Properties

Label 625.2.e.c.374.2
Level $625$
Weight $2$
Character 625.374
Analytic conductor $4.991$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.e (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.99065012633\)
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 374.2
Root \(0.951057 + 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 625.374
Dual form 625.2.e.c.249.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.951057 + 1.30902i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034i q^{7} +(2.12663 - 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})\) \(q+(0.951057 + 1.30902i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034i q^{7} +(2.12663 - 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +(4.23607 - 3.07768i) q^{11} +(0.363271 - 0.500000i) q^{12} +(-1.08981 + 1.50000i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(3.92705 + 2.85317i) q^{16} +(4.97980 - 1.61803i) q^{17} -3.23607i q^{18} +(-0.263932 - 0.812299i) q^{19} +(0.190983 - 0.587785i) q^{21} +(8.05748 + 2.61803i) q^{22} +(2.21238 + 3.04508i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(2.93893 + 4.04508i) q^{27} +(-0.363271 - 0.118034i) q^{28} +(1.11803 - 3.44095i) q^{29} +(-0.927051 - 2.85317i) q^{31} +3.38197i q^{32} +(-4.97980 + 1.61803i) q^{33} +(6.85410 + 4.97980i) q^{34} +(1.00000 - 0.726543i) q^{36} +(-0.138757 + 0.190983i) q^{37} +(0.812299 - 1.11803i) q^{38} +(1.50000 - 1.08981i) q^{39} +(0.618034 + 0.449028i) q^{41} +(0.951057 - 0.309017i) q^{42} +4.85410i q^{43} +(1.00000 + 3.07768i) q^{44} +(-1.88197 + 5.79210i) q^{46} +(0.587785 + 0.190983i) q^{47} +(-2.85317 - 3.92705i) q^{48} +6.61803 q^{49} -5.23607 q^{51} +(-0.673542 - 0.927051i) q^{52} +(3.30220 + 1.07295i) q^{53} +(-2.50000 + 7.69421i) q^{54} +(0.427051 + 1.31433i) q^{56} +0.854102i q^{57} +(5.56758 - 1.80902i) q^{58} +(-8.78115 - 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(2.85317 - 3.92705i) q^{62} +(0.726543 - 1.00000i) q^{63} +(3.42705 - 2.48990i) q^{64} +(-6.85410 - 4.97980i) q^{66} +(-4.53077 + 1.47214i) q^{67} +3.23607i q^{68} +(-1.16312 - 3.57971i) q^{69} +(-2.04508 + 6.29412i) q^{71} +(-4.25325 - 1.38197i) q^{72} +(-5.29007 - 7.28115i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(1.90211 + 2.61803i) q^{77} +(2.85317 + 0.927051i) q^{78} +(2.50000 - 7.69421i) q^{79} +(0.309017 + 0.951057i) q^{81} +1.23607i q^{82} +(-5.93085 + 1.92705i) q^{83} +(0.309017 + 0.224514i) q^{84} +(-6.35410 + 4.61653i) q^{86} +(-2.12663 + 2.92705i) q^{87} +(6.88191 - 9.47214i) q^{88} +(-7.23607 + 5.25731i) q^{89} +(-0.927051 - 0.673542i) q^{91} +(-2.21238 + 0.718847i) q^{92} +3.00000i q^{93} +(0.309017 + 0.951057i) q^{94} +(1.04508 - 3.21644i) q^{96} +(-3.66547 - 1.19098i) q^{97} +(6.29412 + 8.66312i) q^{98} -10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9} + 16 q^{11} - 2 q^{14} + 18 q^{16} - 20 q^{19} + 6 q^{21} - 24 q^{26} + 6 q^{31} + 28 q^{34} + 8 q^{36} + 12 q^{39} - 4 q^{41} + 8 q^{44} - 24 q^{46} + 44 q^{49} - 24 q^{51} - 20 q^{54} - 10 q^{56} - 30 q^{59} - 34 q^{61} + 14 q^{64} - 28 q^{66} + 22 q^{69} + 6 q^{71} - 12 q^{74} + 40 q^{76} + 20 q^{79} - 2 q^{81} - 2 q^{84} - 24 q^{86} - 40 q^{89} + 6 q^{91} - 2 q^{94} - 14 q^{96} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.951057 + 1.30902i 0.672499 + 0.925615i 0.999814 0.0193004i \(-0.00614389\pi\)
−0.327315 + 0.944915i \(0.606144\pi\)
\(3\) −0.951057 0.309017i −0.549093 0.178411i 0.0213149 0.999773i \(-0.493215\pi\)
−0.570408 + 0.821362i \(0.693215\pi\)
\(4\) −0.190983 + 0.587785i −0.0954915 + 0.293893i
\(5\) 0 0
\(6\) −0.500000 1.53884i −0.204124 0.628230i
\(7\) 0.618034i 0.233595i 0.993156 + 0.116797i \(0.0372628\pi\)
−0.993156 + 0.116797i \(0.962737\pi\)
\(8\) 2.12663 0.690983i 0.751876 0.244299i
\(9\) −1.61803 1.17557i −0.539345 0.391857i
\(10\) 0 0
\(11\) 4.23607 3.07768i 1.27722 0.927957i 0.277757 0.960651i \(-0.410409\pi\)
0.999465 + 0.0326948i \(0.0104089\pi\)
\(12\) 0.363271 0.500000i 0.104867 0.144338i
\(13\) −1.08981 + 1.50000i −0.302260 + 0.416025i −0.932948 0.360011i \(-0.882773\pi\)
0.630688 + 0.776037i \(0.282773\pi\)
\(14\) −0.809017 + 0.587785i −0.216219 + 0.157092i
\(15\) 0 0
\(16\) 3.92705 + 2.85317i 0.981763 + 0.713292i
\(17\) 4.97980 1.61803i 1.20778 0.392431i 0.365161 0.930944i \(-0.381014\pi\)
0.842617 + 0.538513i \(0.181014\pi\)
\(18\) 3.23607i 0.762749i
\(19\) −0.263932 0.812299i −0.0605502 0.186354i 0.916206 0.400707i \(-0.131236\pi\)
−0.976756 + 0.214353i \(0.931236\pi\)
\(20\) 0 0
\(21\) 0.190983 0.587785i 0.0416759 0.128265i
\(22\) 8.05748 + 2.61803i 1.71786 + 0.558167i
\(23\) 2.21238 + 3.04508i 0.461314 + 0.634944i 0.974781 0.223165i \(-0.0716390\pi\)
−0.513467 + 0.858110i \(0.671639\pi\)
\(24\) −2.23607 −0.456435
\(25\) 0 0
\(26\) −3.00000 −0.588348
\(27\) 2.93893 + 4.04508i 0.565597 + 0.778477i
\(28\) −0.363271 0.118034i −0.0686518 0.0223063i
\(29\) 1.11803 3.44095i 0.207614 0.638969i −0.791982 0.610544i \(-0.790951\pi\)
0.999596 0.0284251i \(-0.00904922\pi\)
\(30\) 0 0
\(31\) −0.927051 2.85317i −0.166503 0.512444i 0.832641 0.553814i \(-0.186828\pi\)
−0.999144 + 0.0413693i \(0.986828\pi\)
\(32\) 3.38197i 0.597853i
\(33\) −4.97980 + 1.61803i −0.866871 + 0.281664i
\(34\) 6.85410 + 4.97980i 1.17547 + 0.854028i
\(35\) 0 0
\(36\) 1.00000 0.726543i 0.166667 0.121090i
\(37\) −0.138757 + 0.190983i −0.0228116 + 0.0313974i −0.820270 0.571976i \(-0.806177\pi\)
0.797459 + 0.603373i \(0.206177\pi\)
\(38\) 0.812299 1.11803i 0.131772 0.181369i
\(39\) 1.50000 1.08981i 0.240192 0.174510i
\(40\) 0 0
\(41\) 0.618034 + 0.449028i 0.0965207 + 0.0701264i 0.634999 0.772513i \(-0.281001\pi\)
−0.538478 + 0.842639i \(0.681001\pi\)
\(42\) 0.951057 0.309017i 0.146751 0.0476824i
\(43\) 4.85410i 0.740244i 0.928983 + 0.370122i \(0.120684\pi\)
−0.928983 + 0.370122i \(0.879316\pi\)
\(44\) 1.00000 + 3.07768i 0.150756 + 0.463978i
\(45\) 0 0
\(46\) −1.88197 + 5.79210i −0.277481 + 0.853998i
\(47\) 0.587785 + 0.190983i 0.0857373 + 0.0278577i 0.351572 0.936161i \(-0.385647\pi\)
−0.265834 + 0.964019i \(0.585647\pi\)
\(48\) −2.85317 3.92705i −0.411820 0.566821i
\(49\) 6.61803 0.945433
\(50\) 0 0
\(51\) −5.23607 −0.733196
\(52\) −0.673542 0.927051i −0.0934035 0.128559i
\(53\) 3.30220 + 1.07295i 0.453592 + 0.147381i 0.526898 0.849929i \(-0.323355\pi\)
−0.0733062 + 0.997309i \(0.523355\pi\)
\(54\) −2.50000 + 7.69421i −0.340207 + 1.04705i
\(55\) 0 0
\(56\) 0.427051 + 1.31433i 0.0570671 + 0.175634i
\(57\) 0.854102i 0.113129i
\(58\) 5.56758 1.80902i 0.731059 0.237536i
\(59\) −8.78115 6.37988i −1.14321 0.830590i −0.155646 0.987813i \(-0.549746\pi\)
−0.987563 + 0.157223i \(0.949746\pi\)
\(60\) 0 0
\(61\) −7.04508 + 5.11855i −0.902031 + 0.655364i −0.938987 0.343953i \(-0.888234\pi\)
0.0369561 + 0.999317i \(0.488234\pi\)
\(62\) 2.85317 3.92705i 0.362353 0.498736i
\(63\) 0.726543 1.00000i 0.0915358 0.125988i
\(64\) 3.42705 2.48990i 0.428381 0.311237i
\(65\) 0 0
\(66\) −6.85410 4.97980i −0.843682 0.612971i
\(67\) −4.53077 + 1.47214i −0.553521 + 0.179850i −0.572404 0.819972i \(-0.693989\pi\)
0.0188826 + 0.999822i \(0.493989\pi\)
\(68\) 3.23607i 0.392431i
\(69\) −1.16312 3.57971i −0.140023 0.430947i
\(70\) 0 0
\(71\) −2.04508 + 6.29412i −0.242707 + 0.746975i 0.753298 + 0.657679i \(0.228462\pi\)
−0.996005 + 0.0892960i \(0.971538\pi\)
\(72\) −4.25325 1.38197i −0.501251 0.162866i
\(73\) −5.29007 7.28115i −0.619156 0.852194i 0.378136 0.925750i \(-0.376565\pi\)
−0.997291 + 0.0735557i \(0.976565\pi\)
\(74\) −0.381966 −0.0444026
\(75\) 0 0
\(76\) 0.527864 0.0605502
\(77\) 1.90211 + 2.61803i 0.216766 + 0.298353i
\(78\) 2.85317 + 0.927051i 0.323058 + 0.104968i
\(79\) 2.50000 7.69421i 0.281272 0.865666i −0.706219 0.707993i \(-0.749601\pi\)
0.987491 0.157673i \(-0.0503992\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 1.23607i 0.136501i
\(83\) −5.93085 + 1.92705i −0.650996 + 0.211521i −0.615853 0.787861i \(-0.711189\pi\)
−0.0351426 + 0.999382i \(0.511189\pi\)
\(84\) 0.309017 + 0.224514i 0.0337165 + 0.0244965i
\(85\) 0 0
\(86\) −6.35410 + 4.61653i −0.685180 + 0.497813i
\(87\) −2.12663 + 2.92705i −0.227998 + 0.313813i
\(88\) 6.88191 9.47214i 0.733614 1.00973i
\(89\) −7.23607 + 5.25731i −0.767022 + 0.557274i −0.901056 0.433703i \(-0.857207\pi\)
0.134034 + 0.990977i \(0.457207\pi\)
\(90\) 0 0
\(91\) −0.927051 0.673542i −0.0971813 0.0706064i
\(92\) −2.21238 + 0.718847i −0.230657 + 0.0749450i
\(93\) 3.00000i 0.311086i
\(94\) 0.309017 + 0.951057i 0.0318727 + 0.0980940i
\(95\) 0 0
\(96\) 1.04508 3.21644i 0.106664 0.328277i
\(97\) −3.66547 1.19098i −0.372172 0.120926i 0.116958 0.993137i \(-0.462686\pi\)
−0.489130 + 0.872211i \(0.662686\pi\)
\(98\) 6.29412 + 8.66312i 0.635803 + 0.875107i
\(99\) −10.4721 −1.05249
\(100\) 0 0
\(101\) 1.47214 0.146483 0.0732415 0.997314i \(-0.476666\pi\)
0.0732415 + 0.997314i \(0.476666\pi\)
\(102\) −4.97980 6.85410i −0.493073 0.678657i
\(103\) −8.14324 2.64590i −0.802377 0.260708i −0.121011 0.992651i \(-0.538614\pi\)
−0.681366 + 0.731943i \(0.738614\pi\)
\(104\) −1.28115 + 3.94298i −0.125627 + 0.386641i
\(105\) 0 0
\(106\) 1.73607 + 5.34307i 0.168622 + 0.518965i
\(107\) 16.4164i 1.58703i −0.608548 0.793517i \(-0.708248\pi\)
0.608548 0.793517i \(-0.291752\pi\)
\(108\) −2.93893 + 0.954915i −0.282798 + 0.0918867i
\(109\) 8.09017 + 5.87785i 0.774898 + 0.562996i 0.903443 0.428707i \(-0.141031\pi\)
−0.128546 + 0.991704i \(0.541031\pi\)
\(110\) 0 0
\(111\) 0.190983 0.138757i 0.0181273 0.0131703i
\(112\) −1.76336 + 2.42705i −0.166621 + 0.229335i
\(113\) −9.90659 + 13.6353i −0.931934 + 1.28270i 0.0271666 + 0.999631i \(0.491352\pi\)
−0.959100 + 0.283066i \(0.908648\pi\)
\(114\) −1.11803 + 0.812299i −0.104713 + 0.0760788i
\(115\) 0 0
\(116\) 1.80902 + 1.31433i 0.167963 + 0.122032i
\(117\) 3.52671 1.14590i 0.326045 0.105938i
\(118\) 17.5623i 1.61674i
\(119\) 1.00000 + 3.07768i 0.0916698 + 0.282131i
\(120\) 0 0
\(121\) 5.07295 15.6129i 0.461177 1.41936i
\(122\) −13.4005 4.35410i −1.21323 0.394202i
\(123\) −0.449028 0.618034i −0.0404875 0.0557262i
\(124\) 1.85410 0.166503
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) −11.6902 16.0902i −1.03734 1.42777i −0.899294 0.437346i \(-0.855919\pi\)
−0.138043 0.990426i \(-0.544081\pi\)
\(128\) 12.9515 + 4.20820i 1.14476 + 0.371956i
\(129\) 1.50000 4.61653i 0.132068 0.406462i
\(130\) 0 0
\(131\) 2.10081 + 6.46564i 0.183549 + 0.564905i 0.999920 0.0126218i \(-0.00401775\pi\)
−0.816371 + 0.577527i \(0.804018\pi\)
\(132\) 3.23607i 0.281664i
\(133\) 0.502029 0.163119i 0.0435314 0.0141442i
\(134\) −6.23607 4.53077i −0.538714 0.391399i
\(135\) 0 0
\(136\) 9.47214 6.88191i 0.812229 0.590119i
\(137\) −7.02067 + 9.66312i −0.599816 + 0.825576i −0.995691 0.0927283i \(-0.970441\pi\)
0.395875 + 0.918304i \(0.370441\pi\)
\(138\) 3.57971 4.92705i 0.304725 0.419418i
\(139\) 4.04508 2.93893i 0.343100 0.249276i −0.402869 0.915258i \(-0.631987\pi\)
0.745968 + 0.665981i \(0.231987\pi\)
\(140\) 0 0
\(141\) −0.500000 0.363271i −0.0421076 0.0305930i
\(142\) −10.1841 + 3.30902i −0.854631 + 0.277687i
\(143\) 9.70820i 0.811841i
\(144\) −3.00000 9.23305i −0.250000 0.769421i
\(145\) 0 0
\(146\) 4.50000 13.8496i 0.372423 1.14620i
\(147\) −6.29412 2.04508i −0.519131 0.168676i
\(148\) −0.0857567 0.118034i −0.00704916 0.00970233i
\(149\) 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 \(0.298128\pi\)
\(152\) −1.12257 1.54508i −0.0910524 0.125323i
\(153\) −9.95959 3.23607i −0.805185 0.261621i
\(154\) −1.61803 + 4.97980i −0.130385 + 0.401283i
\(155\) 0 0
\(156\) 0.354102 + 1.08981i 0.0283508 + 0.0872549i
\(157\) 13.1803i 1.05191i 0.850514 + 0.525953i \(0.176291\pi\)
−0.850514 + 0.525953i \(0.823709\pi\)
\(158\) 12.4495 4.04508i 0.990428 0.321810i
\(159\) −2.80902 2.04087i −0.222770 0.161852i
\(160\) 0 0
\(161\) −1.88197 + 1.36733i −0.148320 + 0.107761i
\(162\) −0.951057 + 1.30902i −0.0747221 + 0.102846i
\(163\) −6.46564 + 8.89919i −0.506428 + 0.697038i −0.983312 0.181928i \(-0.941766\pi\)
0.476884 + 0.878966i \(0.341766\pi\)
\(164\) −0.381966 + 0.277515i −0.0298265 + 0.0216702i
\(165\) 0 0
\(166\) −8.16312 5.93085i −0.633581 0.460323i
\(167\) −13.8496 + 4.50000i −1.07171 + 0.348220i −0.791154 0.611617i \(-0.790520\pi\)
−0.280558 + 0.959837i \(0.590520\pi\)
\(168\) 1.38197i 0.106621i
\(169\) 2.95492 + 9.09429i 0.227301 + 0.699561i
\(170\) 0 0
\(171\) −0.527864 + 1.62460i −0.0403668 + 0.124236i
\(172\) −2.85317 0.927051i −0.217552 0.0706870i
\(173\) 11.1024 + 15.2812i 0.844100 + 1.16180i 0.985132 + 0.171799i \(0.0549581\pi\)
−0.141032 + 0.990005i \(0.545042\pi\)
\(174\) −5.85410 −0.443798
\(175\) 0 0
\(176\) 25.4164 1.91583
\(177\) 6.37988 + 8.78115i 0.479541 + 0.660032i
\(178\) −13.7638 4.47214i −1.03164 0.335201i
\(179\) 0.163119 0.502029i 0.0121921 0.0375234i −0.944775 0.327719i \(-0.893720\pi\)
0.956967 + 0.290195i \(0.0937202\pi\)
\(180\) 0 0
\(181\) 0.0901699 + 0.277515i 0.00670228 + 0.0206275i 0.954352 0.298685i \(-0.0965480\pi\)
−0.947649 + 0.319313i \(0.896548\pi\)
\(182\) 1.85410i 0.137435i
\(183\) 8.28199 2.69098i 0.612223 0.198923i
\(184\) 6.80902 + 4.94704i 0.501967 + 0.364701i
\(185\) 0 0
\(186\) −3.92705 + 2.85317i −0.287945 + 0.209205i
\(187\) 16.1150 22.1803i 1.17844 1.62199i
\(188\) −0.224514 + 0.309017i −0.0163744 + 0.0225374i
\(189\) −2.50000 + 1.81636i −0.181848 + 0.132120i
\(190\) 0 0
\(191\) 1.47214 + 1.06957i 0.106520 + 0.0773913i 0.639770 0.768566i \(-0.279030\pi\)
−0.533250 + 0.845958i \(0.679030\pi\)
\(192\) −4.02874 + 1.30902i −0.290749 + 0.0944702i
\(193\) 7.70820i 0.554849i −0.960747 0.277424i \(-0.910519\pi\)
0.960747 0.277424i \(-0.0894808\pi\)
\(194\) −1.92705 5.93085i −0.138354 0.425810i
\(195\) 0 0
\(196\) −1.26393 + 3.88998i −0.0902809 + 0.277856i
\(197\) 3.52671 + 1.14590i 0.251268 + 0.0816419i 0.431943 0.901901i \(-0.357828\pi\)
−0.180675 + 0.983543i \(0.557828\pi\)
\(198\) −9.95959 13.7082i −0.707797 0.974200i
\(199\) 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
\(202\) 1.40008 + 1.92705i 0.0985096 + 0.135587i
\(203\) 2.12663 + 0.690983i 0.149260 + 0.0484975i
\(204\) 1.00000 3.07768i 0.0700140 0.215481i
\(205\) 0 0
\(206\) −4.28115 13.1760i −0.298282 0.918018i
\(207\) 7.52786i 0.523223i
\(208\) −8.55951 + 2.78115i −0.593495 + 0.192838i
\(209\) −3.61803 2.62866i −0.250265 0.181828i
\(210\) 0 0
\(211\) 7.42705 5.39607i 0.511299 0.371481i −0.302017 0.953303i \(-0.597660\pi\)
0.813316 + 0.581822i \(0.197660\pi\)
\(212\) −1.26133 + 1.73607i −0.0866283 + 0.119234i
\(213\) 3.88998 5.35410i 0.266537 0.366857i
\(214\) 21.4894 15.6129i 1.46898 1.06728i
\(215\) 0 0
\(216\) 9.04508 + 6.57164i 0.615440 + 0.447143i
\(217\) 1.76336 0.572949i 0.119704 0.0388943i
\(218\) 16.1803i 1.09587i
\(219\) 2.78115 + 8.55951i 0.187933 + 0.578398i
\(220\) 0 0
\(221\) −3.00000 + 9.23305i −0.201802 + 0.621082i
\(222\) 0.363271 + 0.118034i 0.0243812 + 0.00792192i
\(223\) −0.106001 0.145898i −0.00709836 0.00977005i 0.805453 0.592660i \(-0.201922\pi\)
−0.812551 + 0.582890i \(0.801922\pi\)
\(224\) −2.09017 −0.139655
\(225\) 0 0
\(226\) −27.2705 −1.81401
\(227\) −8.67802 11.9443i −0.575981 0.792769i 0.417267 0.908784i \(-0.362988\pi\)
−0.993247 + 0.116015i \(0.962988\pi\)
\(228\) −0.502029 0.163119i −0.0332477 0.0108028i
\(229\) −6.70820 + 20.6457i −0.443291 + 1.36431i 0.441057 + 0.897479i \(0.354604\pi\)
−0.884348 + 0.466829i \(0.845396\pi\)
\(230\) 0 0
\(231\) −1.00000 3.07768i −0.0657952 0.202497i
\(232\) 8.09017i 0.531146i
\(233\) −2.80017 + 0.909830i −0.183445 + 0.0596049i −0.399299 0.916821i \(-0.630746\pi\)
0.215854 + 0.976426i \(0.430746\pi\)
\(234\) 4.85410 + 3.52671i 0.317323 + 0.230548i
\(235\) 0 0
\(236\) 5.42705 3.94298i 0.353271 0.256666i
\(237\) −4.75528 + 6.54508i −0.308889 + 0.425149i
\(238\) −3.07768 + 4.23607i −0.199497 + 0.274584i
\(239\) −16.6074 + 12.0660i −1.07424 + 0.780483i −0.976670 0.214745i \(-0.931108\pi\)
−0.0975727 + 0.995228i \(0.531108\pi\)
\(240\) 0 0
\(241\) −2.04508 1.48584i −0.131736 0.0957114i 0.519966 0.854187i \(-0.325945\pi\)
−0.651702 + 0.758475i \(0.725945\pi\)
\(242\) 25.2623 8.20820i 1.62392 0.527643i
\(243\) 16.0000i 1.02640i
\(244\) −1.66312 5.11855i −0.106470 0.327682i
\(245\) 0 0
\(246\) 0.381966 1.17557i 0.0243533 0.0749516i
\(247\) 1.50609 + 0.489357i 0.0958299 + 0.0311370i
\(248\) −3.94298 5.42705i −0.250380 0.344618i
\(249\) 6.23607 0.395195
\(250\) 0 0
\(251\) −29.1803 −1.84185 −0.920923 0.389744i \(-0.872564\pi\)
−0.920923 + 0.389744i \(0.872564\pi\)
\(252\) 0.449028 + 0.618034i 0.0282861 + 0.0389325i
\(253\) 18.7436 + 6.09017i 1.17840 + 0.382886i
\(254\) 9.94427 30.6053i 0.623959 1.92035i
\(255\) 0 0
\(256\) 4.19098 + 12.8985i 0.261936 + 0.806157i
\(257\) 22.8541i 1.42560i 0.701367 + 0.712800i \(0.252573\pi\)
−0.701367 + 0.712800i \(0.747427\pi\)
\(258\) 7.46969 2.42705i 0.465043 0.151102i
\(259\) −0.118034 0.0857567i −0.00733428 0.00532866i
\(260\) 0 0
\(261\) −5.85410 + 4.25325i −0.362360 + 0.263270i
\(262\) −6.46564 + 8.89919i −0.399448 + 0.549794i
\(263\) 6.41264 8.82624i 0.395420 0.544249i −0.564167 0.825661i \(-0.690803\pi\)
0.959587 + 0.281412i \(0.0908026\pi\)
\(264\) −9.47214 + 6.88191i −0.582970 + 0.423552i
\(265\) 0 0
\(266\) 0.690983 + 0.502029i 0.0423669 + 0.0307813i
\(267\) 8.50651 2.76393i 0.520590 0.169150i
\(268\) 2.94427i 0.179850i
\(269\) 3.94427 + 12.1392i 0.240487 + 0.740141i 0.996346 + 0.0854076i \(0.0272192\pi\)
−0.755860 + 0.654734i \(0.772781\pi\)
\(270\) 0 0
\(271\) −2.47214 + 7.60845i −0.150172 + 0.462181i −0.997640 0.0686657i \(-0.978126\pi\)
0.847468 + 0.530846i \(0.178126\pi\)
\(272\) 24.1724 + 7.85410i 1.46567 + 0.476225i
\(273\) 0.673542 + 0.927051i 0.0407646 + 0.0561077i
\(274\) −19.3262 −1.16754
\(275\) 0 0
\(276\) 2.32624 0.140023
\(277\) 14.5231 + 19.9894i 0.872610 + 1.20104i 0.978413 + 0.206657i \(0.0662584\pi\)
−0.105804 + 0.994387i \(0.533742\pi\)
\(278\) 7.69421 + 2.50000i 0.461468 + 0.149940i
\(279\) −1.85410 + 5.70634i −0.111002 + 0.341630i
\(280\) 0 0
\(281\) 3.11803 + 9.59632i 0.186006 + 0.572469i 0.999964 0.00845524i \(-0.00269142\pi\)
−0.813958 + 0.580924i \(0.802691\pi\)
\(282\) 1.00000i 0.0595491i
\(283\) −28.3929 + 9.22542i −1.68778 + 0.548395i −0.986396 0.164384i \(-0.947436\pi\)
−0.701389 + 0.712779i \(0.747436\pi\)
\(284\) −3.30902 2.40414i −0.196354 0.142660i
\(285\) 0 0
\(286\) −12.7082 + 9.23305i −0.751452 + 0.545962i
\(287\) −0.277515 + 0.381966i −0.0163812 + 0.0225467i
\(288\) 3.97574 5.47214i 0.234273 0.322449i
\(289\) 8.42705 6.12261i 0.495709 0.360154i
\(290\) 0 0
\(291\) 3.11803 + 2.26538i 0.182782 + 0.132799i
\(292\) 5.29007 1.71885i 0.309578 0.100588i
\(293\) 19.5279i 1.14083i 0.821357 + 0.570415i \(0.193218\pi\)
−0.821357 + 0.570415i \(0.806782\pi\)
\(294\) −3.30902 10.1841i −0.192986 0.593949i
\(295\) 0 0
\(296\) −0.163119 + 0.502029i −0.00948110 + 0.0291798i
\(297\) 24.8990 + 8.09017i 1.44479 + 0.469439i
\(298\) 3.75123 + 5.16312i 0.217303 + 0.299091i
\(299\) −6.97871 −0.403589
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) 13.8496 + 19.0623i 0.796954 + 1.09691i
\(303\) −1.40008 0.454915i −0.0804328 0.0261342i
\(304\) 1.28115 3.94298i 0.0734792 0.226146i
\(305\) 0 0
\(306\) −5.23607 16.1150i −0.299326 0.921231i
\(307\) 9.23607i 0.527130i 0.964642 + 0.263565i \(0.0848984\pi\)
−0.964642 + 0.263565i \(0.915102\pi\)
\(308\) −1.90211 + 0.618034i −0.108383 + 0.0352158i
\(309\) 6.92705 + 5.03280i 0.394066 + 0.286306i
\(310\) 0 0
\(311\) −6.88197 + 5.00004i −0.390240 + 0.283526i −0.765554 0.643372i \(-0.777535\pi\)
0.375314 + 0.926898i \(0.377535\pi\)
\(312\) 2.43690 3.35410i 0.137962 0.189889i
\(313\) 9.85359 13.5623i 0.556958 0.766587i −0.433978 0.900924i \(-0.642890\pi\)
0.990936 + 0.134337i \(0.0428904\pi\)
\(314\) −17.2533 + 12.5352i −0.973659 + 0.707405i
\(315\) 0 0
\(316\) 4.04508 + 2.93893i 0.227554 + 0.165328i
\(317\) −7.27794 + 2.36475i −0.408770 + 0.132817i −0.506182 0.862427i \(-0.668944\pi\)
0.0974121 + 0.995244i \(0.468944\pi\)
\(318\) 5.61803i 0.315044i
\(319\) −5.85410 18.0171i −0.327767 1.00876i
\(320\) 0 0
\(321\) −5.07295 + 15.6129i −0.283144 + 0.871429i
\(322\) −3.57971 1.16312i −0.199490 0.0648181i
\(323\) −2.62866 3.61803i −0.146262 0.201313i
\(324\) −0.618034 −0.0343352
\(325\) 0 0
\(326\) −17.7984 −0.985761
\(327\) −5.87785 8.09017i −0.325046 0.447387i
\(328\) 1.62460 + 0.527864i 0.0897034 + 0.0291464i
\(329\) −0.118034 + 0.363271i −0.00650742 + 0.0200278i
\(330\) 0 0
\(331\) −7.14590 21.9928i −0.392774 1.20883i −0.930682 0.365830i \(-0.880785\pi\)
0.537907 0.843004i \(-0.319215\pi\)
\(332\) 3.85410i 0.211521i
\(333\) 0.449028 0.145898i 0.0246066 0.00799516i
\(334\) −19.0623 13.8496i −1.04304 0.757815i
\(335\) 0 0
\(336\) 2.42705 1.76336i 0.132406 0.0961989i
\(337\) 4.61653 6.35410i 0.251478 0.346130i −0.664550 0.747244i \(-0.731377\pi\)
0.916028 + 0.401114i \(0.131377\pi\)
\(338\) −9.09429 + 12.5172i −0.494664 + 0.680847i
\(339\) 13.6353 9.90659i 0.740565 0.538052i
\(340\) 0 0
\(341\) −12.7082 9.23305i −0.688188 0.499998i
\(342\) −2.62866 + 0.854102i −0.142141 + 0.0461845i
\(343\) 8.41641i 0.454443i
\(344\) 3.35410 + 10.3229i 0.180841 + 0.556572i
\(345\) 0 0
\(346\) −9.44427 + 29.0665i −0.507727 + 1.56262i
\(347\) −18.9354 6.15248i −1.01650 0.330282i −0.247063 0.969000i \(-0.579465\pi\)
−0.769441 + 0.638717i \(0.779465\pi\)
\(348\) −1.31433 1.80902i −0.0704554 0.0969735i
\(349\) −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
\(352\) 10.4086 + 14.3262i 0.554781 + 0.763591i
\(353\) −12.2780 3.98936i −0.653491 0.212332i −0.0365381 0.999332i \(-0.511633\pi\)
−0.616953 + 0.787000i \(0.711633\pi\)
\(354\) −5.42705 + 16.7027i −0.288445 + 0.887741i
\(355\) 0 0
\(356\) −1.70820 5.25731i −0.0905346 0.278637i
\(357\) 3.23607i 0.171271i
\(358\) 0.812299 0.263932i 0.0429313 0.0139492i
\(359\) 11.1180 + 8.07772i 0.586787 + 0.426326i 0.841165 0.540779i \(-0.181870\pi\)
−0.254377 + 0.967105i \(0.581870\pi\)
\(360\) 0 0
\(361\) 14.7812 10.7391i 0.777955 0.565218i
\(362\) −0.277515 + 0.381966i −0.0145858 + 0.0200757i
\(363\) −9.64932 + 13.2812i −0.506458 + 0.697080i
\(364\) 0.572949 0.416272i 0.0300307 0.0218186i
\(365\) 0 0
\(366\) 11.3992 + 8.28199i 0.595845 + 0.432907i
\(367\) 24.3112 7.89919i 1.26903 0.412334i 0.404329 0.914614i \(-0.367505\pi\)
0.864705 + 0.502279i \(0.167505\pi\)
\(368\) 18.2705i 0.952416i
\(369\) −0.472136 1.45309i −0.0245784 0.0756446i
\(370\) 0 0
\(371\) −0.663119 + 2.04087i −0.0344274 + 0.105957i
\(372\) −1.76336 0.572949i −0.0914257 0.0297060i
\(373\) −16.6170 22.8713i −0.860395 1.18423i −0.981475 0.191589i \(-0.938636\pi\)
0.121080 0.992643i \(-0.461364\pi\)
\(374\) 44.3607 2.29384
\(375\) 0 0
\(376\) 1.38197 0.0712695
\(377\) 3.94298 + 5.42705i 0.203074 + 0.279507i
\(378\) −4.75528 1.54508i −0.244585 0.0794706i
\(379\) −4.51064 + 13.8823i −0.231696 + 0.713087i 0.765846 + 0.643024i \(0.222320\pi\)
−0.997543 + 0.0700639i \(0.977680\pi\)
\(380\) 0 0
\(381\) 6.14590 + 18.9151i 0.314864 + 0.969051i
\(382\) 2.94427i 0.150642i
\(383\) 31.7279 10.3090i 1.62122 0.526766i 0.648990 0.760797i \(-0.275192\pi\)
0.972229 + 0.234031i \(0.0751916\pi\)
\(384\) −11.0172 8.00448i −0.562220 0.408477i
\(385\) 0 0
\(386\) 10.0902 7.33094i 0.513576 0.373135i
\(387\) 5.70634 7.85410i 0.290070 0.399246i
\(388\) 1.40008 1.92705i 0.0710785 0.0978312i
\(389\) 12.1353 8.81678i 0.615282 0.447028i −0.235988 0.971756i \(-0.575833\pi\)
0.851270 + 0.524727i \(0.175833\pi\)
\(390\) 0 0
\(391\) 15.9443 + 11.5842i 0.806336 + 0.585838i
\(392\) 14.0741 4.57295i 0.710849 0.230969i
\(393\) 6.79837i 0.342933i
\(394\) 1.85410 + 5.70634i 0.0934083 + 0.287481i
\(395\) 0 0
\(396\) 2.00000 6.15537i 0.100504 0.309319i
\(397\) 27.6134 + 8.97214i 1.38588 + 0.450299i 0.904597 0.426268i \(-0.140172\pi\)
0.481280 + 0.876567i \(0.340172\pi\)
\(398\) 16.7027 + 22.9894i 0.837233 + 1.15235i
\(399\) −0.527864 −0.0264263
\(400\) 0 0
\(401\) 26.5967 1.32818 0.664089 0.747653i \(-0.268820\pi\)
0.664089 + 0.747653i \(0.268820\pi\)
\(402\) 4.53077 + 6.23607i 0.225974 + 0.311027i
\(403\) 5.29007 + 1.71885i 0.263517 + 0.0856219i
\(404\) −0.281153 + 0.865300i −0.0139879 + 0.0430503i
\(405\) 0 0
\(406\) 1.11803 + 3.44095i 0.0554871 + 0.170772i
\(407\) 1.23607i 0.0612696i
\(408\) −11.1352 + 3.61803i −0.551273 + 0.179119i
\(409\) 1.28115 + 0.930812i 0.0633489 + 0.0460257i 0.619009 0.785384i \(-0.287534\pi\)
−0.555660 + 0.831410i \(0.687534\pi\)
\(410\) 0 0
\(411\) 9.66312 7.02067i 0.476647 0.346304i
\(412\) 3.11044 4.28115i 0.153240 0.210917i
\(413\) 3.94298 5.42705i 0.194022 0.267048i
\(414\) 9.85410 7.15942i 0.484303 0.351867i
\(415\) 0 0
\(416\) −5.07295 3.68571i −0.248722 0.180707i
\(417\) −4.75528 + 1.54508i −0.232867 + 0.0756631i
\(418\) 7.23607i 0.353928i
\(419\) 2.92705 + 9.00854i 0.142996 + 0.440096i 0.996748 0.0805840i \(-0.0256785\pi\)
−0.853752 + 0.520680i \(0.825679\pi\)
\(420\) 0 0
\(421\) 9.88854 30.4338i 0.481938 1.48325i −0.354429 0.935083i \(-0.615325\pi\)
0.836367 0.548170i \(-0.184675\pi\)
\(422\) 14.1271 + 4.59017i 0.687696 + 0.223446i
\(423\) −0.726543 1.00000i −0.0353257 0.0486217i
\(424\) 7.76393 0.377050
\(425\) 0 0
\(426\) 10.7082 0.518814
\(427\) −3.16344 4.35410i −0.153090 0.210710i
\(428\) 9.64932 + 3.13525i 0.466418 + 0.151548i
\(429\) 3.00000 9.23305i 0.144841 0.445776i
\(430\) 0 0
\(431\) −9.21885 28.3727i −0.444056 1.36666i −0.883515 0.468402i \(-0.844830\pi\)
0.439459 0.898263i \(-0.355170\pi\)
\(432\) 24.2705i 1.16772i
\(433\) 25.5398 8.29837i 1.22736 0.398794i 0.377605 0.925967i \(-0.376748\pi\)
0.849758 + 0.527173i \(0.176748\pi\)
\(434\) 2.42705 + 1.76336i 0.116502 + 0.0846438i
\(435\) 0 0
\(436\) −5.00000 + 3.63271i −0.239457 + 0.173975i
\(437\) 1.88960 2.60081i 0.0903919 0.124414i
\(438\) −8.55951 + 11.7812i −0.408989 + 0.562925i
\(439\) −33.1525 + 24.0867i −1.58228 + 1.14959i −0.668261 + 0.743927i \(0.732961\pi\)
−0.914021 + 0.405667i \(0.867039\pi\)
\(440\) 0 0
\(441\) −10.7082 7.77997i −0.509914 0.370475i
\(442\) −14.9394 + 4.85410i −0.710594 + 0.230886i
\(443\) 29.9443i 1.42270i −0.702840 0.711348i \(-0.748085\pi\)
0.702840 0.711348i \(-0.251915\pi\)
\(444\) 0.0450850 + 0.138757i 0.00213964 + 0.00658513i
\(445\) 0 0
\(446\) 0.0901699 0.277515i 0.00426967 0.0131407i
\(447\) −3.75123 1.21885i −0.177427 0.0576495i
\(448\) 1.53884 + 2.11803i 0.0727034 + 0.100068i
\(449\) −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
\(452\) −6.12261 8.42705i −0.287983 0.396375i
\(453\) −13.8496 4.50000i −0.650710 0.211428i
\(454\) 7.38197 22.7194i 0.346453 1.06627i
\(455\) 0 0
\(456\) 0.590170 + 1.81636i 0.0276372 + 0.0850587i
\(457\) 21.4164i 1.00182i −0.865500 0.500909i \(-0.832999\pi\)
0.865500 0.500909i \(-0.167001\pi\)
\(458\) −33.4055 + 10.8541i −1.56094 + 0.507179i
\(459\) 21.1803 + 15.3884i 0.988614 + 0.718270i
\(460\) 0 0
\(461\) −0.663119 + 0.481784i −0.0308845 + 0.0224389i −0.603120 0.797650i \(-0.706076\pi\)
0.572236 + 0.820089i \(0.306076\pi\)
\(462\) 3.07768 4.23607i 0.143187 0.197080i
\(463\) 14.1801 19.5172i 0.659005 0.907042i −0.340443 0.940265i \(-0.610577\pi\)
0.999448 + 0.0332229i \(0.0105771\pi\)
\(464\) 14.2082 10.3229i 0.659599 0.479227i
\(465\) 0 0
\(466\) −3.85410 2.80017i −0.178538 0.129715i
\(467\) −26.1073 + 8.48278i −1.20810 + 0.392536i −0.842736 0.538328i \(-0.819056\pi\)
−0.365367 + 0.930864i \(0.619056\pi\)
\(468\) 2.29180i 0.105938i
\(469\) −0.909830 2.80017i −0.0420120 0.129300i
\(470\) 0 0
\(471\) 4.07295 12.5352i 0.187672 0.577594i
\(472\) −23.0826 7.50000i −1.06246 0.345215i
\(473\) 14.9394 + 20.5623i 0.686914 + 0.945456i
\(474\) −13.0902 −0.601251
\(475\) 0 0
\(476\) −2.00000 −0.0916698
\(477\) −4.08174 5.61803i −0.186890 0.257232i
\(478\) −31.5891 10.2639i −1.44485 0.469461i
\(479\) 3.35410 10.3229i 0.153253 0.471664i −0.844727 0.535198i \(-0.820237\pi\)
0.997980 + 0.0635340i \(0.0202371\pi\)
\(480\) 0 0
\(481\) −0.135255 0.416272i −0.00616709 0.0189804i
\(482\) 4.09017i 0.186302i
\(483\) 2.21238 0.718847i 0.100667 0.0327087i
\(484\) 8.20820 + 5.96361i 0.373100 + 0.271073i
\(485\) 0 0
\(486\) 20.9443 15.2169i 0.950051 0.690253i
\(487\) −21.4050 + 29.4615i −0.969954 + 1.33503i −0.0278844 + 0.999611i \(0.508877\pi\)
−0.942070 + 0.335417i \(0.891123\pi\)
\(488\) −11.4454 + 15.7533i −0.518110 + 0.713118i
\(489\) 8.89919 6.46564i 0.402435 0.292386i
\(490\) 0 0
\(491\) 34.9894 + 25.4213i 1.57905 + 1.14725i 0.917776 + 0.397099i \(0.129983\pi\)
0.661272 + 0.750147i \(0.270017\pi\)
\(492\) 0.449028 0.145898i 0.0202437 0.00657759i
\(493\) 18.9443i 0.853207i
\(494\) 0.791796 + 2.43690i 0.0356246 + 0.109641i
\(495\) 0 0
\(496\) 4.50000 13.8496i 0.202056 0.621864i
\(497\) −3.88998 1.26393i −0.174490 0.0566951i
\(498\) 5.93085 + 8.16312i 0.265768 + 0.365798i
\(499\) −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
\(502\) −27.7522 38.1976i −1.23864 1.70484i
\(503\) 35.5851 + 11.5623i 1.58666 + 0.515538i 0.963762 0.266764i \(-0.0859543\pi\)
0.622900 + 0.782301i \(0.285954\pi\)
\(504\) 0.854102 2.62866i 0.0380447 0.117090i
\(505\) 0 0
\(506\) 9.85410 + 30.3278i 0.438068 + 1.34824i
\(507\) 9.56231i 0.424677i
\(508\) 11.6902 3.79837i 0.518668 0.168526i
\(509\) −16.4443 11.9475i −0.728880 0.529562i 0.160329 0.987064i \(-0.448744\pi\)
−0.889209 + 0.457502i \(0.848744\pi\)
\(510\) 0 0
\(511\) 4.50000 3.26944i 0.199068 0.144632i
\(512\) 3.11044 4.28115i 0.137463 0.189202i
\(513\) 2.51014 3.45492i 0.110826 0.152538i
\(514\) −29.9164 + 21.7355i −1.31956 + 0.958714i
\(515\) 0 0
\(516\) 2.42705 + 1.76336i 0.106845 + 0.0776274i
\(517\) 3.07768 1.00000i 0.135356 0.0439799i
\(518\) 0.236068i 0.0103722i
\(519\) −5.83688 17.9641i −0.256211 0.788535i
\(520\) 0 0
\(521\) 9.07295 27.9237i 0.397493 1.22336i −0.529510 0.848304i \(-0.677624\pi\)
0.927003 0.375054i \(-0.122376\pi\)
\(522\) −11.1352 3.61803i −0.487373 0.158357i
\(523\) −7.72696 10.6353i −0.337877 0.465047i 0.605943 0.795508i \(-0.292796\pi\)
−0.943820 + 0.330461i \(0.892796\pi\)
\(524\) −4.20163 −0.183549
\(525\) 0 0
\(526\) 17.6525 0.769685
\(527\) −9.23305 12.7082i −0.402198 0.553578i
\(528\) −24.1724 7.85410i −1.05197 0.341806i
\(529\) 2.72949 8.40051i 0.118673 0.365239i
\(530\) 0 0
\(531\) 6.70820 + 20.6457i 0.291111 + 0.895948i
\(532\) 0.326238i 0.0141442i
\(533\) −1.34708 + 0.437694i −0.0583487 + 0.0189586i
\(534\) 11.7082 + 8.50651i 0.506664 + 0.368113i
\(535\) 0 0
\(536\) −8.61803 + 6.26137i −0.372242 + 0.270450i
\(537\) −0.310271 + 0.427051i −0.0133892 + 0.0184286i
\(538\) −12.1392 + 16.7082i −0.523359 + 0.720342i
\(539\) 28.0344 20.3682i 1.20753 0.877321i
\(540\) 0 0
\(541\) −21.9443 15.9434i −0.943458 0.685462i 0.00579261 0.999983i \(-0.498156\pi\)
−0.949251 + 0.314521i \(0.898156\pi\)
\(542\) −12.3107 + 4.00000i −0.528791 + 0.171815i
\(543\) 0.291796i 0.0125222i
\(544\) 5.47214 + 16.8415i 0.234616 + 0.722073i
\(545\) 0 0
\(546\) −0.572949 + 1.76336i −0.0245200 + 0.0754647i
\(547\) −20.2497 6.57953i −0.865815 0.281320i −0.157760 0.987478i \(-0.550427\pi\)
−0.708055 + 0.706157i \(0.750427\pi\)
\(548\) −4.33901 5.97214i −0.185353 0.255117i
\(549\) 17.4164 0.743314
\(550\) 0 0
\(551\) −3.09017 −0.131646
\(552\) −4.94704 6.80902i −0.210560 0.289811i
\(553\) 4.75528 + 1.54508i 0.202215 + 0.0657037i
\(554\) −12.3541 + 38.0220i −0.524875 + 1.61540i
\(555\) 0 0
\(556\) 0.954915 + 2.93893i 0.0404974 + 0.124638i
\(557\) 4.76393i 0.201854i 0.994894 + 0.100927i \(0.0321809\pi\)
−0.994894 + 0.100927i \(0.967819\pi\)
\(558\) −9.23305 + 3.00000i −0.390866 + 0.127000i
\(559\) −7.28115 5.29007i −0.307960 0.223746i
\(560\) 0 0
\(561\) −22.1803 + 16.1150i −0.936455 + 0.680374i
\(562\) −9.59632 + 13.2082i −0.404796 + 0.557154i
\(563\) −4.33901 + 5.97214i −0.182868 + 0.251696i −0.890603 0.454782i \(-0.849717\pi\)
0.707735 + 0.706478i \(0.249717\pi\)
\(564\) 0.309017 0.224514i 0.0130120 0.00945374i
\(565\) 0 0
\(566\) −39.0795 28.3929i −1.64264 1.19344i
\(567\) −0.587785 + 0.190983i −0.0246847 + 0.00802053i
\(568\) 14.7984i 0.620926i
\(569\) −6.34346 19.5232i −0.265932 0.818453i −0.991477 0.130279i \(-0.958413\pi\)
0.725546 0.688174i \(-0.241587\pi\)
\(570\) 0 0
\(571\) −2.51064 + 7.72696i −0.105067 + 0.323363i −0.989746 0.142837i \(-0.954377\pi\)
0.884679 + 0.466201i \(0.154377\pi\)
\(572\) −5.70634 1.85410i −0.238594 0.0775239i
\(573\) −1.06957 1.47214i −0.0446819 0.0614994i
\(574\) −0.763932 −0.0318859
\(575\) 0 0
\(576\) −8.47214 −0.353006
\(577\) 19.8537 + 27.3262i 0.826519 + 1.13761i 0.988561 + 0.150822i \(0.0481921\pi\)
−0.162042 + 0.986784i \(0.551808\pi\)
\(578\) 16.0292 + 5.20820i 0.666727 + 0.216633i
\(579\) −2.38197 + 7.33094i −0.0989911 + 0.304663i
\(580\) 0 0
\(581\) −1.19098 3.66547i −0.0494103 0.152069i
\(582\) 6.23607i 0.258493i
\(583\) 17.2905 5.61803i 0.716101 0.232675i
\(584\) −16.2812 11.8290i −0.673719 0.489485i
\(585\) 0 0
\(586\) −25.5623 + 18.5721i −1.05597 + 0.767206i
\(587\) 3.11044 4.28115i 0.128382 0.176702i −0.739987 0.672621i \(-0.765169\pi\)
0.868369 + 0.495919i \(0.165169\pi\)
\(588\) 2.40414 3.30902i 0.0991451 0.136462i
\(589\) −2.07295 + 1.50609i −0.0854144 + 0.0620572i
\(590\) 0 0
\(591\) −3.00000 2.17963i −0.123404 0.0896579i
\(592\) −1.08981 + 0.354102i −0.0447911 + 0.0145535i
\(593\) 10.9098i 0.448013i 0.974588 + 0.224007i \(0.0719137\pi\)
−0.974588 + 0.224007i \(0.928086\pi\)
\(594\) 13.0902 + 40.2874i 0.537096 + 1.65301i
\(595\) 0 0
\(596\) −0.753289 + 2.31838i −0.0308559 + 0.0949647i
\(597\) −16.7027 5.42705i −0.683598 0.222114i
\(598\) −6.63715 9.13525i −0.271413 0.373568i
\(599\) 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 \(0.482271\pi\)
\(602\) −2.85317 3.92705i −0.116287 0.160055i
\(603\) 9.06154 + 2.94427i 0.369014 + 0.119900i
\(604\) −2.78115 + 8.55951i −0.113164 + 0.348281i
\(605\) 0 0
\(606\) −0.736068 2.26538i −0.0299007 0.0920249i
\(607\) 35.5623i 1.44343i −0.692191 0.721715i \(-0.743354\pi\)
0.692191 0.721715i \(-0.256646\pi\)
\(608\) 2.74717 0.892609i 0.111412 0.0362001i
\(609\) −1.80902 1.31433i −0.0733051 0.0532592i
\(610\) 0 0
\(611\) −0.927051 + 0.673542i −0.0375045 + 0.0272486i
\(612\) 3.80423 5.23607i 0.153777 0.211656i
\(613\) 8.80427 12.1180i 0.355601 0.489443i −0.593316 0.804970i \(-0.702181\pi\)
0.948917 + 0.315527i \(0.102181\pi\)
\(614\) −12.0902 + 8.78402i −0.487920 + 0.354494i
\(615\) 0 0
\(616\) 5.85410 + 4.25325i 0.235868 + 0.171368i
\(617\) −13.5393 + 4.39919i −0.545072 + 0.177105i −0.568593 0.822619i \(-0.692512\pi\)
0.0235215 + 0.999723i \(0.492512\pi\)
\(618\) 13.8541i 0.557294i
\(619\) −9.43363 29.0337i −0.379170 1.16696i −0.940622 0.339455i \(-0.889757\pi\)
0.561453 0.827509i \(-0.310243\pi\)
\(620\) 0 0
\(621\) −5.81559 + 17.8986i −0.233372 + 0.718244i
\(622\) −13.0903 4.25329i −0.524872 0.170541i
\(623\) −3.24920 4.47214i −0.130176 0.179172i
\(624\) 9.00000 0.360288
\(625\) 0 0
\(626\) 27.1246 1.08412
\(627\) 2.62866 + 3.61803i 0.104978 + 0.144490i
\(628\) −7.74721 2.51722i −0.309147 0.100448i
\(629\) −0.381966 + 1.17557i −0.0152300 + 0.0468731i
\(630\) 0 0
\(631\) −3.16312 9.73508i −0.125922 0.387547i 0.868146 0.496309i \(-0.165312\pi\)
−0.994068 + 0.108761i \(0.965312\pi\)
\(632\) 18.0902i 0.719588i
\(633\) −8.73102 + 2.83688i −0.347027 + 0.112756i
\(634\) −10.0172 7.27794i −0.397835 0.289044i
\(635\) 0 0
\(636\) 1.73607 1.26133i 0.0688396 0.0500149i
\(637\) −7.21242 + 9.92705i −0.285767 + 0.393324i
\(638\) 18.0171 24.7984i 0.713303 0.981777i
\(639\) 10.7082 7.77997i 0.423610 0.307771i
\(640\) 0 0
\(641\) 0.881966 + 0.640786i 0.0348356 + 0.0253095i 0.605067 0.796175i \(-0.293146\pi\)
−0.570231 + 0.821484i \(0.693146\pi\)
\(642\) −25.2623 + 8.20820i −0.997022 + 0.323952i
\(643\) 30.8328i 1.21593i 0.793965 + 0.607964i \(0.208013\pi\)
−0.793965 + 0.607964i \(0.791987\pi\)
\(644\) −0.444272 1.36733i −0.0175068 0.0538803i
\(645\) 0 0
\(646\) 2.23607 6.88191i 0.0879769 0.270765i
\(647\) −34.7526 11.2918i −1.36626 0.443926i −0.468135 0.883657i \(-0.655074\pi\)
−0.898130 + 0.439731i \(0.855074\pi\)
\(648\) 1.31433 + 1.80902i 0.0516317 + 0.0710649i
\(649\) −56.8328 −2.23088
\(650\) 0 0
\(651\) −1.85410 −0.0726680
\(652\) −3.99598 5.50000i −0.156495 0.215397i
\(653\) −18.1558 5.89919i −0.710493 0.230853i −0.0685963 0.997645i \(-0.521852\pi\)
−0.641896 + 0.766791i \(0.721852\pi\)
\(654\) 5.00000 15.3884i 0.195515 0.601735i
\(655\) 0 0
\(656\) 1.14590 + 3.52671i 0.0447398 + 0.137695i
\(657\) 18.0000i 0.702247i
\(658\) −0.587785 + 0.190983i −0.0229143 + 0.00744529i
\(659\) 12.5623 + 9.12705i 0.489358 + 0.355539i 0.804937 0.593360i \(-0.202199\pi\)
−0.315579 + 0.948899i \(0.602199\pi\)
\(660\) 0 0
\(661\) −15.9271 + 11.5717i −0.619490 + 0.450086i −0.852744 0.522330i \(-0.825063\pi\)
0.233253 + 0.972416i \(0.425063\pi\)
\(662\) 21.9928 30.2705i 0.854775 1.17650i
\(663\) 5.70634 7.85410i 0.221616 0.305028i
\(664\) −11.2812 + 8.19624i −0.437794 + 0.318076i
\(665\) 0 0
\(666\) 0.618034 + 0.449028i 0.0239483 + 0.0173995i
\(667\) 12.9515 4.20820i 0.501485 0.162942i
\(668\) 9.00000i 0.348220i
\(669\) 0.0557281 + 0.171513i 0.00215457 + 0.00663109i
\(670\) 0 0
\(671\) −14.0902 + 43.3651i −0.543945 + 1.67409i
\(672\) 1.98787 + 0.645898i 0.0766837 + 0.0249161i
\(673\) 7.15942 + 9.85410i 0.275976 + 0.379848i 0.924396 0.381435i \(-0.124570\pi\)
−0.648420 + 0.761283i \(0.724570\pi\)
\(674\) 12.7082 0.489502
\(675\) 0 0
\(676\) −5.90983 −0.227301
\(677\) −6.24112 8.59017i −0.239866 0.330147i 0.672064 0.740493i \(-0.265408\pi\)
−0.911930 + 0.410346i \(0.865408\pi\)
\(678\) 25.9358 + 8.42705i 0.996058 + 0.323639i
\(679\) 0.736068 2.26538i 0.0282477 0.0869375i
\(680\) 0 0
\(681\) 4.56231 + 14.0413i 0.174828 + 0.538065i
\(682\) 25.4164i 0.973245i
\(683\) −12.8128 + 4.16312i −0.490267 + 0.159297i −0.543709 0.839274i \(-0.682981\pi\)
0.0534426 + 0.998571i \(0.482981\pi\)
\(684\) −0.854102 0.620541i −0.0326574 0.0237270i
\(685\) 0 0
\(686\) −11.0172 + 8.00448i −0.420639 + 0.305612i
\(687\) 12.7598 17.5623i 0.486815 0.670044i
\(688\) −13.8496 + 19.0623i −0.528010 + 0.726744i
\(689\) −5.20820 + 3.78398i −0.198417 + 0.144158i
\(690\) 0 0
\(691\) −29.3435 21.3193i −1.11628 0.811023i −0.132637 0.991165i \(-0.542344\pi\)
−0.983641 + 0.180141i \(0.942344\pi\)
\(692\) −11.1024 + 3.60739i −0.422050 + 0.137132i
\(693\) 6.47214i 0.245856i
\(694\) −9.95492 30.6381i −0.377883 1.16301i
\(695\) 0 0
\(696\) −2.50000 + 7.69421i −0.0947623 + 0.291648i
\(697\) 3.80423 + 1.23607i 0.144095 + 0.0468194i
\(698\) −20.6457 28.4164i −0.781452 1.07558i
\(699\) 2.94427 0.111363
\(700\) 0 0
\(701\) −41.0132 −1.54905 −0.774523 0.632546i \(-0.782010\pi\)
−0.774523 + 0.632546i \(0.782010\pi\)
\(702\) −8.81678 12.1353i −0.332768 0.458016i
\(703\) 0.191758 + 0.0623059i 0.00723228 + 0.00234991i
\(704\) 6.85410 21.0948i 0.258324 0.795039i
\(705\) 0 0
\(706\) −6.45492 19.8662i −0.242934 0.747674i
\(707\) 0.909830i 0.0342177i
\(708\) −6.37988 + 2.07295i −0.239771 + 0.0779062i
\(709\) −27.1353 19.7149i −1.01909 0.740409i −0.0529906 0.998595i \(-0.516875\pi\)
−0.966095 + 0.258186i \(0.916875\pi\)
\(710\) 0 0
\(711\) −13.0902 + 9.51057i −0.490920 + 0.356674i
\(712\) −11.7557 + 16.1803i −0.440564 + 0.606384i
\(713\) 6.63715 9.13525i 0.248563 0.342118i
\(714\) 4.23607 3.07768i 0.158531 0.115179i
\(715\) 0 0
\(716\) 0.263932 + 0.191758i 0.00986360 + 0.00716633i
\(717\) 19.5232 6.34346i 0.729106 0.236901i
\(718\) 22.2361i 0.829843i
\(719\) 7.19756 + 22.1518i 0.268424 + 0.826123i 0.990885 + 0.134712i \(0.0430108\pi\)
−0.722461 + 0.691412i \(0.756989\pi\)
\(720\) 0 0
\(721\) 1.63525 5.03280i 0.0609001 0.187431i
\(722\) 28.1154 + 9.13525i 1.04635 + 0.339979i
\(723\) 1.48584 + 2.04508i 0.0552590 + 0.0760575i
\(724\) −0.180340 −0.00670228
\(725\) 0 0
\(726\) −26.5623 −0.985820
\(727\) −14.4374 19.8713i −0.535452 0.736987i 0.452497 0.891766i \(-0.350533\pi\)
−0.987949 + 0.154779i \(0.950533\pi\)
\(728\) −2.43690 0.791796i −0.0903174 0.0293459i
\(729\) −4.01722 + 12.3637i −0.148786 + 0.457916i
\(730\) 0 0
\(731\) 7.85410 + 24.1724i 0.290494 + 0.894050i
\(732\) 5.38197i 0.198923i
\(733\) −19.0009 + 6.17376i −0.701814 + 0.228033i −0.638121 0.769936i \(-0.720288\pi\)
−0.0636931 + 0.997970i \(0.520288\pi\)
\(734\) 33.4615 + 24.3112i 1.23509 + 0.897343i
\(735\) 0 0
\(736\) −10.2984 + 7.48221i −0.379603 + 0.275798i
\(737\) −14.6619 + 20.1803i −0.540077 + 0.743352i
\(738\) 1.45309 2.00000i 0.0534888 0.0736210i
\(739\) 12.9271 9.39205i 0.475529 0.345492i −0.324063 0.946036i \(-0.605049\pi\)
0.799592 + 0.600543i \(0.205049\pi\)
\(740\) 0 0
\(741\) −1.28115 0.930812i −0.0470643 0.0341942i
\(742\) −3.30220 + 1.07295i −0.121227 + 0.0393892i
\(743\) 28.3607i 1.04045i −0.854029 0.520226i \(-0.825848\pi\)
0.854029 0.520226i \(-0.174152\pi\)
\(744\) 2.07295 + 6.37988i 0.0759980 + 0.233898i
\(745\) 0 0
\(746\) 14.1353 43.5038i 0.517528 1.59279i
\(747\) 11.8617 + 3.85410i 0.433997 + 0.141014i
\(748\) 9.95959 + 13.7082i 0.364159 + 0.501222i
\(749\) 10.1459 0.370723
\(750\) 0 0
\(751\) −5.11146 −0.186520 −0.0932598 0.995642i \(-0.529729\pi\)
−0.0932598 + 0.995642i \(0.529729\pi\)
\(752\) 1.76336 + 2.42705i 0.0643030 + 0.0885054i
\(753\) 27.7522 + 9.01722i 1.01134 + 0.328606i
\(754\) −3.35410 + 10.3229i −0.122149 + 0.375937i
\(755\) 0 0
\(756\) −0.590170 1.81636i −0.0214643 0.0660602i
\(757\) 30.4164i 1.10550i 0.833346 + 0.552752i \(0.186422\pi\)
−0.833346 + 0.552752i \(0.813578\pi\)
\(758\) −22.4621 + 7.29837i −0.815860 + 0.265089i
\(759\) −15.9443 11.5842i −0.578740 0.420480i
\(760\) 0 0
\(761\) 14.9271 10.8451i 0.541105 0.393136i −0.283390 0.959005i \(-0.591459\pi\)
0.824495 + 0.565869i \(0.191459\pi\)
\(762\) −18.9151 + 26.0344i −0.685223 + 0.943128i
\(763\) −3.63271 + 5.00000i −0.131513 + 0.181012i
\(764\) −0.909830 + 0.661030i −0.0329165 + 0.0239152i
\(765\) 0 0
\(766\) 43.6697 + 31.7279i 1.57785 + 1.14638i
\(767\) 19.1396 6.21885i 0.691092 0.224550i
\(768\) 13.5623i 0.489388i
\(769\) −4.14590 12.7598i −0.149505 0.460129i 0.848058 0.529904i \(-0.177772\pi\)
−0.997563 + 0.0697749i \(0.977772\pi\)
\(770\) 0 0
\(771\) 7.06231 21.7355i 0.254343 0.782786i
\(772\) 4.53077 + 1.47214i 0.163066 + 0.0529833i
\(773\) −21.2538 29.2533i −0.764445 1.05217i −0.996831 0.0795442i \(-0.974654\pi\)
0.232387 0.972623i \(-0.425346\pi\)
\(774\) 15.7082 0.564620
\(775\) 0 0
\(776\) −8.61803 −0.309369
\(777\) 0.0857567 + 0.118034i 0.00307650 + 0.00423445i
\(778\) 23.0826 + 7.50000i 0.827552 + 0.268888i
\(779\) 0.201626 0.620541i 0.00722401 0.0222332i
\(78