Properties

Label 125.2.e.a.24.2
Level $125$
Weight $2$
Character 125.24
Analytic conductor $0.998$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 24.2
Root \(-0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 125.24
Dual form 125.2.e.a.99.2

$q$-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 0.797522 0.603290i \(-0.206144\pi\)
0.290604 + 0.956844i \(0.406144\pi\)
\(3\) 0.587785 0.809017i 0.339358 0.467086i −0.604896 0.796305i \(-0.706785\pi\)
0.944254 + 0.329218i \(0.106785\pi\)
\(4\) 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 \(-0.962737\pi\)
0.993156 0.116797i \(-0.0372628\pi\)
\(8\) −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 −0.543161 0.839628i \(-0.682773\pi\)
0.0540944 + 0.998536i \(0.482773\pi\)
\(14\) 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 \(-0.981014\pi\)
0.251774 0.967786i \(-0.418986\pi\)
\(18\) 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 0.657441 0.753506i \(-0.271639\pi\)
0.0889808 + 0.996033i \(0.471639\pi\)
\(24\) −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 −0.327414 0.944881i \(-0.606177\pi\)
0.290504 + 0.956874i \(0.406177\pi\)
\(38\) 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 \(-0.879316\pi\)
0.928983 0.370122i \(-0.120684\pi\)
\(44\) −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 −0.834689 0.550722i \(-0.814353\pi\)
0.781700 + 0.623654i \(0.214353\pi\)
\(48\) −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 −0.925845 0.377904i \(-0.876645\pi\)
0.645510 + 0.763752i \(0.276645\pi\)
\(54\) 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 0.945052 0.326920i \(-0.106011\pi\)
−0.602957 + 0.797774i \(0.706011\pi\)
\(68\) 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 −0.238224 0.971210i \(-0.576565\pi\)
−0.763590 + 0.645701i \(0.776565\pi\)
\(74\) −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 0.961329 0.275404i \(-0.0888115\pi\)
−0.558991 + 0.829174i \(0.688811\pi\)
\(84\) −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 −0.678372 0.734718i \(-0.737314\pi\)
0.908387 + 0.418130i \(0.137314\pi\)
\(98\) 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 −0.485566 0.874200i \(-0.661386\pi\)
0.981462 + 0.191658i \(0.0613863\pi\)
\(104\) 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 \(0.291752\pi\)
−0.608548 + 0.793517i \(0.708248\pi\)
\(108\) 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 −0.942311 0.334740i \(-0.891352\pi\)
−0.565590 + 0.824687i \(0.691352\pi\)
\(114\) 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 −0.693837 0.720132i \(-0.744081\pi\)
−0.984609 + 0.174772i \(0.944081\pi\)
\(128\) −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 −0.751027 0.660271i \(-0.770441\pi\)
−0.219496 + 0.975613i \(0.570441\pi\)
\(138\) 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 \(-0.823709\pi\)
0.850514 0.525953i \(-0.176291\pi\)
\(158\) −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 −0.688581 0.725159i \(-0.741766\pi\)
−0.130836 + 0.991404i \(0.541766\pi\)
\(164\) 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 0.999556 0.0297794i \(-0.00948048\pi\)
−0.337202 + 0.941432i \(0.609480\pi\)
\(168\) 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 0.897970 0.440057i \(-0.145042\pi\)
0.467813 + 0.883827i \(0.345042\pi\)
\(174\) −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 \(0.0894808\pi\)
−0.960747 + 0.277424i \(0.910519\pi\)
\(194\) 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 −0.879573 0.475764i \(-0.842172\pi\)
0.724281 + 0.689505i \(0.242172\pi\)
\(198\) −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 0.303269 0.952905i \(-0.401922\pi\)
−0.314754 + 0.949173i \(0.601922\pi\)
\(224\) −2.09017 −0.139655
\(225\) 0 0
\(226\) −27.2705 −1.81401
\(227\) −14.0413 4.56231i −0.931956 0.302811i −0.196594 0.980485i \(-0.562988\pi\)
−0.735362 + 0.677674i \(0.762988\pi\)
\(228\) 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 0.861933 0.507021i \(-0.169254\pi\)
−0.748558 + 0.663069i \(0.769254\pi\)
\(234\) −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 \(-0.747427\pi\)
0.701367 0.712800i \(-0.252573\pi\)
\(258\) −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 0.0288905 0.999583i \(-0.490803\pi\)
0.610913 + 0.791698i \(0.290803\pi\)
\(264\) 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 0.913023 0.407908i \(-0.133742\pi\)
0.498889 + 0.866666i \(0.333742\pi\)
\(278\) −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 \(0.147436\pi\)
0.148474 + 0.988916i \(0.452564\pi\)
\(284\) 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 \(-0.806782\pi\)
0.821357 0.570415i \(-0.193218\pi\)
\(294\) 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 \(-0.915102\pi\)
0.964642 0.263565i \(-0.0848984\pi\)
\(308\) 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 0.178454 0.983948i \(-0.442890\pi\)
0.722723 + 0.691138i \(0.242890\pi\)
\(314\) 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 0.916431 0.400192i \(-0.131056\pi\)
−0.663798 + 0.747912i \(0.731056\pi\)
\(318\) 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 −0.0984135 0.995146i \(-0.531377\pi\)
0.505314 + 0.862936i \(0.331377\pi\)
\(338\) −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 −0.369686 0.929157i \(-0.620535\pi\)
0.997920 + 0.0644668i \(0.0205347\pi\)
\(348\) −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 −0.557833 0.829953i \(-0.688367\pi\)
0.961712 + 0.274061i \(0.0883670\pi\)
\(354\) 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 \(-0.967505\pi\)
0.210488 0.977597i \(-0.432495\pi\)
\(368\) 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 −0.485505 0.874234i \(-0.661364\pi\)
−0.906644 + 0.421897i \(0.861364\pi\)
\(374\) 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 \(-0.875192\pi\)
−0.0778591 0.996964i \(-0.524808\pi\)
\(384\) 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 \(0.459828\pi\)
−0.982388 + 0.186850i \(0.940172\pi\)
\(398\) 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 \(-0.976748\pi\)
0.238781 0.971073i \(-0.423252\pi\)
\(434\) −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 \(0.251915\pi\)
−0.702840 + 0.711348i \(0.748085\pi\)
\(444\) −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 \(0.167001\pi\)
−0.865500 + 0.500909i \(0.832999\pi\)
\(458\) 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 0.277250 0.960798i \(-0.410577\pi\)
0.789042 + 0.614339i \(0.210577\pi\)
\(464\) −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 \(0.0190563\pi\)
−0.251560 + 0.967842i \(0.580944\pi\)
\(468\) 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 −0.959303 0.282377i \(-0.908877\pi\)
−0.610116 + 0.792312i \(0.708877\pi\)
\(488\) −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 \(0.514046\pi\)
−0.936500 + 0.350669i \(0.885954\pi\)
\(504\) −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 0.0226305 0.999744i \(-0.492796\pi\)
−0.569326 + 0.822112i \(0.692796\pi\)
\(524\) −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 −0.452794 0.891615i \(-0.649573\pi\)
0.987897 + 0.155109i \(0.0495729\pi\)
\(548\) −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 \(-0.967819\pi\)
0.994894 0.100927i \(-0.0321809\pi\)
\(558\) 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 −0.453198 0.891410i \(-0.649717\pi\)
0.157312 + 0.987549i \(0.449717\pi\)
\(564\) −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 0.888414 0.459044i \(-0.151808\pi\)
0.448923 + 0.893571i \(0.351808\pi\)
\(578\) −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 −0.203306 0.979115i \(-0.565169\pi\)
0.411032 + 0.911621i \(0.365169\pi\)
\(588\) 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 \(-0.928086\pi\)
0.974588 0.224007i \(-0.0719137\pi\)
\(594\) −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 \(0.256646\pi\)
−0.692191 + 0.721715i \(0.743354\pi\)
\(608\) −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 −0.00685287 0.999977i \(-0.502181\pi\)
0.582227 + 0.813026i \(0.302181\pi\)
\(614\) 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 0.943525 0.331302i \(-0.107488\pi\)
−0.606652 + 0.794968i \(0.707488\pi\)
\(618\) 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 \(-0.791987\pi\)
0.793965 0.607964i \(-0.208013\pi\)
\(644\) 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 \(-0.544926\pi\)
0.985069 0.172158i \(-0.0550739\pi\)
\(648\) 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 −0.530905 0.847431i \(-0.678148\pi\)
0.970014 + 0.243050i \(0.0781480\pi\)
\(654\) −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 0.523650 0.851934i \(-0.324570\pi\)
−0.0771122 + 0.997022i \(0.524570\pi\)
\(674\) 12.7082 0.489502
\(675\) 0 0
\(676\) −5.90983 −0.227301
\(677\) −10.0984 3.28115i −0.388111 0.126105i 0.108460 0.994101i \(-0.465408\pi\)
−0.496571 + 0.867996i \(0.665408\pi\)
\(678\) −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 0.933183 0.359402i \(-0.117019\pi\)
−0.630181 + 0.776448i \(0.717019\pi\)
\(684\) 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 −0.158089 0.987425i \(-0.550533\pi\)
−0.708291 + 0.705921i \(0.750533\pi\)
\(728\) 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 0.968808 0.247814i \(-0.0797121\pi\)
−0.535063 + 0.844812i \(0.679712\pi\)
\(734\) −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 \(0.174152\pi\)
−0.854029 + 0.520226i \(0.825848\pi\)
\(744\) −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 \(-0.813578\pi\)
0.833346 0.552752i \(-0.186422\pi\)
\(758\) 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 −0.383689 0.923462i \(-0.625346\pi\)
−0.853208 + 0.521570i \(0.825346\pi\)
\(774\) 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