Properties

Label 625.2.d.h.251.1
Level $625$
Weight $2$
Character 625.251
Analytic conductor $4.991$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.99065012633\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
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 251.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 625.251
Dual form 625.2.d.h.376.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.30902 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034 q^{7} +(0.690983 + 2.12663i) q^{8} +(1.61803 + 1.17557i) q^{9} +O(q^{10})\) \(q+(1.30902 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034 q^{7} +(0.690983 + 2.12663i) q^{8} +(1.61803 + 1.17557i) q^{9} +(4.23607 - 3.07768i) q^{11} +(-0.500000 - 0.363271i) q^{12} +(-1.50000 - 1.08981i) q^{13} +(0.809017 - 0.587785i) q^{14} +(3.92705 + 2.85317i) q^{16} +(-1.61803 - 4.97980i) q^{17} +3.23607 q^{18} +(0.263932 + 0.812299i) q^{19} +(0.190983 - 0.587785i) q^{21} +(2.61803 - 8.05748i) q^{22} +(-3.04508 + 2.21238i) q^{23} +2.23607 q^{24} -3.00000 q^{26} +(4.04508 - 2.93893i) q^{27} +(0.118034 - 0.363271i) q^{28} +(-1.11803 + 3.44095i) q^{29} +(-0.927051 - 2.85317i) q^{31} +3.38197 q^{32} +(-1.61803 - 4.97980i) q^{33} +(-6.85410 - 4.97980i) q^{34} +(1.00000 - 0.726543i) q^{36} +(0.190983 + 0.138757i) q^{37} +(1.11803 + 0.812299i) q^{38} +(-1.50000 + 1.08981i) q^{39} +(0.618034 + 0.449028i) q^{41} +(-0.309017 - 0.951057i) q^{42} -4.85410 q^{43} +(-1.00000 - 3.07768i) q^{44} +(-1.88197 + 5.79210i) q^{46} +(0.190983 - 0.587785i) q^{47} +(3.92705 - 2.85317i) q^{48} -6.61803 q^{49} -5.23607 q^{51} +(-0.927051 + 0.673542i) q^{52} +(-1.07295 + 3.30220i) q^{53} +(2.50000 - 7.69421i) q^{54} +(0.427051 + 1.31433i) q^{56} +0.854102 q^{57} +(1.80902 + 5.56758i) q^{58} +(8.78115 + 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(-3.92705 - 2.85317i) q^{62} +(1.00000 + 0.726543i) q^{63} +(-3.42705 + 2.48990i) q^{64} +(-6.85410 - 4.97980i) q^{66} +(1.47214 + 4.53077i) q^{67} -3.23607 q^{68} +(1.16312 + 3.57971i) q^{69} +(-2.04508 + 6.29412i) q^{71} +(-1.38197 + 4.25325i) q^{72} +(7.28115 - 5.29007i) q^{73} +0.381966 q^{74} +0.527864 q^{76} +(2.61803 - 1.90211i) q^{77} +(-0.927051 + 2.85317i) q^{78} +(-2.50000 + 7.69421i) q^{79} +(0.309017 + 0.951057i) q^{81} +1.23607 q^{82} +(-1.92705 - 5.93085i) q^{83} +(-0.309017 - 0.224514i) q^{84} +(-6.35410 + 4.61653i) q^{86} +(2.92705 + 2.12663i) q^{87} +(9.47214 + 6.88191i) q^{88} +(7.23607 - 5.25731i) q^{89} +(-0.927051 - 0.673542i) q^{91} +(0.718847 + 2.21238i) q^{92} -3.00000 q^{93} +(-0.309017 - 0.951057i) q^{94} +(1.04508 - 3.21644i) q^{96} +(-1.19098 + 3.66547i) q^{97} +(-8.66312 + 6.29412i) q^{98} +10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} - 2 q^{7} + 5 q^{8} + 2 q^{9} + O(q^{10}) \) \( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} - 2 q^{7} + 5 q^{8} + 2 q^{9} + 8 q^{11} - 2 q^{12} - 6 q^{13} + q^{14} + 9 q^{16} - 2 q^{17} + 4 q^{18} + 10 q^{19} + 3 q^{21} + 6 q^{22} - q^{23} - 12 q^{26} + 5 q^{27} - 4 q^{28} + 3 q^{31} + 18 q^{32} - 2 q^{33} - 14 q^{34} + 4 q^{36} + 3 q^{37} - 6 q^{39} - 2 q^{41} + q^{42} - 6 q^{43} - 4 q^{44} - 12 q^{46} + 3 q^{47} + 9 q^{48} - 22 q^{49} - 12 q^{51} + 3 q^{52} - 11 q^{53} + 10 q^{54} - 5 q^{56} - 10 q^{57} + 5 q^{58} + 15 q^{59} - 17 q^{61} - 9 q^{62} + 4 q^{63} - 7 q^{64} - 14 q^{66} - 12 q^{67} - 4 q^{68} - 11 q^{69} + 3 q^{71} - 10 q^{72} + 9 q^{73} + 6 q^{74} + 20 q^{76} + 6 q^{77} + 3 q^{78} - 10 q^{79} - q^{81} - 4 q^{82} - q^{83} + q^{84} - 12 q^{86} + 5 q^{87} + 20 q^{88} + 20 q^{89} + 3 q^{91} + 23 q^{92} - 12 q^{93} + q^{94} - 7 q^{96} - 7 q^{97} - 19 q^{98} + 24 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30902 0.951057i 0.925615 0.672499i −0.0193004 0.999814i \(-0.506144\pi\)
0.944915 + 0.327315i \(0.106144\pi\)
\(3\) 0.309017 0.951057i 0.178411 0.549093i −0.821362 0.570408i \(-0.806785\pi\)
0.999773 + 0.0213149i \(0.00678525\pi\)
\(4\) 0.190983 0.587785i 0.0954915 0.293893i
\(5\) 0 0
\(6\) −0.500000 1.53884i −0.204124 0.628230i
\(7\) 0.618034 0.233595 0.116797 0.993156i \(-0.462737\pi\)
0.116797 + 0.993156i \(0.462737\pi\)
\(8\) 0.690983 + 2.12663i 0.244299 + 0.751876i
\(9\) 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 \(0.0104089\pi\)
\(12\) −0.500000 0.363271i −0.144338 0.104867i
\(13\) −1.50000 1.08981i −0.416025 0.302260i 0.360011 0.932948i \(-0.382773\pi\)
−0.776037 + 0.630688i \(0.782773\pi\)
\(14\) 0.809017 0.587785i 0.216219 0.157092i
\(15\) 0 0
\(16\) 3.92705 + 2.85317i 0.981763 + 0.713292i
\(17\) −1.61803 4.97980i −0.392431 1.20778i −0.930944 0.365161i \(-0.881014\pi\)
0.538513 0.842617i \(-0.318986\pi\)
\(18\) 3.23607 0.762749
\(19\) 0.263932 + 0.812299i 0.0605502 + 0.186354i 0.976756 0.214353i \(-0.0687644\pi\)
−0.916206 + 0.400707i \(0.868764\pi\)
\(20\) 0 0
\(21\) 0.190983 0.587785i 0.0416759 0.128265i
\(22\) 2.61803 8.05748i 0.558167 1.71786i
\(23\) −3.04508 + 2.21238i −0.634944 + 0.461314i −0.858110 0.513467i \(-0.828361\pi\)
0.223165 + 0.974781i \(0.428361\pi\)
\(24\) 2.23607 0.456435
\(25\) 0 0
\(26\) −3.00000 −0.588348
\(27\) 4.04508 2.93893i 0.778477 0.565597i
\(28\) 0.118034 0.363271i 0.0223063 0.0686518i
\(29\) −1.11803 + 3.44095i −0.207614 + 0.638969i 0.791982 + 0.610544i \(0.209049\pi\)
−0.999596 + 0.0284251i \(0.990951\pi\)
\(30\) 0 0
\(31\) −0.927051 2.85317i −0.166503 0.512444i 0.832641 0.553814i \(-0.186828\pi\)
−0.999144 + 0.0413693i \(0.986828\pi\)
\(32\) 3.38197 0.597853
\(33\) −1.61803 4.97980i −0.281664 0.866871i
\(34\) −6.85410 4.97980i −1.17547 0.854028i
\(35\) 0 0
\(36\) 1.00000 0.726543i 0.166667 0.121090i
\(37\) 0.190983 + 0.138757i 0.0313974 + 0.0228116i 0.603373 0.797459i \(-0.293823\pi\)
−0.571976 + 0.820270i \(0.693823\pi\)
\(38\) 1.11803 + 0.812299i 0.181369 + 0.131772i
\(39\) −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 \(0.681001\pi\)
\(42\) −0.309017 0.951057i −0.0476824 0.146751i
\(43\) −4.85410 −0.740244 −0.370122 0.928983i \(-0.620684\pi\)
−0.370122 + 0.928983i \(0.620684\pi\)
\(44\) −1.00000 3.07768i −0.150756 0.463978i
\(45\) 0 0
\(46\) −1.88197 + 5.79210i −0.277481 + 0.853998i
\(47\) 0.190983 0.587785i 0.0278577 0.0857373i −0.936161 0.351572i \(-0.885647\pi\)
0.964019 + 0.265834i \(0.0856474\pi\)
\(48\) 3.92705 2.85317i 0.566821 0.411820i
\(49\) −6.61803 −0.945433
\(50\) 0 0
\(51\) −5.23607 −0.733196
\(52\) −0.927051 + 0.673542i −0.128559 + 0.0934035i
\(53\) −1.07295 + 3.30220i −0.147381 + 0.453592i −0.997309 0.0733062i \(-0.976645\pi\)
0.849929 + 0.526898i \(0.176645\pi\)
\(54\) 2.50000 7.69421i 0.340207 1.04705i
\(55\) 0 0
\(56\) 0.427051 + 1.31433i 0.0570671 + 0.175634i
\(57\) 0.854102 0.113129
\(58\) 1.80902 + 5.56758i 0.237536 + 0.731059i
\(59\) 8.78115 + 6.37988i 1.14321 + 0.830590i 0.987563 0.157223i \(-0.0502542\pi\)
0.155646 + 0.987813i \(0.450254\pi\)
\(60\) 0 0
\(61\) −7.04508 + 5.11855i −0.902031 + 0.655364i −0.938987 0.343953i \(-0.888234\pi\)
0.0369561 + 0.999317i \(0.488234\pi\)
\(62\) −3.92705 2.85317i −0.498736 0.362353i
\(63\) 1.00000 + 0.726543i 0.125988 + 0.0915358i
\(64\) −3.42705 + 2.48990i −0.428381 + 0.311237i
\(65\) 0 0
\(66\) −6.85410 4.97980i −0.843682 0.612971i
\(67\) 1.47214 + 4.53077i 0.179850 + 0.553521i 0.999822 0.0188826i \(-0.00601088\pi\)
−0.819972 + 0.572404i \(0.806011\pi\)
\(68\) −3.23607 −0.392431
\(69\) 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 \(0.971538\pi\)
\(72\) −1.38197 + 4.25325i −0.162866 + 0.501251i
\(73\) 7.28115 5.29007i 0.852194 0.619156i −0.0735557 0.997291i \(-0.523435\pi\)
0.925750 + 0.378136i \(0.123435\pi\)
\(74\) 0.381966 0.0444026
\(75\) 0 0
\(76\) 0.527864 0.0605502
\(77\) 2.61803 1.90211i 0.298353 0.216766i
\(78\) −0.927051 + 2.85317i −0.104968 + 0.323058i
\(79\) −2.50000 + 7.69421i −0.281272 + 0.865666i 0.706219 + 0.707993i \(0.250399\pi\)
−0.987491 + 0.157673i \(0.949601\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 1.23607 0.136501
\(83\) −1.92705 5.93085i −0.211521 0.650996i −0.999382 0.0351426i \(-0.988811\pi\)
0.787861 0.615853i \(-0.211189\pi\)
\(84\) −0.309017 0.224514i −0.0337165 0.0244965i
\(85\) 0 0
\(86\) −6.35410 + 4.61653i −0.685180 + 0.497813i
\(87\) 2.92705 + 2.12663i 0.313813 + 0.227998i
\(88\) 9.47214 + 6.88191i 1.00973 + 0.733614i
\(89\) 7.23607 5.25731i 0.767022 0.557274i −0.134034 0.990977i \(-0.542793\pi\)
0.901056 + 0.433703i \(0.142793\pi\)
\(90\) 0 0
\(91\) −0.927051 0.673542i −0.0971813 0.0706064i
\(92\) 0.718847 + 2.21238i 0.0749450 + 0.230657i
\(93\) −3.00000 −0.311086
\(94\) −0.309017 0.951057i −0.0318727 0.0980940i
\(95\) 0 0
\(96\) 1.04508 3.21644i 0.106664 0.328277i
\(97\) −1.19098 + 3.66547i −0.120926 + 0.372172i −0.993137 0.116958i \(-0.962686\pi\)
0.872211 + 0.489130i \(0.162686\pi\)
\(98\) −8.66312 + 6.29412i −0.875107 + 0.635803i
\(99\) 10.4721 1.05249
\(100\) 0 0
\(101\) 1.47214 0.146483 0.0732415 0.997314i \(-0.476666\pi\)
0.0732415 + 0.997314i \(0.476666\pi\)
\(102\) −6.85410 + 4.97980i −0.678657 + 0.493073i
\(103\) 2.64590 8.14324i 0.260708 0.802377i −0.731943 0.681366i \(-0.761386\pi\)
0.992651 0.121011i \(-0.0386137\pi\)
\(104\) 1.28115 3.94298i 0.125627 0.386641i
\(105\) 0 0
\(106\) 1.73607 + 5.34307i 0.168622 + 0.518965i
\(107\) −16.4164 −1.58703 −0.793517 0.608548i \(-0.791752\pi\)
−0.793517 + 0.608548i \(0.791752\pi\)
\(108\) −0.954915 2.93893i −0.0918867 0.282798i
\(109\) −8.09017 5.87785i −0.774898 0.562996i 0.128546 0.991704i \(-0.458969\pi\)
−0.903443 + 0.428707i \(0.858969\pi\)
\(110\) 0 0
\(111\) 0.190983 0.138757i 0.0181273 0.0131703i
\(112\) 2.42705 + 1.76336i 0.229335 + 0.166621i
\(113\) −13.6353 9.90659i −1.28270 0.931934i −0.283066 0.959100i \(-0.591352\pi\)
−0.999631 + 0.0271666i \(0.991352\pi\)
\(114\) 1.11803 0.812299i 0.104713 0.0760788i
\(115\) 0 0
\(116\) 1.80902 + 1.31433i 0.167963 + 0.122032i
\(117\) −1.14590 3.52671i −0.105938 0.326045i
\(118\) 17.5623 1.61674
\(119\) −1.00000 3.07768i −0.0916698 0.282131i
\(120\) 0 0
\(121\) 5.07295 15.6129i 0.461177 1.41936i
\(122\) −4.35410 + 13.4005i −0.394202 + 1.21323i
\(123\) 0.618034 0.449028i 0.0557262 0.0404875i
\(124\) −1.85410 −0.166503
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) −16.0902 + 11.6902i −1.42777 + 1.03734i −0.437346 + 0.899294i \(0.644081\pi\)
−0.990426 + 0.138043i \(0.955919\pi\)
\(128\) −4.20820 + 12.9515i −0.371956 + 1.14476i
\(129\) −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 \(0.804018\pi\)
\(132\) −3.23607 −0.281664
\(133\) 0.163119 + 0.502029i 0.0141442 + 0.0435314i
\(134\) 6.23607 + 4.53077i 0.538714 + 0.391399i
\(135\) 0 0
\(136\) 9.47214 6.88191i 0.812229 0.590119i
\(137\) 9.66312 + 7.02067i 0.825576 + 0.599816i 0.918304 0.395875i \(-0.129559\pi\)
−0.0927283 + 0.995691i \(0.529559\pi\)
\(138\) 4.92705 + 3.57971i 0.419418 + 0.304725i
\(139\) −4.04508 + 2.93893i −0.343100 + 0.249276i −0.745968 0.665981i \(-0.768013\pi\)
0.402869 + 0.915258i \(0.368013\pi\)
\(140\) 0 0
\(141\) −0.500000 0.363271i −0.0421076 0.0305930i
\(142\) 3.30902 + 10.1841i 0.277687 + 0.854631i
\(143\) −9.70820 −0.811841
\(144\) 3.00000 + 9.23305i 0.250000 + 0.769421i
\(145\) 0 0
\(146\) 4.50000 13.8496i 0.372423 1.14620i
\(147\) −2.04508 + 6.29412i −0.168676 + 0.519131i
\(148\) 0.118034 0.0857567i 0.00970233 0.00704916i
\(149\) −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 \(0.298128\pi\)
\(152\) −1.54508 + 1.12257i −0.125323 + 0.0910524i
\(153\) 3.23607 9.95959i 0.261621 0.805185i
\(154\) 1.61803 4.97980i 0.130385 0.401283i
\(155\) 0 0
\(156\) 0.354102 + 1.08981i 0.0283508 + 0.0872549i
\(157\) 13.1803 1.05191 0.525953 0.850514i \(-0.323709\pi\)
0.525953 + 0.850514i \(0.323709\pi\)
\(158\) 4.04508 + 12.4495i 0.321810 + 0.990428i
\(159\) 2.80902 + 2.04087i 0.222770 + 0.161852i
\(160\) 0 0
\(161\) −1.88197 + 1.36733i −0.148320 + 0.107761i
\(162\) 1.30902 + 0.951057i 0.102846 + 0.0747221i
\(163\) −8.89919 6.46564i −0.697038 0.506428i 0.181928 0.983312i \(-0.441766\pi\)
−0.878966 + 0.476884i \(0.841766\pi\)
\(164\) 0.381966 0.277515i 0.0298265 0.0216702i
\(165\) 0 0
\(166\) −8.16312 5.93085i −0.633581 0.460323i
\(167\) 4.50000 + 13.8496i 0.348220 + 1.07171i 0.959837 + 0.280558i \(0.0905195\pi\)
−0.611617 + 0.791154i \(0.709480\pi\)
\(168\) 1.38197 0.106621
\(169\) −2.95492 9.09429i −0.227301 0.699561i
\(170\) 0 0
\(171\) −0.527864 + 1.62460i −0.0403668 + 0.124236i
\(172\) −0.927051 + 2.85317i −0.0706870 + 0.217552i
\(173\) −15.2812 + 11.1024i −1.16180 + 0.844100i −0.990005 0.141032i \(-0.954958\pi\)
−0.171799 + 0.985132i \(0.554958\pi\)
\(174\) 5.85410 0.443798
\(175\) 0 0
\(176\) 25.4164 1.91583
\(177\) 8.78115 6.37988i 0.660032 0.479541i
\(178\) 4.47214 13.7638i 0.335201 1.03164i
\(179\) −0.163119 + 0.502029i −0.0121921 + 0.0375234i −0.956967 0.290195i \(-0.906280\pi\)
0.944775 + 0.327719i \(0.106280\pi\)
\(180\) 0 0
\(181\) 0.0901699 + 0.277515i 0.00670228 + 0.0206275i 0.954352 0.298685i \(-0.0965480\pi\)
−0.947649 + 0.319313i \(0.896548\pi\)
\(182\) −1.85410 −0.137435
\(183\) 2.69098 + 8.28199i 0.198923 + 0.612223i
\(184\) −6.80902 4.94704i −0.501967 0.364701i
\(185\) 0 0
\(186\) −3.92705 + 2.85317i −0.287945 + 0.209205i
\(187\) −22.1803 16.1150i −1.62199 1.17844i
\(188\) −0.309017 0.224514i −0.0225374 0.0163744i
\(189\) 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 \(0.679030\pi\)
\(192\) 1.30902 + 4.02874i 0.0944702 + 0.290749i
\(193\) 7.70820 0.554849 0.277424 0.960747i \(-0.410519\pi\)
0.277424 + 0.960747i \(0.410519\pi\)
\(194\) 1.92705 + 5.93085i 0.138354 + 0.425810i
\(195\) 0 0
\(196\) −1.26393 + 3.88998i −0.0902809 + 0.277856i
\(197\) 1.14590 3.52671i 0.0816419 0.251268i −0.901901 0.431943i \(-0.857828\pi\)
0.983543 + 0.180675i \(0.0578282\pi\)
\(198\) 13.7082 9.95959i 0.974200 0.707797i
\(199\) −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
\(202\) 1.92705 1.40008i 0.135587 0.0985096i
\(203\) −0.690983 + 2.12663i −0.0484975 + 0.149260i
\(204\) −1.00000 + 3.07768i −0.0700140 + 0.215481i
\(205\) 0 0
\(206\) −4.28115 13.1760i −0.298282 0.918018i
\(207\) −7.52786 −0.523223
\(208\) −2.78115 8.55951i −0.192838 0.593495i
\(209\) 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 \(0.197660\pi\)
\(212\) 1.73607 + 1.26133i 0.119234 + 0.0866283i
\(213\) 5.35410 + 3.88998i 0.366857 + 0.266537i
\(214\) −21.4894 + 15.6129i −1.46898 + 1.06728i
\(215\) 0 0
\(216\) 9.04508 + 6.57164i 0.615440 + 0.447143i
\(217\) −0.572949 1.76336i −0.0388943 0.119704i
\(218\) −16.1803 −1.09587
\(219\) −2.78115 8.55951i −0.187933 0.578398i
\(220\) 0 0
\(221\) −3.00000 + 9.23305i −0.201802 + 0.621082i
\(222\) 0.118034 0.363271i 0.00792192 0.0243812i
\(223\) 0.145898 0.106001i 0.00977005 0.00709836i −0.582890 0.812551i \(-0.698078\pi\)
0.592660 + 0.805453i \(0.298078\pi\)
\(224\) 2.09017 0.139655
\(225\) 0 0
\(226\) −27.2705 −1.81401
\(227\) −11.9443 + 8.67802i −0.792769 + 0.575981i −0.908784 0.417267i \(-0.862988\pi\)
0.116015 + 0.993247i \(0.462988\pi\)
\(228\) 0.163119 0.502029i 0.0108028 0.0332477i
\(229\) 6.70820 20.6457i 0.443291 1.36431i −0.441057 0.897479i \(-0.645396\pi\)
0.884348 0.466829i \(-0.154604\pi\)
\(230\) 0 0
\(231\) −1.00000 3.07768i −0.0657952 0.202497i
\(232\) −8.09017 −0.531146
\(233\) −0.909830 2.80017i −0.0596049 0.183445i 0.916821 0.399299i \(-0.130746\pi\)
−0.976426 + 0.215854i \(0.930746\pi\)
\(234\) −4.85410 3.52671i −0.317323 0.230548i
\(235\) 0 0
\(236\) 5.42705 3.94298i 0.353271 0.256666i
\(237\) 6.54508 + 4.75528i 0.425149 + 0.308889i
\(238\) −4.23607 3.07768i −0.274584 0.199497i
\(239\) 16.6074 12.0660i 1.07424 0.780483i 0.0975727 0.995228i \(-0.468892\pi\)
0.976670 + 0.214745i \(0.0688921\pi\)
\(240\) 0 0
\(241\) −2.04508 1.48584i −0.131736 0.0957114i 0.519966 0.854187i \(-0.325945\pi\)
−0.651702 + 0.758475i \(0.725945\pi\)
\(242\) −8.20820 25.2623i −0.527643 1.62392i
\(243\) 16.0000 1.02640
\(244\) 1.66312 + 5.11855i 0.106470 + 0.327682i
\(245\) 0 0
\(246\) 0.381966 1.17557i 0.0243533 0.0749516i
\(247\) 0.489357 1.50609i 0.0311370 0.0958299i
\(248\) 5.42705 3.94298i 0.344618 0.250380i
\(249\) −6.23607 −0.395195
\(250\) 0 0
\(251\) −29.1803 −1.84185 −0.920923 0.389744i \(-0.872564\pi\)
−0.920923 + 0.389744i \(0.872564\pi\)
\(252\) 0.618034 0.449028i 0.0389325 0.0282861i
\(253\) −6.09017 + 18.7436i −0.382886 + 1.17840i
\(254\) −9.94427 + 30.6053i −0.623959 + 1.92035i
\(255\) 0 0
\(256\) 4.19098 + 12.8985i 0.261936 + 0.806157i
\(257\) 22.8541 1.42560 0.712800 0.701367i \(-0.247427\pi\)
0.712800 + 0.701367i \(0.247427\pi\)
\(258\) 2.42705 + 7.46969i 0.151102 + 0.465043i
\(259\) 0.118034 + 0.0857567i 0.00733428 + 0.00532866i
\(260\) 0 0
\(261\) −5.85410 + 4.25325i −0.362360 + 0.263270i
\(262\) 8.89919 + 6.46564i 0.549794 + 0.399448i
\(263\) 8.82624 + 6.41264i 0.544249 + 0.395420i 0.825661 0.564167i \(-0.190803\pi\)
−0.281412 + 0.959587i \(0.590803\pi\)
\(264\) 9.47214 6.88191i 0.582970 0.423552i
\(265\) 0 0
\(266\) 0.690983 + 0.502029i 0.0423669 + 0.0307813i
\(267\) −2.76393 8.50651i −0.169150 0.520590i
\(268\) 2.94427 0.179850
\(269\) −3.94427 12.1392i −0.240487 0.740141i −0.996346 0.0854076i \(-0.972781\pi\)
0.755860 0.654734i \(-0.227219\pi\)
\(270\) 0 0
\(271\) −2.47214 + 7.60845i −0.150172 + 0.462181i −0.997640 0.0686657i \(-0.978126\pi\)
0.847468 + 0.530846i \(0.178126\pi\)
\(272\) 7.85410 24.1724i 0.476225 1.46567i
\(273\) −0.927051 + 0.673542i −0.0561077 + 0.0407646i
\(274\) 19.3262 1.16754
\(275\) 0 0
\(276\) 2.32624 0.140023
\(277\) 19.9894 14.5231i 1.20104 0.872610i 0.206657 0.978413i \(-0.433742\pi\)
0.994387 + 0.105804i \(0.0337416\pi\)
\(278\) −2.50000 + 7.69421i −0.149940 + 0.461468i
\(279\) 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 \(0.802691\pi\)
\(282\) −1.00000 −0.0595491
\(283\) −9.22542 28.3929i −0.548395 1.68778i −0.712779 0.701389i \(-0.752564\pi\)
0.164384 0.986396i \(-0.447436\pi\)
\(284\) 3.30902 + 2.40414i 0.196354 + 0.142660i
\(285\) 0 0
\(286\) −12.7082 + 9.23305i −0.751452 + 0.545962i
\(287\) 0.381966 + 0.277515i 0.0225467 + 0.0163812i
\(288\) 5.47214 + 3.97574i 0.322449 + 0.234273i
\(289\) −8.42705 + 6.12261i −0.495709 + 0.360154i
\(290\) 0 0
\(291\) 3.11803 + 2.26538i 0.182782 + 0.132799i
\(292\) −1.71885 5.29007i −0.100588 0.309578i
\(293\) −19.5279 −1.14083 −0.570415 0.821357i \(-0.693218\pi\)
−0.570415 + 0.821357i \(0.693218\pi\)
\(294\) 3.30902 + 10.1841i 0.192986 + 0.593949i
\(295\) 0 0
\(296\) −0.163119 + 0.502029i −0.00948110 + 0.0291798i
\(297\) 8.09017 24.8990i 0.469439 1.44479i
\(298\) −5.16312 + 3.75123i −0.299091 + 0.217303i
\(299\) 6.97871 0.403589
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) 19.0623 13.8496i 1.09691 0.796954i
\(303\) 0.454915 1.40008i 0.0261342 0.0804328i
\(304\) −1.28115 + 3.94298i −0.0734792 + 0.226146i
\(305\) 0 0
\(306\) −5.23607 16.1150i −0.299326 0.921231i
\(307\) 9.23607 0.527130 0.263565 0.964642i \(-0.415102\pi\)
0.263565 + 0.964642i \(0.415102\pi\)
\(308\) −0.618034 1.90211i −0.0352158 0.108383i
\(309\) −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 \(0.377535\pi\)
\(312\) −3.35410 2.43690i −0.189889 0.137962i
\(313\) 13.5623 + 9.85359i 0.766587 + 0.556958i 0.900924 0.433978i \(-0.142890\pi\)
−0.134337 + 0.990936i \(0.542890\pi\)
\(314\) 17.2533 12.5352i 0.973659 0.707405i
\(315\) 0 0
\(316\) 4.04508 + 2.93893i 0.227554 + 0.165328i
\(317\) 2.36475 + 7.27794i 0.132817 + 0.408770i 0.995244 0.0974121i \(-0.0310565\pi\)
−0.862427 + 0.506182i \(0.831056\pi\)
\(318\) 5.61803 0.315044
\(319\) 5.85410 + 18.0171i 0.327767 + 1.00876i
\(320\) 0 0
\(321\) −5.07295 + 15.6129i −0.283144 + 0.871429i
\(322\) −1.16312 + 3.57971i −0.0648181 + 0.199490i
\(323\) 3.61803 2.62866i 0.201313 0.146262i
\(324\) 0.618034 0.0343352
\(325\) 0 0
\(326\) −17.7984 −0.985761
\(327\) −8.09017 + 5.87785i −0.447387 + 0.325046i
\(328\) −0.527864 + 1.62460i −0.0291464 + 0.0897034i
\(329\) 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 \(-0.319215\pi\)
\(332\) −3.85410 −0.211521
\(333\) 0.145898 + 0.449028i 0.00799516 + 0.0246066i
\(334\) 19.0623 + 13.8496i 1.04304 + 0.757815i
\(335\) 0 0
\(336\) 2.42705 1.76336i 0.132406 0.0961989i
\(337\) −6.35410 4.61653i −0.346130 0.251478i 0.401114 0.916028i \(-0.368623\pi\)
−0.747244 + 0.664550i \(0.768623\pi\)
\(338\) −12.5172 9.09429i −0.680847 0.494664i
\(339\) −13.6353 + 9.90659i −0.740565 + 0.538052i
\(340\) 0 0
\(341\) −12.7082 9.23305i −0.688188 0.499998i
\(342\) 0.854102 + 2.62866i 0.0461845 + 0.142141i
\(343\) −8.41641 −0.454443
\(344\) −3.35410 10.3229i −0.180841 0.556572i
\(345\) 0 0
\(346\) −9.44427 + 29.0665i −0.507727 + 1.56262i
\(347\) −6.15248 + 18.9354i −0.330282 + 1.01650i 0.638717 + 0.769441i \(0.279465\pi\)
−0.969000 + 0.247063i \(0.920535\pi\)
\(348\) 1.80902 1.31433i 0.0969735 0.0704554i
\(349\) 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
\(352\) 14.3262 10.4086i 0.763591 0.554781i
\(353\) 3.98936 12.2780i 0.212332 0.653491i −0.787000 0.616953i \(-0.788367\pi\)
0.999332 0.0365381i \(-0.0116330\pi\)
\(354\) 5.42705 16.7027i 0.288445 0.887741i
\(355\) 0 0
\(356\) −1.70820 5.25731i −0.0905346 0.278637i
\(357\) −3.23607 −0.171271
\(358\) 0.263932 + 0.812299i 0.0139492 + 0.0429313i
\(359\) −11.1180 8.07772i −0.586787 0.426326i 0.254377 0.967105i \(-0.418130\pi\)
−0.841165 + 0.540779i \(0.818130\pi\)
\(360\) 0 0
\(361\) 14.7812 10.7391i 0.777955 0.565218i
\(362\) 0.381966 + 0.277515i 0.0200757 + 0.0145858i
\(363\) −13.2812 9.64932i −0.697080 0.506458i
\(364\) −0.572949 + 0.416272i −0.0300307 + 0.0218186i
\(365\) 0 0
\(366\) 11.3992 + 8.28199i 0.595845 + 0.432907i
\(367\) −7.89919 24.3112i −0.412334 1.26903i −0.914614 0.404329i \(-0.867505\pi\)
0.502279 0.864705i \(-0.332495\pi\)
\(368\) −18.2705 −0.952416
\(369\) 0.472136 + 1.45309i 0.0245784 + 0.0756446i
\(370\) 0 0
\(371\) −0.663119 + 2.04087i −0.0344274 + 0.105957i
\(372\) −0.572949 + 1.76336i −0.0297060 + 0.0914257i
\(373\) 22.8713 16.6170i 1.18423 0.860395i 0.191589 0.981475i \(-0.438636\pi\)
0.992643 + 0.121080i \(0.0386358\pi\)
\(374\) −44.3607 −2.29384
\(375\) 0 0
\(376\) 1.38197 0.0712695
\(377\) 5.42705 3.94298i 0.279507 0.203074i
\(378\) 1.54508 4.75528i 0.0794706 0.244585i
\(379\) 4.51064 13.8823i 0.231696 0.713087i −0.765846 0.643024i \(-0.777680\pi\)
0.997543 0.0700639i \(-0.0223203\pi\)
\(380\) 0 0
\(381\) 6.14590 + 18.9151i 0.314864 + 0.969051i
\(382\) 2.94427 0.150642
\(383\) 10.3090 + 31.7279i 0.526766 + 1.62122i 0.760797 + 0.648990i \(0.224808\pi\)
−0.234031 + 0.972229i \(0.575192\pi\)
\(384\) 11.0172 + 8.00448i 0.562220 + 0.408477i
\(385\) 0 0
\(386\) 10.0902 7.33094i 0.513576 0.373135i
\(387\) −7.85410 5.70634i −0.399246 0.290070i
\(388\) 1.92705 + 1.40008i 0.0978312 + 0.0710785i
\(389\) −12.1353 + 8.81678i −0.615282 + 0.447028i −0.851270 0.524727i \(-0.824167\pi\)
0.235988 + 0.971756i \(0.424167\pi\)
\(390\) 0 0
\(391\) 15.9443 + 11.5842i 0.806336 + 0.585838i
\(392\) −4.57295 14.0741i −0.230969 0.710849i
\(393\) 6.79837 0.342933
\(394\) −1.85410 5.70634i −0.0934083 0.287481i
\(395\) 0 0
\(396\) 2.00000 6.15537i 0.100504 0.309319i
\(397\) 8.97214 27.6134i 0.450299 1.38588i −0.426268 0.904597i \(-0.640172\pi\)
0.876567 0.481280i \(-0.159828\pi\)
\(398\) −22.9894 + 16.7027i −1.15235 + 0.837233i
\(399\) 0.527864 0.0264263
\(400\) 0 0
\(401\) 26.5967 1.32818 0.664089 0.747653i \(-0.268820\pi\)
0.664089 + 0.747653i \(0.268820\pi\)
\(402\) 6.23607 4.53077i 0.311027 0.225974i
\(403\) −1.71885 + 5.29007i −0.0856219 + 0.263517i
\(404\) 0.281153 0.865300i 0.0139879 0.0430503i
\(405\) 0 0
\(406\) 1.11803 + 3.44095i 0.0554871 + 0.170772i
\(407\) 1.23607 0.0612696
\(408\) −3.61803 11.1352i −0.179119 0.551273i
\(409\) −1.28115 0.930812i −0.0633489 0.0460257i 0.555660 0.831410i \(-0.312466\pi\)
−0.619009 + 0.785384i \(0.712466\pi\)
\(410\) 0 0
\(411\) 9.66312 7.02067i 0.476647 0.346304i
\(412\) −4.28115 3.11044i −0.210917 0.153240i
\(413\) 5.42705 + 3.94298i 0.267048 + 0.194022i
\(414\) −9.85410 + 7.15942i −0.484303 + 0.351867i
\(415\) 0 0
\(416\) −5.07295 3.68571i −0.248722 0.180707i
\(417\) 1.54508 + 4.75528i 0.0756631 + 0.232867i
\(418\) 7.23607 0.353928
\(419\) −2.92705 9.00854i −0.142996 0.440096i 0.853752 0.520680i \(-0.174321\pi\)
−0.996748 + 0.0805840i \(0.974321\pi\)
\(420\) 0 0
\(421\) 9.88854 30.4338i 0.481938 1.48325i −0.354429 0.935083i \(-0.615325\pi\)
0.836367 0.548170i \(-0.184675\pi\)
\(422\) 4.59017 14.1271i 0.223446 0.687696i
\(423\) 1.00000 0.726543i 0.0486217 0.0353257i
\(424\) −7.76393 −0.377050
\(425\) 0 0
\(426\) 10.7082 0.518814
\(427\) −4.35410 + 3.16344i −0.210710 + 0.153090i
\(428\) −3.13525 + 9.64932i −0.151548 + 0.466418i
\(429\) −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 \(-0.355170\pi\)
\(432\) 24.2705 1.16772
\(433\) 8.29837 + 25.5398i 0.398794 + 1.22736i 0.925967 + 0.377605i \(0.123252\pi\)
−0.527173 + 0.849758i \(0.676748\pi\)
\(434\) −2.42705 1.76336i −0.116502 0.0846438i
\(435\) 0 0
\(436\) −5.00000 + 3.63271i −0.239457 + 0.173975i
\(437\) −2.60081 1.88960i −0.124414 0.0903919i
\(438\) −11.7812 8.55951i −0.562925 0.408989i
\(439\) 33.1525 24.0867i 1.58228 1.14959i 0.668261 0.743927i \(-0.267039\pi\)
0.914021 0.405667i \(-0.132961\pi\)
\(440\) 0 0
\(441\) −10.7082 7.77997i −0.509914 0.370475i
\(442\) 4.85410 + 14.9394i 0.230886 + 0.710594i
\(443\) 29.9443 1.42270 0.711348 0.702840i \(-0.248085\pi\)
0.711348 + 0.702840i \(0.248085\pi\)
\(444\) −0.0450850 0.138757i −0.00213964 0.00658513i
\(445\) 0 0
\(446\) 0.0901699 0.277515i 0.00426967 0.0131407i
\(447\) −1.21885 + 3.75123i −0.0576495 + 0.177427i
\(448\) −2.11803 + 1.53884i −0.100068 + 0.0727034i
\(449\) 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
\(452\) −8.42705 + 6.12261i −0.396375 + 0.287983i
\(453\) 4.50000 13.8496i 0.211428 0.650710i
\(454\) −7.38197 + 22.7194i −0.346453 + 1.06627i
\(455\) 0 0
\(456\) 0.590170 + 1.81636i 0.0276372 + 0.0850587i
\(457\) −21.4164 −1.00182 −0.500909 0.865500i \(-0.667001\pi\)
−0.500909 + 0.865500i \(0.667001\pi\)
\(458\) −10.8541 33.4055i −0.507179 1.56094i
\(459\) −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 \(0.306076\pi\)
\(462\) −4.23607 3.07768i −0.197080 0.143187i
\(463\) 19.5172 + 14.1801i 0.907042 + 0.659005i 0.940265 0.340443i \(-0.110577\pi\)
−0.0332229 + 0.999448i \(0.510577\pi\)
\(464\) −14.2082 + 10.3229i −0.659599 + 0.479227i
\(465\) 0 0
\(466\) −3.85410 2.80017i −0.178538 0.129715i
\(467\) 8.48278 + 26.1073i 0.392536 + 1.20810i 0.930864 + 0.365367i \(0.119056\pi\)
−0.538328 + 0.842736i \(0.680944\pi\)
\(468\) −2.29180 −0.105938
\(469\) 0.909830 + 2.80017i 0.0420120 + 0.129300i
\(470\) 0 0
\(471\) 4.07295 12.5352i 0.187672 0.577594i
\(472\) −7.50000 + 23.0826i −0.345215 + 1.06246i
\(473\) −20.5623 + 14.9394i −0.945456 + 0.686914i
\(474\) 13.0902 0.601251
\(475\) 0 0
\(476\) −2.00000 −0.0916698
\(477\) −5.61803 + 4.08174i −0.257232 + 0.186890i
\(478\) 10.2639 31.5891i 0.469461 1.44485i
\(479\) −3.35410 + 10.3229i −0.153253 + 0.471664i −0.997980 0.0635340i \(-0.979763\pi\)
0.844727 + 0.535198i \(0.179763\pi\)
\(480\) 0 0
\(481\) −0.135255 0.416272i −0.00616709 0.0189804i
\(482\) −4.09017 −0.186302
\(483\) 0.718847 + 2.21238i 0.0327087 + 0.100667i
\(484\) −8.20820 5.96361i −0.373100 0.271073i
\(485\) 0 0
\(486\) 20.9443 15.2169i 0.950051 0.690253i
\(487\) 29.4615 + 21.4050i 1.33503 + 0.969954i 0.999611 + 0.0278844i \(0.00887705\pi\)
0.335417 + 0.942070i \(0.391123\pi\)
\(488\) −15.7533 11.4454i −0.713118 0.518110i
\(489\) −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 \(0.270017\pi\)
\(492\) −0.145898 0.449028i −0.00657759 0.0202437i
\(493\) 18.9443 0.853207
\(494\) −0.791796 2.43690i −0.0356246 0.109641i
\(495\) 0 0
\(496\) 4.50000 13.8496i 0.202056 0.621864i
\(497\) −1.26393 + 3.88998i −0.0566951 + 0.174490i
\(498\) −8.16312 + 5.93085i −0.365798 + 0.265768i
\(499\) 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
\(502\) −38.1976 + 27.7522i −1.70484 + 1.23864i
\(503\) −11.5623 + 35.5851i −0.515538 + 1.58666i 0.266764 + 0.963762i \(0.414046\pi\)
−0.782301 + 0.622900i \(0.785954\pi\)
\(504\) −0.854102 + 2.62866i −0.0380447 + 0.117090i
\(505\) 0 0
\(506\) 9.85410 + 30.3278i 0.438068 + 1.34824i
\(507\) −9.56231 −0.424677
\(508\) 3.79837 + 11.6902i 0.168526 + 0.518668i
\(509\) 16.4443 + 11.9475i 0.728880 + 0.529562i 0.889209 0.457502i \(-0.151256\pi\)
−0.160329 + 0.987064i \(0.551256\pi\)
\(510\) 0 0
\(511\) 4.50000 3.26944i 0.199068 0.144632i
\(512\) −4.28115 3.11044i −0.189202 0.137463i
\(513\) 3.45492 + 2.51014i 0.152538 + 0.110826i
\(514\) 29.9164 21.7355i 1.31956 0.958714i
\(515\) 0 0
\(516\) 2.42705 + 1.76336i 0.106845 + 0.0776274i
\(517\) −1.00000 3.07768i −0.0439799 0.135356i
\(518\) 0.236068 0.0103722
\(519\) 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 \(-0.122376\pi\)
\(522\) −3.61803 + 11.1352i −0.158357 + 0.487373i
\(523\) 10.6353 7.72696i 0.465047 0.337877i −0.330461 0.943820i \(-0.607204\pi\)
0.795508 + 0.605943i \(0.207204\pi\)
\(524\) 4.20163 0.183549
\(525\) 0 0
\(526\) 17.6525 0.769685
\(527\) −12.7082 + 9.23305i −0.553578 + 0.402198i
\(528\) 7.85410 24.1724i 0.341806 1.05197i
\(529\) −2.72949 + 8.40051i −0.118673 + 0.365239i
\(530\) 0 0
\(531\) 6.70820 + 20.6457i 0.291111 + 0.895948i
\(532\) 0.326238 0.0141442
\(533\) −0.437694 1.34708i −0.0189586 0.0583487i
\(534\) −11.7082 8.50651i −0.506664 0.368113i
\(535\) 0 0
\(536\) −8.61803 + 6.26137i −0.372242 + 0.270450i
\(537\) 0.427051 + 0.310271i 0.0184286 + 0.0133892i
\(538\) −16.7082 12.1392i −0.720342 0.523359i
\(539\) −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 \(0.898156\pi\)
\(542\) 4.00000 + 12.3107i 0.171815 + 0.528791i
\(543\) 0.291796 0.0125222
\(544\) −5.47214 16.8415i −0.234616 0.722073i
\(545\) 0 0
\(546\) −0.572949 + 1.76336i −0.0245200 + 0.0754647i
\(547\) −6.57953 + 20.2497i −0.281320 + 0.865815i 0.706157 + 0.708055i \(0.250427\pi\)
−0.987478 + 0.157760i \(0.949573\pi\)
\(548\) 5.97214 4.33901i 0.255117 0.185353i
\(549\) −17.4164 −0.743314
\(550\) 0 0
\(551\) −3.09017 −0.131646
\(552\) −6.80902 + 4.94704i −0.289811 + 0.210560i
\(553\) −1.54508 + 4.75528i −0.0657037 + 0.202215i
\(554\) 12.3541 38.0220i 0.524875 1.61540i
\(555\) 0 0
\(556\) 0.954915 + 2.93893i 0.0404974 + 0.124638i
\(557\) 4.76393 0.201854 0.100927 0.994894i \(-0.467819\pi\)
0.100927 + 0.994894i \(0.467819\pi\)
\(558\) −3.00000 9.23305i −0.127000 0.390866i
\(559\) 7.28115 + 5.29007i 0.307960 + 0.223746i
\(560\) 0 0
\(561\) −22.1803 + 16.1150i −0.936455 + 0.680374i
\(562\) 13.2082 + 9.59632i 0.557154 + 0.404796i
\(563\) −5.97214 4.33901i −0.251696 0.182868i 0.454782 0.890603i \(-0.349717\pi\)
−0.706478 + 0.707735i \(0.749717\pi\)
\(564\) −0.309017 + 0.224514i −0.0130120 + 0.00945374i
\(565\) 0 0
\(566\) −39.0795 28.3929i −1.64264 1.19344i
\(567\) 0.190983 + 0.587785i 0.00802053 + 0.0246847i
\(568\) −14.7984 −0.620926
\(569\) 6.34346 + 19.5232i 0.265932 + 0.818453i 0.991477 + 0.130279i \(0.0415874\pi\)
−0.725546 + 0.688174i \(0.758413\pi\)
\(570\) 0 0
\(571\) −2.51064 + 7.72696i −0.105067 + 0.323363i −0.989746 0.142837i \(-0.954377\pi\)
0.884679 + 0.466201i \(0.154377\pi\)
\(572\) −1.85410 + 5.70634i −0.0775239 + 0.238594i
\(573\) 1.47214 1.06957i 0.0614994 0.0446819i
\(574\) 0.763932 0.0318859
\(575\) 0 0
\(576\) −8.47214 −0.353006
\(577\) 27.3262 19.8537i 1.13761 0.826519i 0.150822 0.988561i \(-0.451808\pi\)
0.986784 + 0.162042i \(0.0518079\pi\)
\(578\) −5.20820 + 16.0292i −0.216633 + 0.666727i
\(579\) 2.38197 7.33094i 0.0989911 0.304663i
\(580\) 0 0
\(581\) −1.19098 3.66547i −0.0494103 0.152069i
\(582\) 6.23607 0.258493
\(583\) 5.61803 + 17.2905i 0.232675 + 0.716101i
\(584\) 16.2812 + 11.8290i 0.673719 + 0.489485i
\(585\) 0 0
\(586\) −25.5623 + 18.5721i −1.05597 + 0.767206i
\(587\) −4.28115 3.11044i −0.176702 0.128382i 0.495919 0.868369i \(-0.334831\pi\)
−0.672621 + 0.739987i \(0.734831\pi\)
\(588\) 3.30902 + 2.40414i 0.136462 + 0.0991451i
\(589\) 2.07295 1.50609i 0.0854144 0.0620572i
\(590\) 0 0
\(591\) −3.00000 2.17963i −0.123404 0.0896579i
\(592\) 0.354102 + 1.08981i 0.0145535 + 0.0447911i
\(593\) −10.9098 −0.448013 −0.224007 0.974588i \(-0.571914\pi\)
−0.224007 + 0.974588i \(0.571914\pi\)
\(594\) −13.0902 40.2874i −0.537096 1.65301i
\(595\) 0 0
\(596\) −0.753289 + 2.31838i −0.0308559 + 0.0949647i
\(597\) −5.42705 + 16.7027i −0.222114 + 0.683598i
\(598\) 9.13525 6.63715i 0.373568 0.271413i
\(599\) −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 \(0.482271\pi\)
\(602\) −3.92705 + 2.85317i −0.160055 + 0.116287i
\(603\) −2.94427 + 9.06154i −0.119900 + 0.369014i
\(604\) 2.78115 8.55951i 0.113164 0.348281i
\(605\) 0 0
\(606\) −0.736068 2.26538i −0.0299007 0.0920249i
\(607\) −35.5623 −1.44343 −0.721715 0.692191i \(-0.756646\pi\)
−0.721715 + 0.692191i \(0.756646\pi\)
\(608\) 0.892609 + 2.74717i 0.0362001 + 0.111412i
\(609\) 1.80902 + 1.31433i 0.0733051 + 0.0532592i
\(610\) 0 0
\(611\) −0.927051 + 0.673542i −0.0375045 + 0.0272486i
\(612\) −5.23607 3.80423i −0.211656 0.153777i
\(613\) 12.1180 + 8.80427i 0.489443 + 0.355601i 0.804970 0.593316i \(-0.202181\pi\)
−0.315527 + 0.948917i \(0.602181\pi\)
\(614\) 12.0902 8.78402i 0.487920 0.354494i
\(615\) 0 0
\(616\) 5.85410 + 4.25325i 0.235868 + 0.171368i
\(617\) 4.39919 + 13.5393i 0.177105 + 0.545072i 0.999723 0.0235215i \(-0.00748780\pi\)
−0.822619 + 0.568593i \(0.807488\pi\)
\(618\) −13.8541 −0.557294
\(619\) 9.43363 + 29.0337i 0.379170 + 1.16696i 0.940622 + 0.339455i \(0.110243\pi\)
−0.561453 + 0.827509i \(0.689757\pi\)
\(620\) 0 0
\(621\) −5.81559 + 17.8986i −0.233372 + 0.718244i
\(622\) −4.25329 + 13.0903i −0.170541 + 0.524872i
\(623\) 4.47214 3.24920i 0.179172 0.130176i
\(624\) −9.00000 −0.360288
\(625\) 0 0
\(626\) 27.1246 1.08412
\(627\) 3.61803 2.62866i 0.144490 0.104978i
\(628\) 2.51722 7.74721i 0.100448 0.309147i
\(629\) 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 \(0.965312\pi\)
\(632\) −18.0902 −0.719588
\(633\) −2.83688 8.73102i −0.112756 0.347027i
\(634\) 10.0172 + 7.27794i 0.397835 + 0.289044i
\(635\) 0 0
\(636\) 1.73607 1.26133i 0.0688396 0.0500149i
\(637\) 9.92705 + 7.21242i 0.393324 + 0.285767i
\(638\) 24.7984 + 18.0171i 0.981777 + 0.713303i
\(639\) −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 \(0.693146\pi\)
\(642\) 8.20820 + 25.2623i 0.323952 + 0.997022i
\(643\) −30.8328 −1.21593 −0.607964 0.793965i \(-0.708013\pi\)
−0.607964 + 0.793965i \(0.708013\pi\)
\(644\) 0.444272 + 1.36733i 0.0175068 + 0.0538803i
\(645\) 0 0
\(646\) 2.23607 6.88191i 0.0879769 0.270765i
\(647\) −11.2918 + 34.7526i −0.443926 + 1.36626i 0.439731 + 0.898130i \(0.355074\pi\)
−0.883657 + 0.468135i \(0.844926\pi\)
\(648\) −1.80902 + 1.31433i −0.0710649 + 0.0516317i
\(649\) 56.8328 2.23088
\(650\) 0 0
\(651\) −1.85410 −0.0726680
\(652\) −5.50000 + 3.99598i −0.215397 + 0.156495i
\(653\) 5.89919 18.1558i 0.230853 0.710493i −0.766791 0.641896i \(-0.778148\pi\)
0.997645 0.0685963i \(-0.0218520\pi\)
\(654\) −5.00000 + 15.3884i −0.195515 + 0.601735i
\(655\) 0 0
\(656\) 1.14590 + 3.52671i 0.0447398 + 0.137695i
\(657\) 18.0000 0.702247
\(658\) −0.190983 0.587785i −0.00744529 0.0229143i
\(659\) −12.5623 9.12705i −0.489358 0.355539i 0.315579 0.948899i \(-0.397801\pi\)
−0.804937 + 0.593360i \(0.797801\pi\)
\(660\) 0 0
\(661\) −15.9271 + 11.5717i −0.619490 + 0.450086i −0.852744 0.522330i \(-0.825063\pi\)
0.233253 + 0.972416i \(0.425063\pi\)
\(662\) −30.2705 21.9928i −1.17650 0.854775i
\(663\) 7.85410 + 5.70634i 0.305028 + 0.221616i
\(664\) 11.2812 8.19624i 0.437794 0.318076i
\(665\) 0 0
\(666\) 0.618034 + 0.449028i 0.0239483 + 0.0173995i
\(667\) −4.20820 12.9515i −0.162942 0.501485i
\(668\) 9.00000 0.348220
\(669\) −0.0557281 0.171513i −0.00215457 0.00663109i
\(670\) 0 0
\(671\) −14.0902 + 43.3651i −0.543945 + 1.67409i
\(672\) 0.645898 1.98787i 0.0249161 0.0766837i
\(673\) −9.85410 + 7.15942i −0.379848 + 0.275976i −0.761283 0.648420i \(-0.775430\pi\)
0.381435 + 0.924396i \(0.375430\pi\)
\(674\) −12.7082 −0.489502
\(675\) 0 0
\(676\) −5.90983 −0.227301
\(677\) −8.59017 + 6.24112i −0.330147 + 0.239866i −0.740493 0.672064i \(-0.765408\pi\)
0.410346 + 0.911930i \(0.365408\pi\)
\(678\) −8.42705 + 25.9358i −0.323639 + 0.996058i
\(679\) −0.736068 + 2.26538i −0.0282477 + 0.0869375i
\(680\) 0 0
\(681\) 4.56231 + 14.0413i 0.174828 + 0.538065i
\(682\) −25.4164 −0.973245
\(683\) −4.16312 12.8128i −0.159297 0.490267i 0.839274 0.543709i \(-0.182981\pi\)
−0.998571 + 0.0534426i \(0.982981\pi\)
\(684\) 0.854102 + 0.620541i 0.0326574 + 0.0237270i
\(685\) 0 0
\(686\) −11.0172 + 8.00448i −0.420639 + 0.305612i
\(687\) −17.5623 12.7598i −0.670044 0.486815i
\(688\) −19.0623 13.8496i −0.726744 0.528010i
\(689\) 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 \(0.942344\pi\)
\(692\) 3.60739 + 11.1024i 0.137132 + 0.422050i
\(693\) 6.47214 0.245856
\(694\) 9.95492 + 30.6381i 0.377883 + 1.16301i
\(695\) 0 0
\(696\) −2.50000 + 7.69421i −0.0947623 + 0.291648i
\(697\) 1.23607 3.80423i 0.0468194 0.144095i
\(698\) 28.4164 20.6457i 1.07558 0.781452i
\(699\) −2.94427 −0.111363
\(700\) 0 0
\(701\) −41.0132 −1.54905 −0.774523 0.632546i \(-0.782010\pi\)
−0.774523 + 0.632546i \(0.782010\pi\)
\(702\) −12.1353 + 8.81678i −0.458016 + 0.332768i
\(703\) −0.0623059 + 0.191758i −0.00234991 + 0.00723228i
\(704\) −6.85410 + 21.0948i −0.258324 + 0.795039i
\(705\) 0 0
\(706\) −6.45492 19.8662i −0.242934 0.747674i
\(707\) 0.909830 0.0342177
\(708\) −2.07295 6.37988i −0.0779062 0.239771i
\(709\) 27.1353 + 19.7149i 1.01909 + 0.740409i 0.966095 0.258186i \(-0.0831247\pi\)
0.0529906 + 0.998595i \(0.483125\pi\)
\(710\) 0 0
\(711\) −13.0902 + 9.51057i −0.490920 + 0.356674i
\(712\) 16.1803 + 11.7557i 0.606384 + 0.440564i
\(713\) 9.13525 + 6.63715i 0.342118 + 0.248563i
\(714\) −4.23607 + 3.07768i −0.158531 + 0.115179i
\(715\) 0 0
\(716\) 0.263932 + 0.191758i 0.00986360 + 0.00716633i
\(717\) −6.34346 19.5232i −0.236901 0.729106i
\(718\) −22.2361 −0.829843
\(719\) −7.19756 22.1518i −0.268424 0.826123i −0.990885 0.134712i \(-0.956989\pi\)
0.722461 0.691412i \(-0.243011\pi\)
\(720\) 0 0
\(721\) 1.63525 5.03280i 0.0609001 0.187431i
\(722\) 9.13525 28.1154i 0.339979 1.04635i
\(723\) −2.04508 + 1.48584i −0.0760575 + 0.0552590i
\(724\) 0.180340 0.00670228
\(725\) 0 0
\(726\) −26.5623 −0.985820
\(727\) −19.8713 + 14.4374i −0.736987 + 0.535452i −0.891766 0.452497i \(-0.850533\pi\)
0.154779 + 0.987949i \(0.450533\pi\)
\(728\) 0.791796 2.43690i 0.0293459 0.0903174i
\(729\) 4.01722 12.3637i 0.148786 0.457916i
\(730\) 0 0
\(731\) 7.85410 + 24.1724i 0.290494 + 0.894050i
\(732\) 5.38197 0.198923
\(733\) −6.17376 19.0009i −0.228033 0.701814i −0.997970 0.0636931i \(-0.979712\pi\)
0.769936 0.638121i \(-0.220288\pi\)
\(734\) −33.4615 24.3112i −1.23509 0.897343i
\(735\) 0 0
\(736\) −10.2984 + 7.48221i −0.379603 + 0.275798i
\(737\) 20.1803 + 14.6619i 0.743352 + 0.540077i
\(738\) 2.00000 + 1.45309i 0.0736210 + 0.0534888i
\(739\) −12.9271 + 9.39205i −0.475529 + 0.345492i −0.799592 0.600543i \(-0.794951\pi\)
0.324063 + 0.946036i \(0.394951\pi\)
\(740\) 0 0
\(741\) −1.28115 0.930812i −0.0470643 0.0341942i
\(742\) 1.07295 + 3.30220i 0.0393892 + 0.121227i
\(743\) 28.3607 1.04045 0.520226 0.854029i \(-0.325848\pi\)
0.520226 + 0.854029i \(0.325848\pi\)
\(744\) −2.07295 6.37988i −0.0759980 0.233898i
\(745\) 0 0
\(746\) 14.1353 43.5038i 0.517528 1.59279i
\(747\) 3.85410 11.8617i 0.141014 0.433997i
\(748\) −13.7082 + 9.95959i −0.501222 + 0.364159i
\(749\) −10.1459 −0.370723
\(750\) 0 0
\(751\) −5.11146 −0.186520 −0.0932598 0.995642i \(-0.529729\pi\)
−0.0932598 + 0.995642i \(0.529729\pi\)
\(752\) 2.42705 1.76336i 0.0885054 0.0643030i
\(753\) −9.01722 + 27.7522i −0.328606 + 1.01134i
\(754\) 3.35410 10.3229i 0.122149 0.375937i
\(755\) 0 0
\(756\) −0.590170 1.81636i −0.0214643 0.0660602i
\(757\) 30.4164 1.10550 0.552752 0.833346i \(-0.313578\pi\)
0.552752 + 0.833346i \(0.313578\pi\)
\(758\) −7.29837 22.4621i −0.265089 0.815860i
\(759\) 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 \(0.191459\pi\)
\(762\) 26.0344 + 18.9151i 0.943128 + 0.685223i
\(763\) −5.00000 3.63271i −0.181012 0.131513i
\(764\) 0.909830 0.661030i 0.0329165 0.0239152i
\(765\) 0 0
\(766\) 43.6697 + 31.7279i 1.57785 + 1.14638i
\(767\) −6.21885 19.1396i −0.224550 0.691092i
\(768\) 13.5623 0.489388
\(769\) 4.14590 + 12.7598i 0.149505 + 0.460129i 0.997563 0.0697749i \(-0.0222281\pi\)
−0.848058 + 0.529904i \(0.822228\pi\)
\(770\) 0 0
\(771\) 7.06231 21.7355i 0.254343 0.782786i
\(772\) 1.47214 4.53077i 0.0529833 0.163066i
\(773\) 29.2533 21.2538i 1.05217 0.764445i 0.0795442 0.996831i \(-0.474654\pi\)
0.972623 + 0.232387i \(0.0746535\pi\)
\(774\) −15.7082 −0.564620
\(775\) 0 0
\(776\) −8.61803 −0.309369
\(777\) 0.118034 0.0857567i 0.00423445 0.00307650i
\(778\) −7.50000 + 23.0826i −0.268888 + 0.827552i
\(779\) −0.201626 + 0.620541i −0.00722401 + 0.0222332i
\(780\) 0 0
\(781\) 10.7082 + 32.9565i 0.383170 + 1.17927i
\(782\) 31.8885