Properties

Label 125.2.d.a.101.1
Level $125$
Weight $2$
Character 125.101
Analytic conductor $0.998$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(0.998130025266\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 101.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 125.101
Dual form 125.2.d.a.26.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 1.53884i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(1.30902 - 0.951057i) q^{6} -0.618034 q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.618034 - 1.90211i) q^{9} +O(q^{10})\) \(q+(0.500000 - 1.53884i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(1.30902 - 0.951057i) q^{6} -0.618034 q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.618034 - 1.90211i) q^{9} +(-1.61803 + 4.97980i) q^{11} +(-0.190983 - 0.587785i) q^{12} +(-0.572949 - 1.76336i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-1.50000 - 4.61653i) q^{16} +(-4.23607 + 3.07768i) q^{17} -3.23607 q^{18} +(-0.690983 + 0.502029i) q^{19} +(-0.500000 - 0.363271i) q^{21} +(6.85410 + 4.97980i) q^{22} +(-1.16312 + 3.57971i) q^{23} +2.23607 q^{24} -3.00000 q^{26} +(1.54508 - 4.75528i) q^{27} +(0.309017 + 0.224514i) q^{28} +(2.92705 + 2.12663i) q^{29} +(2.42705 - 1.76336i) q^{31} -3.38197 q^{32} +(-4.23607 + 3.07768i) q^{33} +(2.61803 + 8.05748i) q^{34} +(-0.381966 + 1.17557i) q^{36} +(0.0729490 + 0.224514i) q^{37} +(0.427051 + 1.31433i) q^{38} +(0.572949 - 1.76336i) q^{39} +(-0.236068 - 0.726543i) q^{41} +(-0.809017 + 0.587785i) q^{42} +4.85410 q^{43} +(2.61803 - 1.90211i) q^{44} +(4.92705 + 3.57971i) q^{46} +(0.500000 + 0.363271i) q^{47} +(1.50000 - 4.61653i) q^{48} -6.61803 q^{49} -5.23607 q^{51} +(-0.354102 + 1.08981i) q^{52} +(-2.80902 - 2.04087i) q^{53} +(-6.54508 - 4.75528i) q^{54} +(-1.11803 + 0.812299i) q^{56} -0.854102 q^{57} +(4.73607 - 3.44095i) q^{58} +(-3.35410 - 10.3229i) q^{59} +(2.69098 - 8.28199i) q^{61} +(-1.50000 - 4.61653i) q^{62} +(0.381966 + 1.17557i) q^{63} +(1.30902 - 4.02874i) q^{64} +(2.61803 + 8.05748i) q^{66} +(3.85410 - 2.80017i) q^{67} +3.23607 q^{68} +(-3.04508 + 2.21238i) q^{69} +(5.35410 + 3.88998i) q^{71} +(-3.61803 - 2.62866i) q^{72} +(2.78115 - 8.55951i) q^{73} +0.381966 q^{74} +0.527864 q^{76} +(1.00000 - 3.07768i) q^{77} +(-2.42705 - 1.76336i) q^{78} +(6.54508 + 4.75528i) q^{79} +(-0.809017 + 0.587785i) q^{81} -1.23607 q^{82} +(-5.04508 + 3.66547i) q^{83} +(0.118034 + 0.363271i) q^{84} +(2.42705 - 7.46969i) q^{86} +(1.11803 + 3.44095i) q^{87} +(3.61803 + 11.1352i) q^{88} +(-2.76393 + 8.50651i) q^{89} +(0.354102 + 1.08981i) q^{91} +(1.88197 - 1.36733i) q^{92} +3.00000 q^{93} +(0.809017 - 0.587785i) q^{94} +(-2.73607 - 1.98787i) q^{96} +(-3.11803 - 2.26538i) q^{97} +(-3.30902 + 10.1841i) q^{98} +10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{6} + 2 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{6} + 2 q^{7} + 5 q^{8} + 2 q^{9} - 2 q^{11} - 3 q^{12} - 9 q^{13} + q^{14} - 6 q^{16} - 8 q^{17} - 4 q^{18} - 5 q^{19} - 2 q^{21} + 14 q^{22} + 11 q^{23} - 12 q^{26} - 5 q^{27} - q^{28} + 5 q^{29} + 3 q^{31} - 18 q^{32} - 8 q^{33} + 6 q^{34} - 6 q^{36} + 7 q^{37} - 5 q^{38} + 9 q^{39} + 8 q^{41} - q^{42} + 6 q^{43} + 6 q^{44} + 13 q^{46} + 2 q^{47} + 6 q^{48} - 22 q^{49} - 12 q^{51} + 12 q^{52} - 9 q^{53} - 15 q^{54} + 10 q^{57} + 10 q^{58} + 13 q^{61} - 6 q^{62} + 6 q^{63} + 3 q^{64} + 6 q^{66} + 2 q^{67} + 4 q^{68} - q^{69} + 8 q^{71} - 10 q^{72} - 9 q^{73} + 6 q^{74} + 20 q^{76} + 4 q^{77} - 3 q^{78} + 15 q^{79} - q^{81} + 4 q^{82} - 9 q^{83} - 4 q^{84} + 3 q^{86} + 10 q^{88} - 20 q^{89} - 12 q^{91} + 12 q^{92} + 12 q^{93} + q^{94} - 2 q^{96} - 8 q^{97} - 11 q^{98} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 1.53884i 0.353553 1.08813i −0.603290 0.797522i \(-0.706144\pi\)
0.956844 0.290604i \(-0.0938561\pi\)
\(3\) 0.809017 + 0.587785i 0.467086 + 0.339358i 0.796305 0.604896i \(-0.206785\pi\)
−0.329218 + 0.944254i \(0.606785\pi\)
\(4\) −0.500000 0.363271i −0.250000 0.181636i
\(5\) 0 0
\(6\) 1.30902 0.951057i 0.534404 0.388267i
\(7\) −0.618034 −0.233595 −0.116797 0.993156i \(-0.537263\pi\)
−0.116797 + 0.993156i \(0.537263\pi\)
\(8\) 1.80902 1.31433i 0.639584 0.464685i
\(9\) −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 \(0.810409\pi\)
\(12\) −0.190983 0.587785i −0.0551320 0.169679i
\(13\) −0.572949 1.76336i −0.158907 0.489067i 0.839628 0.543161i \(-0.182773\pi\)
−0.998536 + 0.0540944i \(0.982773\pi\)
\(14\) −0.309017 + 0.951057i −0.0825883 + 0.254181i
\(15\) 0 0
\(16\) −1.50000 4.61653i −0.375000 1.15413i
\(17\) −4.23607 + 3.07768i −1.02740 + 0.746448i −0.967786 0.251774i \(-0.918986\pi\)
−0.0596113 + 0.998222i \(0.518986\pi\)
\(18\) −3.23607 −0.762749
\(19\) −0.690983 + 0.502029i −0.158522 + 0.115173i −0.664219 0.747538i \(-0.731236\pi\)
0.505696 + 0.862712i \(0.331236\pi\)
\(20\) 0 0
\(21\) −0.500000 0.363271i −0.109109 0.0792723i
\(22\) 6.85410 + 4.97980i 1.46130 + 1.06170i
\(23\) −1.16312 + 3.57971i −0.242527 + 0.746422i 0.753506 + 0.657441i \(0.228361\pi\)
−0.996033 + 0.0889808i \(0.971639\pi\)
\(24\) 2.23607 0.456435
\(25\) 0 0
\(26\) −3.00000 −0.588348
\(27\) 1.54508 4.75528i 0.297352 0.915155i
\(28\) 0.309017 + 0.224514i 0.0583987 + 0.0424292i
\(29\) 2.92705 + 2.12663i 0.543540 + 0.394905i 0.825398 0.564551i \(-0.190951\pi\)
−0.281858 + 0.959456i \(0.590951\pi\)
\(30\) 0 0
\(31\) 2.42705 1.76336i 0.435911 0.316708i −0.348097 0.937459i \(-0.613172\pi\)
0.784008 + 0.620750i \(0.213172\pi\)
\(32\) −3.38197 −0.597853
\(33\) −4.23607 + 3.07768i −0.737405 + 0.535756i
\(34\) 2.61803 + 8.05748i 0.448989 + 1.38185i
\(35\) 0 0
\(36\) −0.381966 + 1.17557i −0.0636610 + 0.195928i
\(37\) 0.0729490 + 0.224514i 0.0119927 + 0.0369099i 0.956874 0.290504i \(-0.0938229\pi\)
−0.944881 + 0.327414i \(0.893823\pi\)
\(38\) 0.427051 + 1.31433i 0.0692768 + 0.213212i
\(39\) 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 \(0.918999\pi\)
\(42\) −0.809017 + 0.587785i −0.124834 + 0.0906972i
\(43\) 4.85410 0.740244 0.370122 0.928983i \(-0.379316\pi\)
0.370122 + 0.928983i \(0.379316\pi\)
\(44\) 2.61803 1.90211i 0.394683 0.286754i
\(45\) 0 0
\(46\) 4.92705 + 3.57971i 0.726454 + 0.527800i
\(47\) 0.500000 + 0.363271i 0.0729325 + 0.0529886i 0.623654 0.781700i \(-0.285647\pi\)
−0.550722 + 0.834689i \(0.685647\pi\)
\(48\) 1.50000 4.61653i 0.216506 0.666338i
\(49\) −6.61803 −0.945433
\(50\) 0 0
\(51\) −5.23607 −0.733196
\(52\) −0.354102 + 1.08981i −0.0491051 + 0.151130i
\(53\) −2.80902 2.04087i −0.385848 0.280335i 0.377904 0.925845i \(-0.376645\pi\)
−0.763752 + 0.645510i \(0.776645\pi\)
\(54\) −6.54508 4.75528i −0.890673 0.647112i
\(55\) 0 0
\(56\) −1.11803 + 0.812299i −0.149404 + 0.108548i
\(57\) −0.854102 −0.113129
\(58\) 4.73607 3.44095i 0.621876 0.451820i
\(59\) −3.35410 10.3229i −0.436667 1.34392i −0.891369 0.453279i \(-0.850254\pi\)
0.454702 0.890644i \(-0.349746\pi\)
\(60\) 0 0
\(61\) 2.69098 8.28199i 0.344545 1.06040i −0.617282 0.786742i \(-0.711766\pi\)
0.961827 0.273659i \(-0.0882338\pi\)
\(62\) −1.50000 4.61653i −0.190500 0.586299i
\(63\) 0.381966 + 1.17557i 0.0481232 + 0.148108i
\(64\) 1.30902 4.02874i 0.163627 0.503593i
\(65\) 0 0
\(66\) 2.61803 + 8.05748i 0.322258 + 0.991807i
\(67\) 3.85410 2.80017i 0.470853 0.342095i −0.326920 0.945052i \(-0.606011\pi\)
0.797774 + 0.602957i \(0.206011\pi\)
\(68\) 3.23607 0.392431
\(69\) −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 \(0.571538\pi\)
\(72\) −3.61803 2.62866i −0.426389 0.309790i
\(73\) 2.78115 8.55951i 0.325509 1.00181i −0.645701 0.763590i \(-0.723435\pi\)
0.971210 0.238224i \(-0.0765653\pi\)
\(74\) 0.381966 0.0444026
\(75\) 0 0
\(76\) 0.527864 0.0605502
\(77\) 1.00000 3.07768i 0.113961 0.350735i
\(78\) −2.42705 1.76336i −0.274809 0.199661i
\(79\) 6.54508 + 4.75528i 0.736380 + 0.535011i 0.891575 0.452873i \(-0.149601\pi\)
−0.155196 + 0.987884i \(0.549601\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) −1.23607 −0.136501
\(83\) −5.04508 + 3.66547i −0.553770 + 0.402337i −0.829174 0.558991i \(-0.811189\pi\)
0.275404 + 0.961329i \(0.411189\pi\)
\(84\) 0.118034 + 0.363271i 0.0128786 + 0.0396361i
\(85\) 0 0
\(86\) 2.42705 7.46969i 0.261716 0.805478i
\(87\) 1.11803 + 3.44095i 0.119866 + 0.368909i
\(88\) 3.61803 + 11.1352i 0.385684 + 1.18701i
\(89\) −2.76393 + 8.50651i −0.292976 + 0.901688i 0.690918 + 0.722934i \(0.257207\pi\)
−0.983894 + 0.178754i \(0.942793\pi\)
\(90\) 0 0
\(91\) 0.354102 + 1.08981i 0.0371200 + 0.114244i
\(92\) 1.88197 1.36733i 0.196209 0.142554i
\(93\) 3.00000 0.311086
\(94\) 0.809017 0.587785i 0.0834437 0.0606254i
\(95\) 0 0
\(96\) −2.73607 1.98787i −0.279249 0.202886i
\(97\) −3.11803 2.26538i −0.316588 0.230015i 0.418130 0.908387i \(-0.362686\pi\)
−0.734718 + 0.678372i \(0.762686\pi\)
\(98\) −3.30902 + 10.1841i −0.334261 + 1.02875i
\(99\) 10.4721 1.05249
\(100\) 0 0
\(101\) 1.47214 0.146483 0.0732415 0.997314i \(-0.476666\pi\)
0.0732415 + 0.997314i \(0.476666\pi\)
\(102\) −2.61803 + 8.05748i −0.259224 + 0.797809i
\(103\) 6.92705 + 5.03280i 0.682543 + 0.495896i 0.874200 0.485566i \(-0.161386\pi\)
−0.191658 + 0.981462i \(0.561386\pi\)
\(104\) −3.35410 2.43690i −0.328897 0.238957i
\(105\) 0 0
\(106\) −4.54508 + 3.30220i −0.441458 + 0.320738i
\(107\) 16.4164 1.58703 0.793517 0.608548i \(-0.208248\pi\)
0.793517 + 0.608548i \(0.208248\pi\)
\(108\) −2.50000 + 1.81636i −0.240563 + 0.174779i
\(109\) 3.09017 + 9.51057i 0.295985 + 0.910947i 0.982889 + 0.184199i \(0.0589691\pi\)
−0.686904 + 0.726748i \(0.741031\pi\)
\(110\) 0 0
\(111\) −0.0729490 + 0.224514i −0.00692401 + 0.0213099i
\(112\) 0.927051 + 2.85317i 0.0875981 + 0.269599i
\(113\) −5.20820 16.0292i −0.489947 1.50790i −0.824687 0.565590i \(-0.808648\pi\)
0.334740 0.942311i \(-0.391352\pi\)
\(114\) −0.427051 + 1.31433i −0.0399970 + 0.123098i
\(115\) 0 0
\(116\) −0.690983 2.12663i −0.0641562 0.197452i
\(117\) −3.00000 + 2.17963i −0.277350 + 0.201507i
\(118\) −17.5623 −1.61674
\(119\) 2.61803 1.90211i 0.239995 0.174366i
\(120\) 0 0
\(121\) −13.2812 9.64932i −1.20738 0.877211i
\(122\) −11.3992 8.28199i −1.03203 0.749817i
\(123\) 0.236068 0.726543i 0.0212855 0.0655101i
\(124\) −1.85410 −0.166503
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) −6.14590 + 18.9151i −0.545360 + 1.67845i 0.174772 + 0.984609i \(0.444081\pi\)
−0.720132 + 0.693837i \(0.755919\pi\)
\(128\) −11.0172 8.00448i −0.973794 0.707503i
\(129\) 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 \(0.395982\pi\)
\(132\) 3.23607 0.281664
\(133\) 0.427051 0.310271i 0.0370300 0.0269039i
\(134\) −2.38197 7.33094i −0.205771 0.633297i
\(135\) 0 0
\(136\) −3.61803 + 11.1352i −0.310244 + 0.954832i
\(137\) 3.69098 + 11.3597i 0.315342 + 0.970523i 0.975613 + 0.219496i \(0.0704412\pi\)
−0.660271 + 0.751027i \(0.729559\pi\)
\(138\) 1.88197 + 5.79210i 0.160204 + 0.493056i
\(139\) 1.54508 4.75528i 0.131052 0.403338i −0.863903 0.503659i \(-0.831987\pi\)
0.994955 + 0.100321i \(0.0319869\pi\)
\(140\) 0 0
\(141\) 0.190983 + 0.587785i 0.0160837 + 0.0495004i
\(142\) 8.66312 6.29412i 0.726993 0.528191i
\(143\) 9.70820 0.811841
\(144\) −7.85410 + 5.70634i −0.654508 + 0.475528i
\(145\) 0 0
\(146\) −11.7812 8.55951i −0.975015 0.708390i
\(147\) −5.35410 3.88998i −0.441599 0.320840i
\(148\) 0.0450850 0.138757i 0.00370596 0.0114058i
\(149\) −3.94427 −0.323127 −0.161564 0.986862i \(-0.551654\pi\)
−0.161564 + 0.986862i \(0.551654\pi\)
\(150\) 0 0
\(151\) 14.5623 1.18506 0.592532 0.805547i \(-0.298128\pi\)
0.592532 + 0.805547i \(0.298128\pi\)
\(152\) −0.590170 + 1.81636i −0.0478691 + 0.147326i
\(153\) 8.47214 + 6.15537i 0.684932 + 0.497632i
\(154\) −4.23607 3.07768i −0.341352 0.248007i
\(155\) 0 0
\(156\) −0.927051 + 0.673542i −0.0742235 + 0.0539265i
\(157\) −13.1803 −1.05191 −0.525953 0.850514i \(-0.676291\pi\)
−0.525953 + 0.850514i \(0.676291\pi\)
\(158\) 10.5902 7.69421i 0.842509 0.612118i
\(159\) −1.07295 3.30220i −0.0850904 0.261881i
\(160\) 0 0
\(161\) 0.718847 2.21238i 0.0566531 0.174360i
\(162\) 0.500000 + 1.53884i 0.0392837 + 0.120903i
\(163\) −3.39919 10.4616i −0.266245 0.819417i −0.991404 0.130836i \(-0.958234\pi\)
0.725159 0.688581i \(-0.241766\pi\)
\(164\) −0.145898 + 0.449028i −0.0113927 + 0.0350632i
\(165\) 0 0
\(166\) 3.11803 + 9.59632i 0.242006 + 0.744819i
\(167\) 11.7812 8.55951i 0.911653 0.662355i −0.0297794 0.999556i \(-0.509480\pi\)
0.941432 + 0.337202i \(0.109480\pi\)
\(168\) −1.38197 −0.106621
\(169\) 7.73607 5.62058i 0.595082 0.432352i
\(170\) 0 0
\(171\) 1.38197 + 1.00406i 0.105682 + 0.0767822i
\(172\) −2.42705 1.76336i −0.185061 0.134455i
\(173\) −5.83688 + 17.9641i −0.443770 + 1.36578i 0.440057 + 0.897970i \(0.354958\pi\)
−0.883827 + 0.467813i \(0.845042\pi\)
\(174\) 5.85410 0.443798
\(175\) 0 0
\(176\) 25.4164 1.91583
\(177\) 3.35410 10.3229i 0.252110 0.775914i
\(178\) 11.7082 + 8.50651i 0.877567 + 0.637590i
\(179\) 0.427051 + 0.310271i 0.0319193 + 0.0231907i 0.603631 0.797264i \(-0.293720\pi\)
−0.571711 + 0.820455i \(0.693720\pi\)
\(180\) 0 0
\(181\) −0.236068 + 0.171513i −0.0175468 + 0.0127485i −0.596524 0.802595i \(-0.703452\pi\)
0.578977 + 0.815344i \(0.303452\pi\)
\(182\) 1.85410 0.137435
\(183\) 7.04508 5.11855i 0.520788 0.378374i
\(184\) 2.60081 + 8.00448i 0.191734 + 0.590098i
\(185\) 0 0
\(186\) 1.50000 4.61653i 0.109985 0.338500i
\(187\) −8.47214 26.0746i −0.619544 1.90676i
\(188\) −0.118034 0.363271i −0.00860851 0.0264943i
\(189\) −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 \(0.920970\pi\)
\(192\) 3.42705 2.48990i 0.247326 0.179693i
\(193\) −7.70820 −0.554849 −0.277424 0.960747i \(-0.589481\pi\)
−0.277424 + 0.960747i \(0.589481\pi\)
\(194\) −5.04508 + 3.66547i −0.362216 + 0.263165i
\(195\) 0 0
\(196\) 3.30902 + 2.40414i 0.236358 + 0.171724i
\(197\) 3.00000 + 2.17963i 0.213741 + 0.155292i 0.689505 0.724281i \(-0.257828\pi\)
−0.475764 + 0.879573i \(0.657828\pi\)
\(198\) 5.23607 16.1150i 0.372111 1.14524i
\(199\) −17.5623 −1.24496 −0.622479 0.782636i \(-0.713875\pi\)
−0.622479 + 0.782636i \(0.713875\pi\)
\(200\) 0 0
\(201\) 4.76393 0.336022
\(202\) 0.736068 2.26538i 0.0517896 0.159392i
\(203\) −1.80902 1.31433i −0.126968 0.0922477i
\(204\) 2.61803 + 1.90211i 0.183299 + 0.133175i
\(205\) 0 0
\(206\) 11.2082 8.14324i 0.780913 0.567366i
\(207\) 7.52786 0.523223
\(208\) −7.28115 + 5.29007i −0.504857 + 0.366800i
\(209\) −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 \(0.997660\pi\)
\(212\) 0.663119 + 2.04087i 0.0455432 + 0.140168i
\(213\) 2.04508 + 6.29412i 0.140127 + 0.431266i
\(214\) 8.20820 25.2623i 0.561101 1.72689i
\(215\) 0 0
\(216\) −3.45492 10.6331i −0.235077 0.723493i
\(217\) −1.50000 + 1.08981i −0.101827 + 0.0739814i
\(218\) 16.1803 1.09587
\(219\) 7.28115 5.29007i 0.492015 0.357470i
\(220\) 0 0
\(221\) 7.85410 + 5.70634i 0.528324 + 0.383850i
\(222\) 0.309017 + 0.224514i 0.0207399 + 0.0150684i
\(223\) 0.0557281 0.171513i 0.00373183 0.0114854i −0.949173 0.314754i \(-0.898078\pi\)
0.952905 + 0.303269i \(0.0980780\pi\)
\(224\) 2.09017 0.139655
\(225\) 0 0
\(226\) −27.2705 −1.81401
\(227\) −4.56231 + 14.0413i −0.302811 + 0.931956i 0.677674 + 0.735362i \(0.262988\pi\)
−0.980485 + 0.196594i \(0.937012\pi\)
\(228\) 0.427051 + 0.310271i 0.0282821 + 0.0205482i
\(229\) −17.5623 12.7598i −1.16055 0.843189i −0.170702 0.985323i \(-0.554604\pi\)
−0.989847 + 0.142134i \(0.954604\pi\)
\(230\) 0 0
\(231\) 2.61803 1.90211i 0.172254 0.125150i
\(232\) 8.09017 0.531146
\(233\) −2.38197 + 1.73060i −0.156048 + 0.113375i −0.663069 0.748558i \(-0.730746\pi\)
0.507021 + 0.861933i \(0.330746\pi\)
\(234\) 1.85410 + 5.70634i 0.121206 + 0.373035i
\(235\) 0 0
\(236\) −2.07295 + 6.37988i −0.134937 + 0.415295i
\(237\) 2.50000 + 7.69421i 0.162392 + 0.499793i
\(238\) −1.61803 4.97980i −0.104882 0.322792i
\(239\) −6.34346 + 19.5232i −0.410324 + 1.26285i 0.506043 + 0.862508i \(0.331108\pi\)
−0.916367 + 0.400340i \(0.868892\pi\)
\(240\) 0 0
\(241\) 0.781153 + 2.40414i 0.0503185 + 0.154864i 0.973058 0.230559i \(-0.0740554\pi\)
−0.922740 + 0.385423i \(0.874055\pi\)
\(242\) −21.4894 + 15.6129i −1.38139 + 1.00364i
\(243\) −16.0000 −1.02640
\(244\) −4.35410 + 3.16344i −0.278743 + 0.202519i
\(245\) 0 0
\(246\) −1.00000 0.726543i −0.0637577 0.0463227i
\(247\) 1.28115 + 0.930812i 0.0815178 + 0.0592262i
\(248\) 2.07295 6.37988i 0.131632 0.405123i
\(249\) −6.23607 −0.395195
\(250\) 0 0
\(251\) −29.1803 −1.84185 −0.920923 0.389744i \(-0.872564\pi\)
−0.920923 + 0.389744i \(0.872564\pi\)
\(252\) 0.236068 0.726543i 0.0148709 0.0457679i
\(253\) −15.9443 11.5842i −1.00241 0.728292i
\(254\) 26.0344 + 18.9151i 1.63355 + 1.18684i
\(255\) 0 0
\(256\) −10.9721 + 7.97172i −0.685758 + 0.498233i
\(257\) −22.8541 −1.42560 −0.712800 0.701367i \(-0.752573\pi\)
−0.712800 + 0.701367i \(0.752573\pi\)
\(258\) 6.35410 4.61653i 0.395589 0.287412i
\(259\) −0.0450850 0.138757i −0.00280144 0.00862196i
\(260\) 0 0
\(261\) 2.23607 6.88191i 0.138409 0.425980i
\(262\) 3.39919 + 10.4616i 0.210002 + 0.646321i
\(263\) 3.37132 + 10.3759i 0.207885 + 0.639803i 0.999583 + 0.0288905i \(0.00919740\pi\)
−0.791698 + 0.610913i \(0.790803\pi\)
\(264\) −3.61803 + 11.1352i −0.222675 + 0.685322i
\(265\) 0 0
\(266\) −0.263932 0.812299i −0.0161827 0.0498053i
\(267\) −7.23607 + 5.25731i −0.442840 + 0.321742i
\(268\) −2.94427 −0.179850
\(269\) 10.3262 7.50245i 0.629602 0.457433i −0.226660 0.973974i \(-0.572781\pi\)
0.856262 + 0.516541i \(0.172781\pi\)
\(270\) 0 0
\(271\) 6.47214 + 4.70228i 0.393154 + 0.285643i 0.766747 0.641950i \(-0.221874\pi\)
−0.373593 + 0.927593i \(0.621874\pi\)
\(272\) 20.5623 + 14.9394i 1.24677 + 0.905834i
\(273\) −0.354102 + 1.08981i −0.0214312 + 0.0659585i
\(274\) 19.3262 1.16754
\(275\) 0 0
\(276\) 2.32624 0.140023
\(277\) 7.63525 23.4989i 0.458758 1.41191i −0.407908 0.913023i \(-0.633742\pi\)
0.866666 0.498889i \(-0.166258\pi\)
\(278\) −6.54508 4.75528i −0.392548 0.285203i
\(279\) −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 \(0.397309\pi\)
\(282\) 1.00000 0.0595491
\(283\) −24.1525 + 17.5478i −1.43572 + 1.04311i −0.446799 + 0.894634i \(0.647436\pi\)
−0.988916 + 0.148474i \(0.952564\pi\)
\(284\) −1.26393 3.88998i −0.0750006 0.230828i
\(285\) 0 0
\(286\) 4.85410 14.9394i 0.287029 0.883385i
\(287\) 0.145898 + 0.449028i 0.00861209 + 0.0265053i
\(288\) 2.09017 + 6.43288i 0.123164 + 0.379061i
\(289\) 3.21885 9.90659i 0.189344 0.582741i
\(290\) 0 0
\(291\) −1.19098 3.66547i −0.0698167 0.214874i
\(292\) −4.50000 + 3.26944i −0.263343 + 0.191330i
\(293\) 19.5279 1.14083 0.570415 0.821357i \(-0.306782\pi\)
0.570415 + 0.821357i \(0.306782\pi\)
\(294\) −8.66312 + 6.29412i −0.505243 + 0.367081i
\(295\) 0 0
\(296\) 0.427051 + 0.310271i 0.0248218 + 0.0180341i
\(297\) 21.1803 + 15.3884i 1.22901 + 0.892927i
\(298\) −1.97214 + 6.06961i −0.114243 + 0.351603i
\(299\) 6.97871 0.403589
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) 7.28115 22.4091i 0.418983 1.28950i
\(303\) 1.19098 + 0.865300i 0.0684202 + 0.0497102i
\(304\) 3.35410 + 2.43690i 0.192371 + 0.139766i
\(305\) 0 0
\(306\) 13.7082 9.95959i 0.783646 0.569352i
\(307\) −9.23607 −0.527130 −0.263565 0.964642i \(-0.584898\pi\)
−0.263565 + 0.964642i \(0.584898\pi\)
\(308\) −1.61803 + 1.17557i −0.0921960 + 0.0669843i
\(309\) 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 \(0.0224650\pi\)
\(312\) −1.28115 3.94298i −0.0725310 0.223227i
\(313\) 5.18034 + 15.9434i 0.292810 + 0.901177i 0.983948 + 0.178454i \(0.0571096\pi\)
−0.691138 + 0.722723i \(0.742890\pi\)
\(314\) −6.59017 + 20.2825i −0.371905 + 1.14461i
\(315\) 0 0
\(316\) −1.54508 4.75528i −0.0869178 0.267506i
\(317\) 6.19098 4.49801i 0.347720 0.252634i −0.400192 0.916431i \(-0.631056\pi\)
0.747912 + 0.663798i \(0.231056\pi\)
\(318\) −5.61803 −0.315044
\(319\) −15.3262 + 11.1352i −0.858105 + 0.623449i
\(320\) 0 0
\(321\) 13.2812 + 9.64932i 0.741282 + 0.538573i
\(322\) −3.04508 2.21238i −0.169696 0.123291i
\(323\) 1.38197 4.25325i 0.0768946 0.236657i
\(324\) 0.618034 0.0343352
\(325\) 0 0
\(326\) −17.7984 −0.985761
\(327\) −3.09017 + 9.51057i −0.170887 + 0.525935i
\(328\) −1.38197 1.00406i −0.0763063 0.0554398i
\(329\) −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 \(0.0807850\pi\)
\(332\) 3.85410 0.211521
\(333\) 0.381966 0.277515i 0.0209316 0.0152077i
\(334\) −7.28115 22.4091i −0.398407 1.22617i
\(335\) 0 0
\(336\) −0.927051 + 2.85317i −0.0505748 + 0.155653i
\(337\) −2.42705 7.46969i −0.132210 0.406900i 0.862936 0.505314i \(-0.168623\pi\)
−0.995146 + 0.0984135i \(0.968623\pi\)
\(338\) −4.78115 14.7149i −0.260060 0.800384i
\(339\) 5.20820 16.0292i 0.282871 0.870587i
\(340\) 0 0
\(341\) 4.85410 + 14.9394i 0.262864 + 0.809013i
\(342\) 2.23607 1.62460i 0.120913 0.0878482i
\(343\) 8.41641 0.454443
\(344\) 8.78115 6.37988i 0.473448 0.343980i
\(345\) 0 0
\(346\) 24.7254 + 17.9641i 1.32925 + 0.965755i
\(347\) −16.1074 11.7027i −0.864690 0.628234i 0.0644668 0.997920i \(-0.479465\pi\)
−0.929157 + 0.369686i \(0.879465\pi\)
\(348\) 0.690983 2.12663i 0.0370406 0.113999i
\(349\) 21.7082 1.16201 0.581007 0.813899i \(-0.302659\pi\)
0.581007 + 0.813899i \(0.302659\pi\)
\(350\) 0 0
\(351\) −9.27051 −0.494823
\(352\) 5.47214 16.8415i 0.291666 0.897655i
\(353\) 10.4443 + 7.58821i 0.555893 + 0.403880i 0.829953 0.557833i \(-0.188367\pi\)
−0.274061 + 0.961712i \(0.588367\pi\)
\(354\) −14.2082 10.3229i −0.755158 0.548654i
\(355\) 0 0
\(356\) 4.47214 3.24920i 0.237023 0.172207i
\(357\) 3.23607 0.171271
\(358\) 0.690983 0.502029i 0.0365196 0.0265330i
\(359\) 4.24671 + 13.0700i 0.224133 + 0.689810i 0.998378 + 0.0569247i \(0.0181295\pi\)
−0.774246 + 0.632885i \(0.781870\pi\)
\(360\) 0 0
\(361\) −5.64590 + 17.3763i −0.297153 + 0.914541i
\(362\) 0.145898 + 0.449028i 0.00766823 + 0.0236004i
\(363\) −5.07295 15.6129i −0.266261 0.819466i
\(364\) 0.218847 0.673542i 0.0114707 0.0353032i
\(365\) 0 0
\(366\) −4.35410 13.4005i −0.227593 0.700458i
\(367\) −20.6803 + 15.0251i −1.07950 + 0.784306i −0.977597 0.210488i \(-0.932495\pi\)
−0.101908 + 0.994794i \(0.532495\pi\)
\(368\) 18.2705 0.952416
\(369\) −1.23607 + 0.898056i −0.0643471 + 0.0467509i
\(370\) 0 0
\(371\) 1.73607 + 1.26133i 0.0901322 + 0.0654848i
\(372\) −1.50000 1.08981i −0.0777714 0.0565042i
\(373\) 8.73607 26.8869i 0.452336 1.39215i −0.421897 0.906644i \(-0.638636\pi\)
0.874234 0.485505i \(-0.161364\pi\)
\(374\) −44.3607 −2.29384
\(375\) 0 0
\(376\) 1.38197 0.0712695
\(377\) 2.07295 6.37988i 0.106762 0.328581i
\(378\) 4.04508 + 2.93893i 0.208057 + 0.151162i
\(379\) −11.8090 8.57975i −0.606588 0.440712i 0.241623 0.970370i \(-0.422320\pi\)
−0.848211 + 0.529658i \(0.822320\pi\)
\(380\) 0 0
\(381\) −16.0902 + 11.6902i −0.824324 + 0.598907i
\(382\) −2.94427 −0.150642
\(383\) 26.9894 19.6089i 1.37909 1.00197i 0.382127 0.924110i \(-0.375192\pi\)
0.996964 0.0778591i \(-0.0248084\pi\)
\(384\) −4.20820 12.9515i −0.214749 0.660929i
\(385\) 0 0
\(386\) −3.85410 + 11.8617i −0.196169 + 0.603745i
\(387\) −3.00000 9.23305i −0.152499 0.469342i
\(388\) 0.736068 + 2.26538i 0.0373682 + 0.115007i
\(389\) 4.63525 14.2658i 0.235017 0.723307i −0.762102 0.647456i \(-0.775833\pi\)
0.997119 0.0758507i \(-0.0241672\pi\)
\(390\) 0 0
\(391\) −6.09017 18.7436i −0.307993 0.947905i
\(392\) −11.9721 + 8.69827i −0.604684 + 0.439329i
\(393\) −6.79837 −0.342933
\(394\) 4.85410 3.52671i 0.244546 0.177673i
\(395\) 0 0
\(396\) −5.23607 3.80423i −0.263122 0.191170i
\(397\) 23.4894 + 17.0660i 1.17890 + 0.856519i 0.992047 0.125870i \(-0.0401721\pi\)
0.186850 + 0.982388i \(0.440172\pi\)
\(398\) −8.78115 + 27.0256i −0.440159 + 1.35467i
\(399\) 0.527864 0.0264263
\(400\) 0 0
\(401\) 26.5967 1.32818 0.664089 0.747653i \(-0.268820\pi\)
0.664089 + 0.747653i \(0.268820\pi\)
\(402\) 2.38197 7.33094i 0.118802 0.365634i
\(403\) −4.50000 3.26944i −0.224161 0.162862i
\(404\) −0.736068 0.534785i −0.0366208 0.0266065i
\(405\) 0 0
\(406\) −2.92705 + 2.12663i −0.145267 + 0.105543i
\(407\) −1.23607 −0.0612696
\(408\) −9.47214 + 6.88191i −0.468941 + 0.340705i
\(409\) 0.489357 + 1.50609i 0.0241971 + 0.0744711i 0.962426 0.271544i \(-0.0875344\pi\)
−0.938229 + 0.346016i \(0.887534\pi\)
\(410\) 0 0
\(411\) −3.69098 + 11.3597i −0.182063 + 0.560332i
\(412\) −1.63525 5.03280i −0.0805632 0.247948i
\(413\) 2.07295 + 6.37988i 0.102003 + 0.313933i
\(414\) 3.76393 11.5842i 0.184987 0.569332i
\(415\) 0 0
\(416\) 1.93769 + 5.96361i 0.0950033 + 0.292390i
\(417\) 4.04508 2.93893i 0.198089 0.143920i
\(418\) −7.23607 −0.353928
\(419\) 7.66312 5.56758i 0.374368 0.271994i −0.384652 0.923062i \(-0.625679\pi\)
0.759020 + 0.651068i \(0.225679\pi\)
\(420\) 0 0
\(421\) −25.8885 18.8091i −1.26173 0.916701i −0.262889 0.964826i \(-0.584675\pi\)
−0.998841 + 0.0481252i \(0.984675\pi\)
\(422\) 12.0172 + 8.73102i 0.584989 + 0.425020i
\(423\) 0.381966 1.17557i 0.0185718 0.0571582i
\(424\) −7.76393 −0.377050
\(425\) 0 0
\(426\) 10.7082 0.518814
\(427\) −1.66312 + 5.11855i −0.0804840 + 0.247704i
\(428\) −8.20820 5.96361i −0.396759 0.288262i
\(429\) 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 \(0.0448299\pi\)
\(432\) −24.2705 −1.16772
\(433\) 21.7254 15.7844i 1.04406 0.758552i 0.0729839 0.997333i \(-0.476748\pi\)
0.971073 + 0.238781i \(0.0767478\pi\)
\(434\) 0.927051 + 2.85317i 0.0444999 + 0.136957i
\(435\) 0 0
\(436\) 1.90983 5.87785i 0.0914643 0.281498i
\(437\) −0.993422 3.05744i −0.0475218 0.146257i
\(438\) −4.50000 13.8496i −0.215018 0.661758i
\(439\) −12.6631 + 38.9731i −0.604378 + 1.86008i −0.103365 + 0.994644i \(0.532961\pi\)
−0.501013 + 0.865440i \(0.667039\pi\)
\(440\) 0 0
\(441\) 4.09017 + 12.5882i 0.194770 + 0.599440i
\(442\) 12.7082 9.23305i 0.604468 0.439171i
\(443\) −29.9443 −1.42270 −0.711348 0.702840i \(-0.751915\pi\)
−0.711348 + 0.702840i \(0.751915\pi\)
\(444\) 0.118034 0.0857567i 0.00560165 0.00406983i
\(445\) 0 0
\(446\) −0.236068 0.171513i −0.0111781 0.00812140i
\(447\) −3.19098 2.31838i −0.150928 0.109656i
\(448\) −0.809017 + 2.48990i −0.0382225 + 0.117637i
\(449\) 4.67376 0.220568 0.110284 0.993900i \(-0.464824\pi\)
0.110284 + 0.993900i \(0.464824\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) −3.21885 + 9.90659i −0.151402 + 0.465967i
\(453\) 11.7812 + 8.55951i 0.553527 + 0.402161i
\(454\) 19.3262 + 14.0413i 0.907025 + 0.658992i
\(455\) 0 0
\(456\) −1.54508 + 1.12257i −0.0723552 + 0.0525692i
\(457\) 21.4164 1.00182 0.500909 0.865500i \(-0.332999\pi\)
0.500909 + 0.865500i \(0.332999\pi\)
\(458\) −28.4164 + 20.6457i −1.32781 + 0.964712i
\(459\) 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 \(0.0939238\pi\)
\(462\) −1.61803 4.97980i −0.0752778 0.231681i
\(463\) 7.45492 + 22.9439i 0.346459 + 1.06629i 0.960798 + 0.277250i \(0.0894229\pi\)
−0.614339 + 0.789042i \(0.710577\pi\)
\(464\) 5.42705 16.7027i 0.251945 0.775405i
\(465\) 0 0
\(466\) 1.47214 + 4.53077i 0.0681954 + 0.209884i
\(467\) 22.2082 16.1352i 1.02767 0.746648i 0.0598315 0.998208i \(-0.480944\pi\)
0.967842 + 0.251560i \(0.0809437\pi\)
\(468\) 2.29180 0.105938
\(469\) −2.38197 + 1.73060i −0.109989 + 0.0799117i
\(470\) 0 0
\(471\) −10.6631 7.74721i −0.491331 0.356973i
\(472\) −19.6353 14.2658i −0.903786 0.656639i
\(473\) −7.85410 + 24.1724i −0.361132 + 1.11145i
\(474\) 13.0902 0.601251
\(475\) 0 0
\(476\) −2.00000 −0.0916698
\(477\) −2.14590 + 6.60440i −0.0982539 + 0.302394i
\(478\) 26.8713 + 19.5232i 1.22907 + 0.892969i
\(479\) 8.78115 + 6.37988i 0.401221 + 0.291504i 0.770038 0.637998i \(-0.220237\pi\)
−0.368817 + 0.929502i \(0.620237\pi\)
\(480\) 0 0
\(481\) 0.354102 0.257270i 0.0161457 0.0117305i
\(482\) 4.09017 0.186302
\(483\) 1.88197 1.36733i 0.0856324 0.0622156i
\(484\) 3.13525 + 9.64932i 0.142512 + 0.438606i
\(485\) 0 0
\(486\) −8.00000 + 24.6215i −0.362887 + 1.11685i
\(487\) 11.2533 + 34.6341i 0.509935 + 1.56942i 0.792312 + 0.610116i \(0.208877\pi\)
−0.282377 + 0.959303i \(0.591123\pi\)
\(488\) −6.01722 18.5191i −0.272387 0.838320i
\(489\) 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 \(-0.529983\pi\)
\(492\) −0.381966 + 0.277515i −0.0172204 + 0.0125113i
\(493\) −18.9443 −0.853207
\(494\) 2.07295 1.50609i 0.0932664 0.0677620i
\(495\) 0 0
\(496\) −11.7812 8.55951i −0.528989 0.384333i
\(497\) −3.30902 2.40414i −0.148430 0.107840i
\(498\) −3.11803 + 9.59632i −0.139722 + 0.430021i
\(499\) 7.56231 0.338535 0.169268 0.985570i \(-0.445860\pi\)
0.169268 + 0.985570i \(0.445860\pi\)
\(500\) 0 0
\(501\) 14.5623 0.650596
\(502\) −14.5902 + 44.9039i −0.651191 + 2.00416i
\(503\) −30.2705 21.9928i −1.34970 0.980611i −0.999027 0.0441115i \(-0.985954\pi\)
−0.350669 0.936500i \(-0.614046\pi\)
\(504\) 2.23607 + 1.62460i 0.0996024 + 0.0723654i
\(505\) 0 0
\(506\) −25.7984 + 18.7436i −1.14688 + 0.833255i
\(507\) 9.56231 0.424677
\(508\) 9.94427 7.22494i 0.441206 0.320555i
\(509\) −6.28115 19.3314i −0.278407 0.856849i −0.988298 0.152537i \(-0.951256\pi\)
0.709891 0.704312i \(-0.248744\pi\)
\(510\) 0 0
\(511\) −1.71885 + 5.29007i −0.0760373 + 0.234019i
\(512\) −1.63525 5.03280i −0.0722687 0.222420i
\(513\) 1.31966 + 4.06150i 0.0582644 + 0.179319i
\(514\) −11.4271 + 35.1688i −0.504026 + 1.55123i
\(515\) 0 0
\(516\) −0.927051 2.85317i −0.0408111 0.125604i
\(517\) −2.61803 + 1.90211i −0.115141 + 0.0836548i
\(518\) −0.236068 −0.0103722
\(519\) −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 \(0.922376\pi\)
\(522\) −9.47214 6.88191i −0.414584 0.301213i
\(523\) 4.06231 12.5025i 0.177632 0.546696i −0.822112 0.569326i \(-0.807204\pi\)
0.999744 + 0.0226305i \(0.00720412\pi\)
\(524\) 4.20163 0.183549
\(525\) 0 0
\(526\) 17.6525 0.769685
\(527\) −4.85410 + 14.9394i −0.211448 + 0.650770i
\(528\) 20.5623 + 14.9394i 0.894860 + 0.650153i
\(529\) 7.14590 + 5.19180i 0.310691 + 0.225730i
\(530\) 0 0
\(531\) −17.5623 + 12.7598i −0.762139 + 0.553727i
\(532\) −0.326238 −0.0141442
\(533\) −1.14590 + 0.832544i −0.0496344 + 0.0360615i
\(534\) 4.47214 + 13.7638i 0.193528 + 0.595619i
\(535\) 0 0
\(536\) 3.29180 10.1311i 0.142184 0.437597i
\(537\) 0.163119 + 0.502029i 0.00703910 + 0.0216641i
\(538\) −6.38197 19.6417i −0.275146 0.846813i
\(539\) 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 \(0.701844\pi\)
\(542\) 10.4721 7.60845i 0.449817 0.326811i
\(543\) −0.291796 −0.0125222
\(544\) 14.3262 10.4086i 0.614232 0.446266i
\(545\) 0 0
\(546\) 1.50000 + 1.08981i 0.0641941 + 0.0466397i
\(547\) −17.2254 12.5150i −0.736506 0.535103i 0.155109 0.987897i \(-0.450427\pi\)
−0.891615 + 0.452794i \(0.850427\pi\)
\(548\) 2.28115 7.02067i 0.0974460 0.299908i
\(549\) −17.4164 −0.743314
\(550\) 0 0
\(551\) −3.09017 −0.131646
\(552\) −2.60081 + 8.00448i −0.110698 + 0.340693i
\(553\) −4.04508 2.93893i −0.172015 0.124976i
\(554\) −32.3435 23.4989i −1.37414 0.998373i
\(555\) 0 0
\(556\) −2.50000 + 1.81636i −0.106024 + 0.0770307i
\(557\) −4.76393 −0.201854 −0.100927 0.994894i \(-0.532181\pi\)
−0.100927 + 0.994894i \(0.532181\pi\)
\(558\) −7.85410 + 5.70634i −0.332491 + 0.241569i
\(559\) −2.78115 8.55951i −0.117630 0.362029i
\(560\) 0 0
\(561\) 8.47214 26.0746i 0.357694 1.10087i
\(562\) 5.04508 + 15.5272i 0.212814 + 0.654974i
\(563\) −2.28115 7.02067i −0.0961391 0.295886i 0.891410 0.453198i \(-0.149717\pi\)
−0.987549 + 0.157312i \(0.949717\pi\)
\(564\) 0.118034 0.363271i 0.00497013 0.0152965i
\(565\) 0 0
\(566\) 14.9271 + 45.9407i 0.627431 + 1.93103i
\(567\) 0.500000 0.363271i 0.0209980 0.0152560i
\(568\) 14.7984 0.620926
\(569\) −16.6074 + 12.0660i −0.696218 + 0.505832i −0.878698 0.477377i \(-0.841587\pi\)
0.182480 + 0.983210i \(0.441587\pi\)
\(570\) 0 0
\(571\) 6.57295 + 4.77553i 0.275069 + 0.199850i 0.716764 0.697316i \(-0.245623\pi\)
−0.441695 + 0.897165i \(0.645623\pi\)
\(572\) −4.85410 3.52671i −0.202960 0.147459i
\(573\) 0.562306 1.73060i 0.0234907 0.0722968i
\(574\) 0.763932 0.0318859
\(575\) 0 0
\(576\) −8.47214 −0.353006
\(577\) 10.4377 32.1239i 0.434527 1.33734i −0.459044 0.888414i \(-0.651808\pi\)
0.893571 0.448923i \(-0.148192\pi\)
\(578\) −13.6353 9.90659i −0.567152 0.412060i
\(579\) −6.23607 4.53077i −0.259162 0.188292i
\(580\) 0 0
\(581\) 3.11803 2.26538i 0.129358 0.0939840i
\(582\) −6.23607 −0.258493
\(583\) 14.7082 10.6861i 0.609152 0.442575i
\(584\) −6.21885 19.1396i −0.257338 0.792004i
\(585\) 0 0
\(586\) 9.76393 30.0503i 0.403344 1.24137i
\(587\) −1.63525 5.03280i −0.0674942 0.207726i 0.911621 0.411032i \(-0.134831\pi\)
−0.979115 + 0.203306i \(0.934831\pi\)
\(588\) 1.26393 + 3.88998i 0.0521237 + 0.160420i
\(589\) −0.791796 + 2.43690i −0.0326254 + 0.100411i
\(590\) 0 0
\(591\) 1.14590 + 3.52671i 0.0471359 + 0.145070i
\(592\) 0.927051 0.673542i 0.0381016 0.0276824i
\(593\) 10.9098 0.448013 0.224007 0.974588i \(-0.428086\pi\)
0.224007 + 0.974588i \(0.428086\pi\)
\(594\) 34.2705 24.8990i 1.40614 1.02162i
\(595\) 0 0
\(596\) 1.97214 + 1.43284i 0.0807818 + 0.0586914i
\(597\) −14.2082 10.3229i −0.581503 0.422487i
\(598\) 3.48936 10.7391i 0.142690 0.439156i
\(599\) −9.47214 −0.387021 −0.193510 0.981098i \(-0.561987\pi\)
−0.193510 + 0.981098i \(0.561987\pi\)
\(600\) 0 0
\(601\) 2.72949 0.111338 0.0556691 0.998449i \(-0.482271\pi\)
0.0556691 + 0.998449i \(0.482271\pi\)
\(602\) −1.50000 + 4.61653i −0.0611354 + 0.188156i
\(603\) −7.70820 5.60034i −0.313902 0.228063i
\(604\) −7.28115 5.29007i −0.296266 0.215250i
\(605\) 0 0
\(606\) 1.92705 1.40008i 0.0782811 0.0568745i
\(607\) 35.5623 1.44343 0.721715 0.692191i \(-0.243354\pi\)
0.721715 + 0.692191i \(0.243354\pi\)
\(608\) 2.33688 1.69784i 0.0947730 0.0688566i
\(609\) −0.690983 2.12663i −0.0280000 0.0861753i
\(610\) 0 0
\(611\) 0.354102 1.08981i 0.0143254 0.0440891i
\(612\) −2.00000 6.15537i −0.0808452 0.248816i
\(613\) 4.62868 + 14.2456i 0.186951 + 0.575374i 0.999977 0.00685287i \(-0.00218135\pi\)
−0.813026 + 0.582227i \(0.802181\pi\)
\(614\) −4.61803 + 14.2128i −0.186369 + 0.573584i
\(615\) 0 0
\(616\) −2.23607 6.88191i −0.0900937 0.277280i
\(617\) 11.5172 8.36775i 0.463666 0.336873i −0.331302 0.943525i \(-0.607488\pi\)
0.794968 + 0.606652i \(0.207488\pi\)
\(618\) 13.8541 0.557294
\(619\) −24.6976 + 17.9438i −0.992679 + 0.721223i −0.960506 0.278259i \(-0.910243\pi\)
−0.0321727 + 0.999482i \(0.510243\pi\)
\(620\) 0 0
\(621\) 15.2254 + 11.0619i 0.610975 + 0.443900i
\(622\) −11.1353 8.09024i −0.446483 0.324389i
\(623\) 1.70820 5.25731i 0.0684377 0.210630i
\(624\) −9.00000 −0.360288
\(625\) 0 0
\(626\) 27.1246 1.08412
\(627\) 1.38197 4.25325i 0.0551904 0.169859i
\(628\) 6.59017 + 4.78804i 0.262976 + 0.191064i
\(629\) −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 \(0.234688\pi\)
\(632\) 18.0902 0.719588
\(633\) −7.42705 + 5.39607i −0.295199 + 0.214474i
\(634\) −3.82624 11.7759i −0.151959 0.467683i
\(635\) 0 0
\(636\) −0.663119 + 2.04087i −0.0262944 + 0.0809258i
\(637\) 3.79180 + 11.6699i 0.150236 + 0.462380i
\(638\) 9.47214 + 29.1522i 0.375005 + 1.15415i
\(639\) 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 \(0.906854\pi\)
\(642\) 21.4894 15.6129i 0.848117 0.616193i
\(643\) 30.8328 1.21593 0.607964 0.793965i \(-0.291987\pi\)
0.607964 + 0.793965i \(0.291987\pi\)
\(644\) −1.16312 + 0.845055i −0.0458333 + 0.0332998i
\(645\) 0 0
\(646\) −5.85410 4.25325i −0.230327 0.167342i
\(647\) −29.5623 21.4783i −1.16221 0.844398i −0.172158 0.985069i \(-0.555074\pi\)
−0.990056 + 0.140671i \(0.955074\pi\)
\(648\) −0.690983 + 2.12663i −0.0271444 + 0.0835418i
\(649\) 56.8328 2.23088
\(650\) 0 0
\(651\) −1.85410 −0.0726680
\(652\) −2.10081 + 6.46564i −0.0822742 + 0.253214i
\(653\) 15.4443 + 11.2209i 0.604381 + 0.439109i 0.847431 0.530905i \(-0.178148\pi\)
−0.243050 + 0.970014i \(0.578148\pi\)
\(654\) 13.0902 + 9.51057i 0.511866 + 0.371893i
\(655\) 0 0
\(656\) −3.00000 + 2.17963i −0.117130 + 0.0851002i
\(657\) −18.0000 −0.702247
\(658\) −0.500000 + 0.363271i −0.0194920 + 0.0141618i
\(659\) 4.79837 + 14.7679i 0.186918 + 0.575275i 0.999976 0.00690786i \(-0.00219886\pi\)
−0.813058 + 0.582183i \(0.802199\pi\)
\(660\) 0 0
\(661\) 6.08359 18.7234i 0.236624 0.728255i −0.760277 0.649598i \(-0.774937\pi\)
0.996902 0.0786563i \(-0.0250630\pi\)
\(662\) −11.5623 35.5851i −0.449382 1.38305i
\(663\) 3.00000 + 9.23305i 0.116510 + 0.358582i
\(664\) −4.30902 + 13.2618i −0.167222 + 0.514657i
\(665\) 0 0
\(666\) −0.236068 0.726543i −0.00914745 0.0281530i
\(667\) −11.0172 + 8.00448i −0.426588 + 0.309935i
\(668\) −9.00000 −0.348220
\(669\) 0.145898 0.106001i 0.00564074 0.00409824i
\(670\) 0 0
\(671\) 36.8885 + 26.8011i 1.42407 + 1.03464i
\(672\) 1.69098 + 1.22857i 0.0652311 + 0.0473932i
\(673\) −3.76393 + 11.5842i −0.145089 + 0.446538i −0.997022 0.0771122i \(-0.975430\pi\)
0.851934 + 0.523650i \(0.175430\pi\)
\(674\) −12.7082 −0.489502
\(675\) 0 0
\(676\) −5.90983 −0.227301
\(677\) −3.28115 + 10.0984i −0.126105 + 0.388111i −0.994101 0.108460i \(-0.965408\pi\)
0.867996 + 0.496571i \(0.165408\pi\)
\(678\) −22.0623 16.0292i −0.847298 0.615598i
\(679\) 1.92705 + 1.40008i 0.0739534 + 0.0537303i
\(680\) 0 0
\(681\) −11.9443 + 8.67802i −0.457705 + 0.332543i
\(682\) 25.4164 0.973245
\(683\) −10.8992 + 7.91872i −0.417046 + 0.303002i −0.776448 0.630181i \(-0.782981\pi\)
0.359402 + 0.933183i \(0.382981\pi\)
\(684\) −0.326238 1.00406i −0.0124740 0.0383911i
\(685\) 0 0
\(686\) 4.20820 12.9515i 0.160670 0.494491i
\(687\) −6.70820 20.6457i −0.255934 0.787684i
\(688\) −7.28115 22.4091i −0.277591 0.854338i
\(689\) −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 \(0.657656\pi\)
\(692\) 9.44427 6.86167i 0.359017 0.260841i
\(693\) −6.47214 −0.245856
\(694\) −26.0623 + 18.9354i −0.989312 + 0.718777i
\(695\) 0 0
\(696\) 6.54508 + 4.75528i 0.248091 + 0.180249i
\(697\) 3.23607 + 2.35114i 0.122575 + 0.0890558i
\(698\) 10.8541 33.4055i 0.410834 1.26442i
\(699\) −2.94427 −0.111363
\(700\) 0 0
\(701\) −41.0132 −1.54905 −0.774523 0.632546i \(-0.782010\pi\)
−0.774523 + 0.632546i \(0.782010\pi\)
\(702\) −4.63525 + 14.2658i −0.174946 + 0.538430i
\(703\) −0.163119 0.118513i −0.00615215 0.00446980i
\(704\) 17.9443 + 13.0373i 0.676300 + 0.491361i
\(705\) 0 0
\(706\) 16.8992 12.2780i 0.636009 0.462088i
\(707\) −0.909830 −0.0342177
\(708\) −5.42705 + 3.94298i −0.203961 + 0.148186i
\(709\) −10.3647 31.8994i −0.389256 1.19801i −0.933345 0.358980i \(-0.883125\pi\)
0.544089 0.839027i \(-0.316875\pi\)
\(710\) 0 0
\(711\) 5.00000 15.3884i 0.187515 0.577111i
\(712\) 6.18034 + 19.0211i 0.231618 + 0.712847i
\(713\) 3.48936 + 10.7391i 0.130677 + 0.402184i
\(714\) 1.61803 4.97980i 0.0605534 0.186364i
\(715\) 0 0
\(716\) −0.100813 0.310271i −0.00376756 0.0115954i
\(717\) −16.6074 + 12.0660i −0.620214 + 0.450612i
\(718\) 22.2361 0.829843
\(719\) 18.8435 13.6906i 0.702742 0.510572i −0.178082 0.984016i \(-0.556989\pi\)
0.880824 + 0.473443i \(0.156989\pi\)
\(720\) 0 0
\(721\) −4.28115 3.11044i −0.159438 0.115839i
\(722\) 23.9164 + 17.3763i 0.890077 + 0.646678i
\(723\) −0.781153 + 2.40414i −0.0290514 + 0.0894110i
\(724\) 0.180340 0.00670228
\(725\) 0 0
\(726\) −26.5623 −0.985820
\(727\) −7.59017 + 23.3601i −0.281504 + 0.866380i 0.705921 + 0.708291i \(0.250533\pi\)
−0.987425 + 0.158089i \(0.949467\pi\)
\(728\) 2.07295 + 1.50609i 0.0768286 + 0.0558192i
\(729\) −10.5172 7.64121i −0.389527 0.283008i
\(730\) 0 0
\(731\) −20.5623 + 14.9394i −0.760524 + 0.552553i
\(732\) −5.38197 −0.198923
\(733\) −16.1631 + 11.7432i −0.596998 + 0.433745i −0.844812 0.535063i \(-0.820288\pi\)
0.247814 + 0.968808i \(0.420288\pi\)
\(734\) 12.7812 + 39.3363i 0.471761 + 1.45193i
\(735\) 0 0
\(736\) 3.93363 12.1065i 0.144995 0.446250i
\(737\) 7.70820 + 23.7234i 0.283935 + 0.873863i
\(738\) 0.763932 + 2.35114i 0.0281207 + 0.0865467i
\(739\) 4.93769 15.1967i 0.181636 0.559018i −0.818238 0.574879i \(-0.805049\pi\)
0.999874 + 0.0158612i \(0.00504898\pi\)
\(740\) 0 0
\(741\) 0.489357 + 1.50609i 0.0179770 + 0.0553274i
\(742\) 2.80902 2.04087i 0.103122 0.0749227i
\(743\) −28.3607 −1.04045 −0.520226 0.854029i \(-0.674152\pi\)
−0.520226 + 0.854029i \(0.674152\pi\)
\(744\) 5.42705 3.94298i 0.198965 0.144557i
\(745\) 0 0
\(746\) −37.0066 26.8869i −1.35491 0.984398i
\(747\) 10.0902 + 7.33094i 0.369180 + 0.268225i
\(748\) −5.23607 + 16.1150i −0.191450 + 0.589221i
\(749\) −10.1459 −0.370723
\(750\) 0 0
\(751\) −5.11146 −0.186520 −0.0932598 0.995642i \(-0.529729\pi\)
−0.0932598 + 0.995642i \(0.529729\pi\)
\(752\) 0.927051 2.85317i 0.0338061 0.104044i
\(753\) −23.6074 17.1518i −0.860301 0.625045i
\(754\) −8.78115 6.37988i −0.319791 0.232342i
\(755\) 0 0
\(756\) 1.54508 1.12257i 0.0561942 0.0408275i
\(757\) −30.4164 −1.10550 −0.552752 0.833346i \(-0.686422\pi\)
−0.552752 + 0.833346i \(0.686422\pi\)
\(758\) −19.1074 + 13.8823i −0.694012 + 0.504229i
\(759\) −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 \(0.991459\pi\)
\(762\) 9.94427 + 30.6053i 0.360243 + 1.10871i
\(763\) −1.90983 5.87785i −0.0691405 0.212793i
\(764\) −0.347524 + 1.06957i −0.0125730 + 0.0386957i
\(765\) 0 0
\(766\) −16.6803 51.3368i −0.602685 1.85487i
\(767\) −16.2812 + 11.8290i −0.587878 + 0.427119i
\(768\) −13.5623 −0.489388
\(769\) −10.8541 + 7.88597i −0.391409 + 0.284375i −0.766033 0.642802i \(-0.777772\pi\)
0.374624 + 0.927177i \(0.377772\pi\)
\(770\) 0 0
\(771\) −18.4894 13.4333i −0.665878 0.483789i
\(772\) 3.85410 + 2.80017i 0.138712 + 0.100780i
\(773\) 11.1738 34.3893i 0.401892 1.23690i −0.521570 0.853208i \(-0.674654\pi\)
0.923462 0.383689i \(-0.125346\pi\)
\(774\) −15.7082 −0.564620
\(775\) 0 0
\(776\) −8.61803 −0.309369
\(777\) 0.0450850 0.138757i 0.00161741 0.00497789i
\(778\) −19.6353 14.2658i −0.703958 0.511455i
\(779\) 0.527864 + 0.383516i 0.0189127 + 0.0137409i
\(780\) 0 0