238 + 0.574879i \(0.194951\pi\)
\(740\) 0 0
\(741\) 0.489357 + 1.50609i 0.0179770 + 0.0553274i
\(742\) −2.04087 2.80902i −0.0749227 0.103122i
\(743\) 28.3607i 1.04045i −0.854029 0.520226i \(-0.825848\pi\)
0.854029 0.520226i \(-0.174152\pi\)
\(744\) −5.42705 + 3.94298i −0.198965 + 0.144557i
\(745\) 0 0
\(746\) −37.0066 26.8869i −1.35491 0.984398i
\(747\) 7.33094 10.0902i 0.268225 0.369180i
\(748\) −16.1150 5.23607i −0.589221 0.191450i
\(749\) 10.1459 0.370723
\(750\) 0 0
\(751\) −5.11146 −0.186520 −0.0932598 0.995642i \(-0.529729\pi\)
−0.0932598 + 0.995642i \(0.529729\pi\)
\(752\) −2.85317 0.927051i −0.104044 0.0338061i
\(753\) 17.1518 23.6074i 0.625045 0.860301i
\(754\) 8.78115 + 6.37988i 0.319791 + 0.232342i
\(755\) 0 0
\(756\) 1.54508 1.12257i 0.0561942 0.0408275i
\(757\) 30.4164i 1.10550i 0.833346 + 0.552752i \(0.186422\pi\)
−0.833346 + 0.552752i \(0.813578\pi\)
\(758\) −13.8823 19.1074i −0.504229 0.694012i
\(759\) 6.09017 + 18.7436i 0.221059 + 0.680350i
\(760\) 0 0
\(761\) −5.70163 + 17.5478i −0.206684 + 0.636107i 0.792956 + 0.609279i \(0.208541\pi\)
−0.999640 + 0.0268287i \(0.991459\pi\)
\(762\) 30.6053 9.94427i 1.10871 0.360243i
\(763\) 5.87785 1.90983i 0.212793 0.0691405i
\(764\) 0.347524 1.06957i 0.0125730 0.0386957i
\(765\) 0 0
\(766\) −16.6803 51.3368i −0.602685 1.85487i
\(767\) 11.8290 + 16.2812i 0.427119 + 0.587878i
\(768\) 13.5623i 0.489388i
\(769\) 10.8541 7.88597i 0.391409 0.284375i −0.374624 0.927177i \(-0.622228\pi\)
0.766033 + 0.642802i \(0.222228\pi\)
\(770\) 0 0
\(771\) −18.4894 13.4333i −0.665878 0.483789i
\(772\) 2.80017 3.85410i 0.100780 0.138712i
\(773\) 34.3893 + 11.1738i 1.23690 + 0.401892i 0.853208 0.521570i \(-0.174654\pi\)
0.383689 + 0.923462i \(0.374654\pi\)
\(774\) 15.7082 0.564620
\(775\) 0 0
\(776\) −8.61803 −0.309369
\(777\) −0.138757 0.0450850i −0.00497789 0.00161741i
\(778\) 14.2658 19.6353i 0.511455 0.703958i
\(779\) −0.527864 0.383516i −0.0189127 0.0137409i
\(780\) 0 0