Properties

Label 210.3.o.b.61.4
Level 210
Weight 3
Character 210.61
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 61.4
Root \(-2.63284 + 4.56021i\) of \(x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + 595763862 x^{4} - 630430976 x^{3} + 1087013404 x^{2} + 294123256 x + 101626561\)
Character \(\chi\) \(=\) 210.61
Dual form 210.3.o.b.31.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(1.94434 + 6.72455i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(1.94434 + 6.72455i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(0.263223 + 0.455915i) q^{11} +(3.00000 + 1.73205i) q^{12} +4.22307i q^{13} +(-9.61071 - 2.37366i) q^{14} -3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-28.8825 + 16.6753i) q^{17} +(2.12132 + 3.67423i) q^{18} +(2.75133 + 1.58848i) q^{19} -4.47214i q^{20} +(-8.74014 - 8.40298i) q^{21} -0.744507 q^{22} +(-5.52954 + 9.57744i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-5.17218 - 2.98616i) q^{26} +5.19615i q^{27} +(9.70292 - 10.0922i) q^{28} -56.1302 q^{29} +(2.73861 - 4.74342i) q^{30} +(-1.63817 + 0.945800i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-0.789668 - 0.455915i) q^{33} -47.1649i q^{34} +(-3.75308 + 15.1959i) q^{35} -6.00000 q^{36} +(4.87682 - 8.44690i) q^{37} +(-3.89097 + 2.24645i) q^{38} +(-3.65729 - 6.33460i) q^{39} +(5.47723 + 3.16228i) q^{40} -4.07377i q^{41} +(16.4717 - 4.76263i) q^{42} +46.3519 q^{43} +(0.526446 - 0.911831i) q^{44} +(5.80948 - 3.35410i) q^{45} +(-7.81995 - 13.5445i) q^{46} +(54.7969 + 31.6370i) q^{47} -6.92820i q^{48} +(-41.4391 + 26.1496i) q^{49} -7.07107 q^{50} +(28.8825 - 50.0259i) q^{51} +(7.31457 - 4.22307i) q^{52} +(23.2606 + 40.2885i) q^{53} +(-6.36396 - 3.67423i) q^{54} +1.17717i q^{55} +(5.49942 + 19.0199i) q^{56} -5.50267 q^{57} +(39.6900 - 68.7452i) q^{58} +(-43.7614 + 25.2657i) q^{59} +(3.87298 + 6.70820i) q^{60} +(89.4583 + 51.6488i) q^{61} -2.67513i q^{62} +(20.3874 + 5.03529i) q^{63} +8.00000 q^{64} +(-4.72153 + 8.17794i) q^{65} +(1.11676 - 0.644762i) q^{66} +(-4.36948 - 7.56816i) q^{67} +(57.7649 + 33.3506i) q^{68} -19.1549i q^{69} +(-15.9572 - 15.3417i) q^{70} +29.0608 q^{71} +(4.24264 - 7.34847i) q^{72} +(14.4912 - 8.36647i) q^{73} +(6.89686 + 11.9457i) q^{74} +(-7.50000 - 4.33013i) q^{75} -6.35393i q^{76} +(-2.55403 + 2.65651i) q^{77} +10.3444 q^{78} +(66.1473 - 114.571i) q^{79} +(-7.74597 + 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.98933 + 2.88059i) q^{82} -12.4838i q^{83} +(-5.81425 + 23.5413i) q^{84} -74.5742 q^{85} +(-32.7757 + 56.7692i) q^{86} +(84.1953 - 48.6102i) q^{87} +(0.744507 + 1.28952i) q^{88} +(-59.1101 - 34.1272i) q^{89} +9.48683i q^{90} +(-28.3982 + 8.21107i) q^{91} +22.1182 q^{92} +(1.63817 - 2.83740i) q^{93} +(-77.4945 + 44.7415i) q^{94} +(3.55196 + 6.15217i) q^{95} +(8.48528 + 4.89898i) q^{96} +149.281i q^{97} +(-2.72468 - 69.2429i) q^{98} +1.57934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} + O(q^{10}) \) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} - 4q^{11} + 48q^{12} + 8q^{14} - 32q^{16} + 12q^{17} - 72q^{19} - 24q^{21} - 48q^{22} - 12q^{23} + 40q^{25} + 32q^{28} + 72q^{29} + 120q^{31} + 12q^{33} - 20q^{35} - 96q^{36} + 44q^{37} - 72q^{38} + 36q^{39} - 24q^{42} - 56q^{43} - 8q^{44} + 8q^{46} - 24q^{47} - 40q^{49} - 12q^{51} - 72q^{52} + 32q^{53} + 16q^{56} + 144q^{57} - 88q^{58} + 132q^{59} + 96q^{61} + 60q^{63} + 128q^{64} + 20q^{65} + 72q^{66} - 164q^{67} - 24q^{68} - 136q^{71} - 348q^{73} - 112q^{74} - 120q^{75} + 96q^{77} + 280q^{79} - 72q^{81} + 264q^{82} - 24q^{84} + 120q^{85} - 88q^{86} - 108q^{87} + 48q^{88} - 300q^{89} - 272q^{91} + 48q^{92} - 120q^{93} + 200q^{95} + 384q^{98} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 1.22474i −0.353553 + 0.612372i
\(3\) −1.50000 + 0.866025i −0.500000 + 0.288675i
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) 1.93649 + 1.11803i 0.387298 + 0.223607i
\(6\) 2.44949i 0.408248i
\(7\) 1.94434 + 6.72455i 0.277762 + 0.960650i
\(8\) 2.82843 0.353553
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) −2.73861 + 1.58114i −0.273861 + 0.158114i
\(11\) 0.263223 + 0.455915i 0.0239293 + 0.0414468i 0.877742 0.479133i \(-0.159049\pi\)
−0.853813 + 0.520580i \(0.825716\pi\)
\(12\) 3.00000 + 1.73205i 0.250000 + 0.144338i
\(13\) 4.22307i 0.324851i 0.986721 + 0.162426i \(0.0519318\pi\)
−0.986721 + 0.162426i \(0.948068\pi\)
\(14\) −9.61071 2.37366i −0.686479 0.169547i
\(15\) −3.87298 −0.258199
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −28.8825 + 16.6753i −1.69897 + 0.980900i −0.752228 + 0.658903i \(0.771021\pi\)
−0.946741 + 0.321997i \(0.895646\pi\)
\(18\) 2.12132 + 3.67423i 0.117851 + 0.204124i
\(19\) 2.75133 + 1.58848i 0.144807 + 0.0836044i 0.570653 0.821191i \(-0.306690\pi\)
−0.425846 + 0.904796i \(0.640023\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −8.74014 8.40298i −0.416197 0.400142i
\(22\) −0.744507 −0.0338412
\(23\) −5.52954 + 9.57744i −0.240415 + 0.416410i −0.960832 0.277130i \(-0.910617\pi\)
0.720418 + 0.693540i \(0.243950\pi\)
\(24\) −4.24264 + 2.44949i −0.176777 + 0.102062i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) −5.17218 2.98616i −0.198930 0.114852i
\(27\) 5.19615i 0.192450i
\(28\) 9.70292 10.0922i 0.346533 0.360437i
\(29\) −56.1302 −1.93552 −0.967762 0.251866i \(-0.918956\pi\)
−0.967762 + 0.251866i \(0.918956\pi\)
\(30\) 2.73861 4.74342i 0.0912871 0.158114i
\(31\) −1.63817 + 0.945800i −0.0528443 + 0.0305097i −0.526189 0.850367i \(-0.676380\pi\)
0.473345 + 0.880877i \(0.343046\pi\)
\(32\) −2.82843 4.89898i −0.0883883 0.153093i
\(33\) −0.789668 0.455915i −0.0239293 0.0138156i
\(34\) 47.1649i 1.38720i
\(35\) −3.75308 + 15.1959i −0.107231 + 0.434168i
\(36\) −6.00000 −0.166667
\(37\) 4.87682 8.44690i 0.131806 0.228294i −0.792567 0.609785i \(-0.791256\pi\)
0.924373 + 0.381491i \(0.124589\pi\)
\(38\) −3.89097 + 2.24645i −0.102394 + 0.0591172i
\(39\) −3.65729 6.33460i −0.0937765 0.162426i
\(40\) 5.47723 + 3.16228i 0.136931 + 0.0790569i
\(41\) 4.07377i 0.0993603i −0.998765 0.0496802i \(-0.984180\pi\)
0.998765 0.0496802i \(-0.0158202\pi\)
\(42\) 16.4717 4.76263i 0.392184 0.113396i
\(43\) 46.3519 1.07795 0.538975 0.842322i \(-0.318812\pi\)
0.538975 + 0.842322i \(0.318812\pi\)
\(44\) 0.526446 0.911831i 0.0119647 0.0207234i
\(45\) 5.80948 3.35410i 0.129099 0.0745356i
\(46\) −7.81995 13.5445i −0.169999 0.294447i
\(47\) 54.7969 + 31.6370i 1.16589 + 0.673127i 0.952709 0.303885i \(-0.0982839\pi\)
0.213182 + 0.977012i \(0.431617\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −41.4391 + 26.1496i −0.845696 + 0.533665i
\(50\) −7.07107 −0.141421
\(51\) 28.8825 50.0259i 0.566323 0.980900i
\(52\) 7.31457 4.22307i 0.140665 0.0812129i
\(53\) 23.2606 + 40.2885i 0.438878 + 0.760160i 0.997603 0.0691934i \(-0.0220426\pi\)
−0.558725 + 0.829353i \(0.688709\pi\)
\(54\) −6.36396 3.67423i −0.117851 0.0680414i
\(55\) 1.17717i 0.0214031i
\(56\) 5.49942 + 19.0199i 0.0982038 + 0.339641i
\(57\) −5.50267 −0.0965380
\(58\) 39.6900 68.7452i 0.684311 1.18526i
\(59\) −43.7614 + 25.2657i −0.741719 + 0.428231i −0.822694 0.568485i \(-0.807530\pi\)
0.0809752 + 0.996716i \(0.474197\pi\)
\(60\) 3.87298 + 6.70820i 0.0645497 + 0.111803i
\(61\) 89.4583 + 51.6488i 1.46653 + 0.846702i 0.999299 0.0374335i \(-0.0119182\pi\)
0.467231 + 0.884135i \(0.345252\pi\)
\(62\) 2.67513i 0.0431472i
\(63\) 20.3874 + 5.03529i 0.323609 + 0.0799252i
\(64\) 8.00000 0.125000
\(65\) −4.72153 + 8.17794i −0.0726390 + 0.125814i
\(66\) 1.11676 0.644762i 0.0169206 0.00976912i
\(67\) −4.36948 7.56816i −0.0652161 0.112958i 0.831574 0.555414i \(-0.187440\pi\)
−0.896790 + 0.442457i \(0.854107\pi\)
\(68\) 57.7649 + 33.3506i 0.849484 + 0.490450i
\(69\) 19.1549i 0.277607i
\(70\) −15.9572 15.3417i −0.227960 0.219167i
\(71\) 29.0608 0.409307 0.204653 0.978835i \(-0.434393\pi\)
0.204653 + 0.978835i \(0.434393\pi\)
\(72\) 4.24264 7.34847i 0.0589256 0.102062i
\(73\) 14.4912 8.36647i 0.198509 0.114609i −0.397451 0.917623i \(-0.630105\pi\)
0.595960 + 0.803014i \(0.296772\pi\)
\(74\) 6.89686 + 11.9457i 0.0932008 + 0.161429i
\(75\) −7.50000 4.33013i −0.100000 0.0577350i
\(76\) 6.35393i 0.0836044i
\(77\) −2.55403 + 2.65651i −0.0331692 + 0.0345001i
\(78\) 10.3444 0.132620
\(79\) 66.1473 114.571i 0.837308 1.45026i −0.0548297 0.998496i \(-0.517462\pi\)
0.892137 0.451764i \(-0.149205\pi\)
\(80\) −7.74597 + 4.47214i −0.0968246 + 0.0559017i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 4.98933 + 2.88059i 0.0608455 + 0.0351292i
\(83\) 12.4838i 0.150407i −0.997168 0.0752033i \(-0.976039\pi\)
0.997168 0.0752033i \(-0.0239606\pi\)
\(84\) −5.81425 + 23.5413i −0.0692173 + 0.280254i
\(85\) −74.5742 −0.877344
\(86\) −32.7757 + 56.7692i −0.381113 + 0.660107i
\(87\) 84.1953 48.6102i 0.967762 0.558738i
\(88\) 0.744507 + 1.28952i 0.00846030 + 0.0146537i
\(89\) −59.1101 34.1272i −0.664158 0.383452i 0.129701 0.991553i \(-0.458598\pi\)
−0.793860 + 0.608101i \(0.791931\pi\)
\(90\) 9.48683i 0.105409i
\(91\) −28.3982 + 8.21107i −0.312068 + 0.0902315i
\(92\) 22.1182 0.240415
\(93\) 1.63817 2.83740i 0.0176148 0.0305097i
\(94\) −77.4945 + 44.7415i −0.824409 + 0.475973i
\(95\) 3.55196 + 6.15217i 0.0373890 + 0.0647597i
\(96\) 8.48528 + 4.89898i 0.0883883 + 0.0510310i
\(97\) 149.281i 1.53898i 0.638659 + 0.769490i \(0.279490\pi\)
−0.638659 + 0.769490i \(0.720510\pi\)
\(98\) −2.72468 69.2429i −0.0278029 0.706560i
\(99\) 1.57934 0.0159529
\(100\) 5.00000 8.66025i 0.0500000 0.0866025i
\(101\) 83.7839 48.3726i 0.829543 0.478937i −0.0241531 0.999708i \(-0.507689\pi\)
0.853696 + 0.520771i \(0.174356\pi\)
\(102\) 40.8460 + 70.7473i 0.400451 + 0.693601i
\(103\) 90.7268 + 52.3811i 0.880843 + 0.508555i 0.870936 0.491396i \(-0.163513\pi\)
0.00990642 + 0.999951i \(0.496847\pi\)
\(104\) 11.9446i 0.114852i
\(105\) −7.53038 26.0441i −0.0717179 0.248039i
\(106\) −65.7908 −0.620668
\(107\) 62.3022 107.911i 0.582263 1.00851i −0.412947 0.910755i \(-0.635501\pi\)
0.995211 0.0977548i \(-0.0311661\pi\)
\(108\) 9.00000 5.19615i 0.0833333 0.0481125i
\(109\) −42.3042 73.2731i −0.388112 0.672230i 0.604083 0.796921i \(-0.293539\pi\)
−0.992196 + 0.124691i \(0.960206\pi\)
\(110\) −1.44173 0.832384i −0.0131066 0.00756712i
\(111\) 16.8938i 0.152196i
\(112\) −27.1832 6.71372i −0.242707 0.0599439i
\(113\) −116.241 −1.02868 −0.514340 0.857586i \(-0.671963\pi\)
−0.514340 + 0.857586i \(0.671963\pi\)
\(114\) 3.89097 6.73936i 0.0341313 0.0591172i
\(115\) −21.4158 + 12.3644i −0.186224 + 0.107517i
\(116\) 56.1302 + 97.2204i 0.483881 + 0.838107i
\(117\) 10.9719 + 6.33460i 0.0937765 + 0.0541419i
\(118\) 71.4621i 0.605611i
\(119\) −168.291 161.799i −1.41421 1.35966i
\(120\) −10.9545 −0.0912871
\(121\) 60.3614 104.549i 0.498855 0.864042i
\(122\) −126.513 + 73.0424i −1.03699 + 0.598708i
\(123\) 3.52799 + 6.11066i 0.0286829 + 0.0496802i
\(124\) 3.27635 + 1.89160i 0.0264222 + 0.0152548i
\(125\) 11.1803i 0.0894427i
\(126\) −20.5830 + 21.4089i −0.163357 + 0.169912i
\(127\) −81.3744 −0.640743 −0.320372 0.947292i \(-0.603808\pi\)
−0.320372 + 0.947292i \(0.603808\pi\)
\(128\) −5.65685 + 9.79796i −0.0441942 + 0.0765466i
\(129\) −69.5278 + 40.1419i −0.538975 + 0.311178i
\(130\) −6.67726 11.5654i −0.0513635 0.0889642i
\(131\) 208.389 + 120.313i 1.59075 + 0.918421i 0.993178 + 0.116608i \(0.0372020\pi\)
0.597574 + 0.801814i \(0.296131\pi\)
\(132\) 1.82366i 0.0138156i
\(133\) −5.33231 + 21.5900i −0.0400926 + 0.162331i
\(134\) 12.3588 0.0922295
\(135\) −5.80948 + 10.0623i −0.0430331 + 0.0745356i
\(136\) −81.6919 + 47.1649i −0.600676 + 0.346800i
\(137\) −116.831 202.357i −0.852778 1.47706i −0.878691 0.477391i \(-0.841582\pi\)
0.0259125 0.999664i \(-0.491751\pi\)
\(138\) 23.4598 + 13.5445i 0.169999 + 0.0981489i
\(139\) 211.491i 1.52152i 0.649033 + 0.760760i \(0.275174\pi\)
−0.649033 + 0.760760i \(0.724826\pi\)
\(140\) 30.0731 8.69534i 0.214808 0.0621096i
\(141\) −109.594 −0.777261
\(142\) −20.5491 + 35.5920i −0.144712 + 0.250648i
\(143\) −1.92536 + 1.11161i −0.0134641 + 0.00777348i
\(144\) 6.00000 + 10.3923i 0.0416667 + 0.0721688i
\(145\) −108.696 62.7555i −0.749625 0.432796i
\(146\) 23.6640i 0.162082i
\(147\) 39.5125 75.1117i 0.268792 0.510964i
\(148\) −19.5073 −0.131806
\(149\) −72.0402 + 124.777i −0.483491 + 0.837431i −0.999820 0.0189590i \(-0.993965\pi\)
0.516329 + 0.856390i \(0.327298\pi\)
\(150\) 10.6066 6.12372i 0.0707107 0.0408248i
\(151\) −46.7563 80.9842i −0.309644 0.536319i 0.668640 0.743586i \(-0.266877\pi\)
−0.978285 + 0.207267i \(0.933543\pi\)
\(152\) 7.78195 + 4.49291i 0.0511970 + 0.0295586i
\(153\) 100.052i 0.653933i
\(154\) −1.44757 5.00647i −0.00939982 0.0325095i
\(155\) −4.22975 −0.0272887
\(156\) −7.31457 + 12.6692i −0.0468883 + 0.0812129i
\(157\) −148.286 + 85.6127i −0.944494 + 0.545304i −0.891366 0.453284i \(-0.850252\pi\)
−0.0531280 + 0.998588i \(0.516919\pi\)
\(158\) 93.5464 + 162.027i 0.592066 + 1.02549i
\(159\) −69.7817 40.2885i −0.438878 0.253387i
\(160\) 12.6491i 0.0790569i
\(161\) −75.1553 18.5619i −0.466803 0.115291i
\(162\) 12.7279 0.0785674
\(163\) −46.5064 + 80.5515i −0.285316 + 0.494181i −0.972686 0.232126i \(-0.925432\pi\)
0.687370 + 0.726307i \(0.258765\pi\)
\(164\) −7.05598 + 4.07377i −0.0430243 + 0.0248401i
\(165\) −1.01946 1.76575i −0.00617853 0.0107015i
\(166\) 15.2894 + 8.82735i 0.0921049 + 0.0531768i
\(167\) 104.991i 0.628688i −0.949309 0.314344i \(-0.898216\pi\)
0.949309 0.314344i \(-0.101784\pi\)
\(168\) −24.7208 23.7672i −0.147148 0.141471i
\(169\) 151.166 0.894472
\(170\) 52.7319 91.3344i 0.310188 0.537261i
\(171\) 8.25400 4.76545i 0.0482690 0.0278681i
\(172\) −46.3519 80.2838i −0.269488 0.466766i
\(173\) 176.805 + 102.079i 1.02200 + 0.590049i 0.914681 0.404176i \(-0.132442\pi\)
0.107314 + 0.994225i \(0.465775\pi\)
\(174\) 137.490i 0.790174i
\(175\) −24.2573 + 25.2306i −0.138613 + 0.144175i
\(176\) −2.10578 −0.0119647
\(177\) 43.7614 75.7970i 0.247240 0.428231i
\(178\) 83.5943 48.2632i 0.469631 0.271141i
\(179\) 97.9495 + 169.653i 0.547204 + 0.947785i 0.998465 + 0.0553926i \(0.0176410\pi\)
−0.451261 + 0.892392i \(0.649026\pi\)
\(180\) −11.6190 6.70820i −0.0645497 0.0372678i
\(181\) 119.031i 0.657632i −0.944394 0.328816i \(-0.893350\pi\)
0.944394 0.328816i \(-0.106650\pi\)
\(182\) 10.0241 40.5867i 0.0550776 0.223004i
\(183\) −178.917 −0.977687
\(184\) −15.6399 + 27.0891i −0.0849994 + 0.147223i
\(185\) 18.8878 10.9049i 0.102096 0.0589454i
\(186\) 2.31673 + 4.01269i 0.0124555 + 0.0215736i
\(187\) −15.2050 8.77864i −0.0813104 0.0469446i
\(188\) 126.548i 0.673127i
\(189\) −34.9418 + 10.1031i −0.184877 + 0.0534554i
\(190\) −10.0464 −0.0528760
\(191\) 32.8657 56.9250i 0.172072 0.298037i −0.767072 0.641561i \(-0.778287\pi\)
0.939144 + 0.343524i \(0.111621\pi\)
\(192\) −12.0000 + 6.92820i −0.0625000 + 0.0360844i
\(193\) 48.4350 + 83.8919i 0.250959 + 0.434673i 0.963790 0.266662i \(-0.0859209\pi\)
−0.712831 + 0.701335i \(0.752588\pi\)
\(194\) −182.831 105.558i −0.942429 0.544112i
\(195\) 16.3559i 0.0838763i
\(196\) 86.7315 + 45.6251i 0.442508 + 0.232781i
\(197\) 186.672 0.947574 0.473787 0.880640i \(-0.342887\pi\)
0.473787 + 0.880640i \(0.342887\pi\)
\(198\) −1.11676 + 1.93428i −0.00564020 + 0.00976912i
\(199\) 99.8454 57.6458i 0.501736 0.289677i −0.227694 0.973733i \(-0.573119\pi\)
0.729430 + 0.684055i \(0.239785\pi\)
\(200\) 7.07107 + 12.2474i 0.0353553 + 0.0612372i
\(201\) 13.1084 + 7.56816i 0.0652161 + 0.0376525i
\(202\) 136.818i 0.677319i
\(203\) −109.136 377.450i −0.537616 1.85936i
\(204\) −115.530 −0.566323
\(205\) 4.55462 7.88883i 0.0222176 0.0384821i
\(206\) −128.307 + 74.0781i −0.622850 + 0.359602i
\(207\) 16.5886 + 28.7323i 0.0801382 + 0.138803i
\(208\) −14.6291 8.44614i −0.0703324 0.0406064i
\(209\) 1.67250i 0.00800239i
\(210\) 37.2221 + 9.19314i 0.177248 + 0.0437768i
\(211\) 139.433 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(212\) 46.5211 80.5769i 0.219439 0.380080i
\(213\) −43.5912 + 25.1674i −0.204653 + 0.118157i
\(214\) 88.1086 + 152.609i 0.411722 + 0.713124i
\(215\) 89.7600 + 51.8230i 0.417488 + 0.241037i
\(216\) 14.6969i 0.0680414i
\(217\) −9.54524 9.17703i −0.0439873 0.0422905i
\(218\) 119.654 0.548874
\(219\) −14.4912 + 25.0994i −0.0661697 + 0.114609i
\(220\) 2.03892 1.17717i 0.00926780 0.00535076i
\(221\) −70.4209 121.973i −0.318647 0.551912i
\(222\) −20.6906 11.9457i −0.0932008 0.0538095i
\(223\) 258.055i 1.15720i 0.815612 + 0.578599i \(0.196400\pi\)
−0.815612 + 0.578599i \(0.803600\pi\)
\(224\) 27.4440 28.5452i 0.122518 0.127434i
\(225\) 15.0000 0.0666667
\(226\) 82.1947 142.365i 0.363693 0.629935i
\(227\) 286.682 165.516i 1.26292 0.729146i 0.289280 0.957245i \(-0.406584\pi\)
0.973638 + 0.228099i \(0.0732509\pi\)
\(228\) 5.50267 + 9.53090i 0.0241345 + 0.0418022i
\(229\) 211.516 + 122.119i 0.923653 + 0.533271i 0.884799 0.465974i \(-0.154296\pi\)
0.0388541 + 0.999245i \(0.487629\pi\)
\(230\) 34.9719i 0.152052i
\(231\) 1.53044 6.19662i 0.00662529 0.0268252i
\(232\) −158.760 −0.684311
\(233\) −105.745 + 183.155i −0.453840 + 0.786074i −0.998621 0.0525044i \(-0.983280\pi\)
0.544781 + 0.838579i \(0.316613\pi\)
\(234\) −15.5165 + 8.95848i −0.0663100 + 0.0382841i
\(235\) 70.7425 + 122.530i 0.301032 + 0.521402i
\(236\) 87.5228 + 50.5313i 0.370859 + 0.214116i
\(237\) 229.141i 0.966840i
\(238\) 317.162 91.7044i 1.33262 0.385313i
\(239\) 344.134 1.43989 0.719946 0.694030i \(-0.244167\pi\)
0.719946 + 0.694030i \(0.244167\pi\)
\(240\) 7.74597 13.4164i 0.0322749 0.0559017i
\(241\) −148.392 + 85.6742i −0.615735 + 0.355495i −0.775207 0.631708i \(-0.782354\pi\)
0.159472 + 0.987203i \(0.449021\pi\)
\(242\) 85.3639 + 147.855i 0.352744 + 0.610970i
\(243\) 13.5000 + 7.79423i 0.0555556 + 0.0320750i
\(244\) 206.595i 0.846702i
\(245\) −109.483 + 4.30810i −0.446868 + 0.0175841i
\(246\) −9.97867 −0.0405637
\(247\) −6.70827 + 11.6191i −0.0271590 + 0.0470408i
\(248\) −4.63346 + 2.67513i −0.0186833 + 0.0107868i
\(249\) 10.8112 + 18.7256i 0.0434187 + 0.0752033i
\(250\) −13.6931 7.90569i −0.0547723 0.0316228i
\(251\) 327.538i 1.30493i −0.757818 0.652467i \(-0.773734\pi\)
0.757818 0.652467i \(-0.226266\pi\)
\(252\) −11.6660 40.3473i −0.0462937 0.160108i
\(253\) −5.82200 −0.0230119
\(254\) 57.5404 99.6629i 0.226537 0.392374i
\(255\) 111.861 64.5832i 0.438672 0.253267i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −190.836 110.179i −0.742552 0.428713i 0.0804442 0.996759i \(-0.474366\pi\)
−0.822997 + 0.568046i \(0.807699\pi\)
\(258\) 113.538i 0.440072i
\(259\) 66.2837 + 16.3708i 0.255922 + 0.0632077i
\(260\) 18.8861 0.0726390
\(261\) −84.1953 + 145.831i −0.322587 + 0.558738i
\(262\) −294.706 + 170.149i −1.12483 + 0.649422i
\(263\) −66.5976 115.350i −0.253223 0.438594i 0.711189 0.703001i \(-0.248157\pi\)
−0.964411 + 0.264407i \(0.914824\pi\)
\(264\) −2.23352 1.28952i −0.00846030 0.00488456i
\(265\) 104.024i 0.392545i
\(266\) −22.6718 21.7972i −0.0852322 0.0819443i
\(267\) 118.220 0.442772
\(268\) −8.73896 + 15.1363i −0.0326080 + 0.0564788i
\(269\) −22.9633 + 13.2578i −0.0853653 + 0.0492857i −0.542075 0.840330i \(-0.682361\pi\)
0.456710 + 0.889616i \(0.349028\pi\)
\(270\) −8.21584 14.2302i −0.0304290 0.0527046i
\(271\) −92.6776 53.5074i −0.341984 0.197444i 0.319165 0.947699i \(-0.396598\pi\)
−0.661149 + 0.750255i \(0.729931\pi\)
\(272\) 133.402i 0.490450i
\(273\) 35.4864 36.9102i 0.129987 0.135202i
\(274\) 330.447 1.20601
\(275\) −1.31611 + 2.27958i −0.00478587 + 0.00828937i
\(276\) −33.1772 + 19.1549i −0.120207 + 0.0694017i
\(277\) −220.191 381.381i −0.794912 1.37683i −0.922895 0.385052i \(-0.874184\pi\)
0.127983 0.991776i \(-0.459150\pi\)
\(278\) −259.023 149.547i −0.931737 0.537939i
\(279\) 5.67480i 0.0203398i
\(280\) −10.6153 + 42.9804i −0.0379119 + 0.153501i
\(281\) 322.069 1.14615 0.573076 0.819502i \(-0.305750\pi\)
0.573076 + 0.819502i \(0.305750\pi\)
\(282\) 77.4945 134.224i 0.274803 0.475973i
\(283\) −59.3514 + 34.2665i −0.209722 + 0.121083i −0.601182 0.799112i \(-0.705303\pi\)
0.391460 + 0.920195i \(0.371970\pi\)
\(284\) −29.0608 50.3347i −0.102327 0.177235i
\(285\) −10.6559 6.15217i −0.0373890 0.0215866i
\(286\) 3.14410i 0.0109934i
\(287\) 27.3943 7.92079i 0.0954505 0.0275986i
\(288\) −16.9706 −0.0589256
\(289\) 411.631 712.966i 1.42433 2.46701i
\(290\) 153.719 88.7496i 0.530065 0.306033i
\(291\) −129.281 223.922i −0.444265 0.769490i
\(292\) −28.9823 16.7329i −0.0992545 0.0573046i
\(293\) 147.510i 0.503448i 0.967799 + 0.251724i \(0.0809975\pi\)
−0.967799 + 0.251724i \(0.919003\pi\)
\(294\) 64.0531 + 101.505i 0.217868 + 0.345254i
\(295\) −112.991 −0.383022
\(296\) 13.7937 23.8914i 0.0466004 0.0807143i
\(297\) −2.36901 + 1.36775i −0.00797645 + 0.00460521i
\(298\) −101.880 176.462i −0.341880 0.592153i
\(299\) −40.4462 23.3516i −0.135272 0.0780991i
\(300\) 17.3205i 0.0577350i
\(301\) 90.1237 + 311.695i 0.299414 + 1.03553i
\(302\) 132.247 0.437903
\(303\) −83.7839 + 145.118i −0.276514 + 0.478937i
\(304\) −11.0053 + 6.35393i −0.0362018 + 0.0209011i
\(305\) 115.490 + 200.035i 0.378657 + 0.655852i
\(306\) −122.538 70.7473i −0.400451 0.231200i
\(307\) 376.010i 1.22479i 0.790553 + 0.612394i \(0.209793\pi\)
−0.790553 + 0.612394i \(0.790207\pi\)
\(308\) 7.15524 + 1.76720i 0.0232313 + 0.00573767i
\(309\) −181.454 −0.587228
\(310\) 2.99088 5.18036i 0.00964801 0.0167108i
\(311\) −337.599 + 194.913i −1.08553 + 0.626730i −0.932383 0.361473i \(-0.882274\pi\)
−0.153146 + 0.988204i \(0.548941\pi\)
\(312\) −10.3444 17.9170i −0.0331550 0.0574262i
\(313\) −123.890 71.5282i −0.395816 0.228524i 0.288861 0.957371i \(-0.406723\pi\)
−0.684677 + 0.728847i \(0.740057\pi\)
\(314\) 242.149i 0.771176i
\(315\) 33.8504 + 32.5446i 0.107462 + 0.103316i
\(316\) −264.589 −0.837308
\(317\) −192.222 + 332.938i −0.606378 + 1.05028i 0.385454 + 0.922727i \(0.374045\pi\)
−0.991832 + 0.127551i \(0.959288\pi\)
\(318\) 98.6862 56.9765i 0.310334 0.179171i
\(319\) −14.7747 25.5906i −0.0463158 0.0802214i
\(320\) 15.4919 + 8.94427i 0.0484123 + 0.0279508i
\(321\) 215.821i 0.672340i
\(322\) 75.8764 78.9208i 0.235641 0.245096i
\(323\) −105.954 −0.328030
\(324\) −9.00000 + 15.5885i −0.0277778 + 0.0481125i
\(325\) −18.2864 + 10.5577i −0.0562659 + 0.0324851i
\(326\) −65.7700 113.917i −0.201749 0.349439i
\(327\) 126.913 + 73.2731i 0.388112 + 0.224077i
\(328\) 11.5224i 0.0351292i
\(329\) −106.201 + 429.997i −0.322799 + 1.30698i
\(330\) 2.88346 0.00873776
\(331\) −96.9539 + 167.929i −0.292912 + 0.507338i −0.974497 0.224400i \(-0.927958\pi\)
0.681585 + 0.731739i \(0.261291\pi\)
\(332\) −21.6225 + 12.4838i −0.0651280 + 0.0376017i
\(333\) −14.6305 25.3407i −0.0439353 0.0760982i
\(334\) 128.587 + 74.2397i 0.384991 + 0.222275i
\(335\) 19.5409i 0.0583310i
\(336\) 46.5890 13.4708i 0.138658 0.0400916i
\(337\) 125.477 0.372337 0.186168 0.982518i \(-0.440393\pi\)
0.186168 + 0.982518i \(0.440393\pi\)
\(338\) −106.890 + 185.139i −0.316243 + 0.547750i
\(339\) 174.361 100.668i 0.514340 0.296954i
\(340\) 74.5742 + 129.166i 0.219336 + 0.379901i
\(341\) −0.862410 0.497912i −0.00252906 0.00146015i
\(342\) 13.4787i 0.0394115i
\(343\) −256.416 227.816i −0.747568 0.664186i
\(344\) 131.103 0.381113
\(345\) 21.4158 37.0933i 0.0620748 0.107517i
\(346\) −250.040 + 144.361i −0.722660 + 0.417228i
\(347\) 251.798 + 436.128i 0.725644 + 1.25685i 0.958708 + 0.284391i \(0.0917913\pi\)
−0.233065 + 0.972461i \(0.574875\pi\)
\(348\) −168.391 97.2204i −0.483881 0.279369i
\(349\) 47.7682i 0.136872i −0.997656 0.0684358i \(-0.978199\pi\)
0.997656 0.0684358i \(-0.0218008\pi\)
\(350\) −13.7485 47.5497i −0.0392815 0.135856i
\(351\) −21.9437 −0.0625177
\(352\) 1.48901 2.57905i 0.00423015 0.00732684i
\(353\) 28.5012 16.4552i 0.0807399 0.0466152i −0.459087 0.888392i \(-0.651823\pi\)
0.539826 + 0.841776i \(0.318490\pi\)
\(354\) 61.8880 + 107.193i 0.174825 + 0.302805i
\(355\) 56.2760 + 32.4909i 0.158524 + 0.0915238i
\(356\) 136.509i 0.383452i
\(357\) 392.559 + 96.9543i 1.09960 + 0.271581i
\(358\) −277.043 −0.773863
\(359\) −133.898 + 231.919i −0.372976 + 0.646013i −0.990022 0.140914i \(-0.954996\pi\)
0.617046 + 0.786927i \(0.288329\pi\)
\(360\) 16.4317 9.48683i 0.0456435 0.0263523i
\(361\) −175.453 303.894i −0.486021 0.841812i
\(362\) 145.783 + 84.1679i 0.402716 + 0.232508i
\(363\) 209.098i 0.576028i
\(364\) 42.6202 + 40.9761i 0.117089 + 0.112572i
\(365\) 37.4160 0.102510
\(366\) 126.513 219.127i 0.345665 0.598708i
\(367\) −137.458 + 79.3613i −0.374545 + 0.216243i −0.675442 0.737413i \(-0.736047\pi\)
0.300897 + 0.953657i \(0.402714\pi\)
\(368\) −22.1182 38.3098i −0.0601037 0.104103i
\(369\) −10.5840 6.11066i −0.0286829 0.0165601i
\(370\) 30.8437i 0.0833614i
\(371\) −225.695 + 234.751i −0.608343 + 0.632752i
\(372\) −6.55270 −0.0176148
\(373\) −207.172 + 358.832i −0.555421 + 0.962017i 0.442450 + 0.896793i \(0.354109\pi\)
−0.997871 + 0.0652235i \(0.979224\pi\)
\(374\) 21.5032 12.4149i 0.0574951 0.0331948i
\(375\) −9.68246 16.7705i −0.0258199 0.0447214i
\(376\) 154.989 + 89.4829i 0.412205 + 0.237986i
\(377\) 237.042i 0.628758i
\(378\) 12.3339 49.9387i 0.0326293 0.132113i
\(379\) −72.8000 −0.192084 −0.0960422 0.995377i \(-0.530618\pi\)
−0.0960422 + 0.995377i \(0.530618\pi\)
\(380\) 7.10391 12.3043i 0.0186945 0.0323798i
\(381\) 122.062 70.4723i 0.320372 0.184967i
\(382\) 46.4791 + 80.5042i 0.121673 + 0.210744i
\(383\) −246.830 142.507i −0.644464 0.372082i 0.141868 0.989886i \(-0.454689\pi\)
−0.786332 + 0.617804i \(0.788023\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −7.91593 + 2.28881i −0.0205608 + 0.00594497i
\(386\) −136.995 −0.354909
\(387\) 69.5278 120.426i 0.179658 0.311178i
\(388\) 258.562 149.281i 0.666398 0.384745i
\(389\) 48.5692 + 84.1242i 0.124856 + 0.216258i 0.921677 0.387959i \(-0.126820\pi\)
−0.796820 + 0.604216i \(0.793486\pi\)
\(390\) 20.0318 + 11.5654i 0.0513635 + 0.0296547i
\(391\) 368.827i 0.943291i
\(392\) −117.207 + 73.9622i −0.298999 + 0.188679i
\(393\) −416.777 −1.06050
\(394\) −131.997 + 228.626i −0.335018 + 0.580268i
\(395\) 256.187 147.910i 0.648576 0.374455i
\(396\) −1.57934 2.73549i −0.00398822 0.00690781i
\(397\) −685.636 395.852i −1.72704 0.997108i −0.901520 0.432737i \(-0.857548\pi\)
−0.825522 0.564371i \(-0.809119\pi\)
\(398\) 163.047i 0.409665i
\(399\) −10.6990 37.0030i −0.0268146 0.0927392i
\(400\) −20.0000 −0.0500000
\(401\) −251.613 + 435.807i −0.627464 + 1.08680i 0.360594 + 0.932723i \(0.382574\pi\)
−0.988059 + 0.154077i \(0.950759\pi\)
\(402\) −18.5381 + 10.7030i −0.0461147 + 0.0266244i
\(403\) −3.99418 6.91812i −0.00991112 0.0171666i
\(404\) −167.568 96.7453i −0.414772 0.239468i
\(405\) 20.1246i 0.0496904i
\(406\) 539.451 + 133.234i 1.32870 + 0.328162i
\(407\) 5.13476 0.0126161
\(408\) 81.6919 141.495i 0.200225 0.346800i
\(409\) 649.395 374.928i 1.58776 0.916696i 0.594088 0.804400i \(-0.297513\pi\)
0.993675 0.112296i \(-0.0358204\pi\)
\(410\) 6.44120 + 11.1565i 0.0157102 + 0.0272109i
\(411\) 350.492 + 202.357i 0.852778 + 0.492352i
\(412\) 209.525i 0.508555i
\(413\) −254.987 245.151i −0.617402 0.593585i
\(414\) −46.9197 −0.113333
\(415\) 13.9573 24.1747i 0.0336319 0.0582522i
\(416\) 20.6887 11.9446i 0.0497325 0.0287131i
\(417\) −183.157 317.237i −0.439225 0.760760i
\(418\) −2.04839 1.18264i −0.00490044 0.00282927i
\(419\) 465.759i 1.11160i 0.831317 + 0.555799i \(0.187587\pi\)
−0.831317 + 0.555799i \(0.812413\pi\)
\(420\) −37.5793 + 39.0871i −0.0894744 + 0.0930645i
\(421\) 345.980 0.821805 0.410902 0.911679i \(-0.365214\pi\)
0.410902 + 0.911679i \(0.365214\pi\)
\(422\) −98.5939 + 170.770i −0.233635 + 0.404667i
\(423\) 164.391 94.9110i 0.388630 0.224376i
\(424\) 65.7908 + 113.953i 0.155167 + 0.268757i
\(425\) −144.412 83.3765i −0.339794 0.196180i
\(426\) 71.1841i 0.167099i
\(427\) −173.378 + 701.990i −0.406037 + 1.64400i
\(428\) −249.209 −0.582263
\(429\) 1.92536 3.33482i 0.00448802 0.00777348i
\(430\) −126.940 + 73.2888i −0.295209 + 0.170439i
\(431\) −247.300 428.336i −0.573782 0.993819i −0.996173 0.0874056i \(-0.972142\pi\)
0.422391 0.906414i \(-0.361191\pi\)
\(432\) −18.0000 10.3923i −0.0416667 0.0240563i
\(433\) 730.022i 1.68596i −0.537943 0.842981i \(-0.680799\pi\)
0.537943 0.842981i \(-0.319201\pi\)
\(434\) 17.9890 5.20135i 0.0414494 0.0119847i
\(435\) 217.391 0.499750
\(436\) −84.6085 + 146.546i −0.194056 + 0.336115i
\(437\) −30.4272 + 17.5672i −0.0696275 + 0.0401994i
\(438\) −20.4936 35.4959i −0.0467890 0.0810410i
\(439\) −321.631 185.694i −0.732645 0.422993i 0.0867437 0.996231i \(-0.472354\pi\)
−0.819389 + 0.573238i \(0.805687\pi\)
\(440\) 3.32953i 0.00756712i
\(441\) 5.77993 + 146.886i 0.0131064 + 0.333076i
\(442\) 199.180 0.450635
\(443\) −204.354 + 353.951i −0.461295 + 0.798987i −0.999026 0.0441299i \(-0.985948\pi\)
0.537731 + 0.843117i \(0.319282\pi\)
\(444\) 29.2609 16.8938i 0.0659029 0.0380491i
\(445\) −76.3108 132.174i −0.171485 0.297021i
\(446\) −316.052 182.473i −0.708636 0.409131i
\(447\) 249.555i 0.558288i
\(448\) 15.5547 + 53.7964i 0.0347203 + 0.120081i
\(449\) 725.469 1.61574 0.807872 0.589358i \(-0.200619\pi\)
0.807872 + 0.589358i \(0.200619\pi\)
\(450\) −10.6066 + 18.3712i −0.0235702 + 0.0408248i
\(451\) 1.85730 1.07231i 0.00411817 0.00237763i
\(452\) 116.241 + 201.335i 0.257170 + 0.445432i
\(453\) 140.269 + 80.9842i 0.309644 + 0.178773i
\(454\) 468.150i 1.03117i
\(455\) −64.1732 15.8495i −0.141040 0.0348341i
\(456\) −15.5639 −0.0341313
\(457\) −200.765 + 347.736i −0.439311 + 0.760909i −0.997636 0.0687128i \(-0.978111\pi\)
0.558325 + 0.829622i \(0.311444\pi\)
\(458\) −299.129 + 172.702i −0.653121 + 0.377080i
\(459\) −86.6474 150.078i −0.188774 0.326967i
\(460\) 42.8316 + 24.7288i 0.0931122 + 0.0537584i
\(461\) 653.050i 1.41659i −0.705915 0.708297i \(-0.749464\pi\)
0.705915 0.708297i \(-0.250536\pi\)
\(462\) 6.50709 + 6.25607i 0.0140846 + 0.0135413i
\(463\) −869.580 −1.87814 −0.939072 0.343722i \(-0.888312\pi\)
−0.939072 + 0.343722i \(0.888312\pi\)
\(464\) 112.260 194.441i 0.241941 0.419053i
\(465\) 6.34462 3.66307i 0.0136443 0.00787757i
\(466\) −149.546 259.021i −0.320913 0.555838i
\(467\) 640.168 + 369.601i 1.37081 + 0.791437i 0.991030 0.133641i \(-0.0426668\pi\)
0.379779 + 0.925077i \(0.376000\pi\)
\(468\) 25.3384i 0.0541419i
\(469\) 42.3967 44.0978i 0.0903981 0.0940252i
\(470\) −200.090 −0.425723
\(471\) 148.286 256.838i 0.314831 0.545304i
\(472\) −123.776 + 71.4621i −0.262237 + 0.151403i
\(473\) 12.2009 + 21.1325i 0.0257947 + 0.0446777i
\(474\) −280.639 162.027i −0.592066 0.341829i
\(475\) 15.8848i 0.0334417i
\(476\) −111.953 + 453.288i −0.235196 + 0.952285i
\(477\) 139.563 0.292586
\(478\) −243.339 + 421.476i −0.509078 + 0.881750i
\(479\) −525.006 + 303.112i −1.09605 + 0.632802i −0.935180 0.354174i \(-0.884762\pi\)
−0.160866 + 0.986976i \(0.551429\pi\)
\(480\) 10.9545 + 18.9737i 0.0228218 + 0.0395285i
\(481\) 35.6718 + 20.5951i 0.0741618 + 0.0428173i
\(482\) 242.323i 0.502745i
\(483\) 128.808 37.2435i 0.266683 0.0771088i
\(484\) −241.446 −0.498855
\(485\) −166.901 + 289.082i −0.344126 + 0.596044i
\(486\) −19.0919 + 11.0227i −0.0392837 + 0.0226805i
\(487\) −324.788 562.549i −0.666916 1.15513i −0.978762 0.205000i \(-0.934281\pi\)
0.311846 0.950133i \(-0.399053\pi\)
\(488\) 253.026 + 146.085i 0.518497 + 0.299354i
\(489\) 161.103i 0.329454i
\(490\) 72.1396 137.135i 0.147224 0.279866i
\(491\) 266.629 0.543033 0.271516 0.962434i \(-0.412475\pi\)
0.271516 + 0.962434i \(0.412475\pi\)
\(492\) 7.05598 12.2213i 0.0143414 0.0248401i
\(493\) 1621.18 935.988i 3.28839 1.89856i
\(494\) −9.48693 16.4318i −0.0192043 0.0332628i
\(495\) 3.05837 + 1.76575i 0.00617853 + 0.00356718i
\(496\) 7.56640i 0.0152548i
\(497\) 56.5039 + 195.421i 0.113690 + 0.393200i
\(498\) −30.5788 −0.0614033
\(499\) 340.553 589.855i 0.682471 1.18207i −0.291754 0.956493i \(-0.594239\pi\)
0.974225 0.225581i \(-0.0724279\pi\)
\(500\) 19.3649 11.1803i 0.0387298 0.0223607i
\(501\) 90.9247 + 157.486i 0.181487 + 0.314344i
\(502\) 401.151 + 231.604i 0.799105 + 0.461364i
\(503\) 453.326i 0.901245i −0.892715 0.450622i \(-0.851202\pi\)
0.892715 0.450622i \(-0.148798\pi\)
\(504\) 57.6643 + 14.2419i 0.114413 + 0.0282578i
\(505\) 216.329 0.428374
\(506\) 4.11678 7.13047i 0.00813592 0.0140918i
\(507\) −226.749 + 130.913i −0.447236 + 0.258212i
\(508\) 81.3744 + 140.945i 0.160186 + 0.277450i
\(509\) −43.5300 25.1321i −0.0855206 0.0493754i 0.456630 0.889657i \(-0.349056\pi\)
−0.542150 + 0.840281i \(0.682390\pi\)
\(510\) 182.669i 0.358174i
\(511\) 84.4364 + 81.1792i 0.165238 + 0.158863i
\(512\) 22.6274 0.0441942
\(513\) −8.25400 + 14.2963i −0.0160897 + 0.0278681i
\(514\) 269.883 155.817i 0.525064 0.303146i
\(515\) 117.128 + 202.871i 0.227433 + 0.393925i
\(516\) 139.056 + 80.2838i 0.269488 + 0.155589i
\(517\) 33.3103i 0.0644300i
\(518\) −66.9197 + 69.6048i −0.129189 + 0.134372i
\(519\) −353.610 −0.681330
\(520\) −13.3545 + 23.1307i −0.0256818 + 0.0444821i
\(521\) −89.2971 + 51.5557i −0.171396 + 0.0989553i −0.583244 0.812297i \(-0.698217\pi\)
0.411848 + 0.911252i \(0.364883\pi\)
\(522\) −119.070 206.236i −0.228104 0.395087i
\(523\) −317.716 183.434i −0.607488 0.350733i 0.164494 0.986378i \(-0.447401\pi\)
−0.771982 + 0.635645i \(0.780734\pi\)
\(524\) 481.253i 0.918421i
\(525\) 14.5356 58.8533i 0.0276869 0.112102i
\(526\) 188.366 0.358111
\(527\) 31.5430 54.6341i 0.0598539 0.103670i
\(528\) 3.15867 1.82366i 0.00598234 0.00345390i
\(529\) 203.348 + 352.210i 0.384402 + 0.665803i
\(530\) −127.403 73.5563i −0.240384 0.138786i
\(531\) 151.594i 0.285488i
\(532\) 42.7273 12.3542i 0.0803145 0.0232222i
\(533\) 17.2038 0.0322773
\(534\) −83.5943 + 144.790i −0.156544 + 0.271141i
\(535\) 241.295 139.312i 0.451019 0.260396i
\(536\) −12.3588 21.4060i −0.0230574 0.0399365i
\(537\) −293.848 169.653i −0.547204 0.315928i
\(538\) 37.4988i 0.0697005i
\(539\) −22.8297 12.0096i −0.0423557 0.0222812i
\(540\) 23.2379 0.0430331
\(541\) 266.559 461.693i 0.492714 0.853407i −0.507250 0.861799i \(-0.669338\pi\)
0.999965 + 0.00839227i \(0.00267137\pi\)
\(542\) 131.066 75.6709i 0.241819 0.139614i
\(543\) 103.084 + 178.547i 0.189842 + 0.328816i
\(544\) 163.384 + 94.3297i 0.300338 + 0.173400i
\(545\) 189.190i 0.347138i
\(546\) 20.1129 + 69.5612i 0.0368369 + 0.127401i
\(547\) 69.6218 0.127279 0.0636396 0.997973i \(-0.479729\pi\)
0.0636396 + 0.997973i \(0.479729\pi\)
\(548\) −233.661 + 404.713i −0.426389 + 0.738528i
\(549\) 268.375 154.946i 0.488843 0.282234i
\(550\) −1.86127 3.22381i −0.00338412 0.00586147i
\(551\) −154.433 89.1619i −0.280277 0.161818i
\(552\) 54.1782i 0.0981489i
\(553\) 899.048 + 222.047i 1.62576 + 0.401532i
\(554\) 622.793 1.12418
\(555\) −18.8878 + 32.7147i −0.0340321 + 0.0589454i
\(556\) 366.314 211.491i 0.658838 0.380380i
\(557\) −8.43122 14.6033i −0.0151368 0.0262178i 0.858358 0.513052i \(-0.171485\pi\)
−0.873495 + 0.486834i \(0.838152\pi\)
\(558\) −6.95018 4.01269i −0.0124555 0.00719120i
\(559\) 195.747i 0.350174i
\(560\) −45.1339 43.3928i −0.0805962 0.0774871i
\(561\) 30.4101 0.0542069
\(562\) −227.737 + 394.452i −0.405226 + 0.701872i
\(563\) 793.093 457.892i 1.40869 0.813308i 0.413428 0.910537i \(-0.364331\pi\)
0.995262 + 0.0972290i \(0.0309979\pi\)
\(564\) 109.594 + 189.822i 0.194315 + 0.336564i
\(565\) −225.099 129.961i −0.398406 0.230020i
\(566\) 96.9204i 0.171237i
\(567\) 43.6632 45.4151i 0.0770073 0.0800971i
\(568\) 82.1963 0.144712
\(569\) −203.828 + 353.040i −0.358221 + 0.620456i −0.987664 0.156590i \(-0.949950\pi\)
0.629443 + 0.777047i \(0.283283\pi\)
\(570\) 15.0697 8.70048i 0.0264380 0.0152640i
\(571\) 447.910 + 775.803i 0.784431 + 1.35867i 0.929339 + 0.369229i \(0.120378\pi\)
−0.144908 + 0.989445i \(0.546289\pi\)
\(572\) 3.85072 + 2.22322i 0.00673203 + 0.00388674i
\(573\) 113.850i 0.198691i
\(574\) −9.66974 + 39.1519i −0.0168462 + 0.0682088i
\(575\) −55.2954 −0.0961659
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) 590.115 340.703i 1.02273 0.590473i 0.107836 0.994169i \(-0.465608\pi\)
0.914893 + 0.403695i \(0.132274\pi\)
\(578\) 582.134 + 1008.29i 1.00715 + 1.74444i
\(579\) −145.305 83.8919i −0.250959 0.144891i
\(580\) 251.022i 0.432796i
\(581\) 83.9476 24.2726i 0.144488 0.0417773i
\(582\) 365.662 0.628286
\(583\) −12.2454 + 21.2097i −0.0210041 + 0.0363802i
\(584\) 40.9872 23.6640i 0.0701835 0.0405205i
\(585\) 14.1646 + 24.5338i 0.0242130 + 0.0419381i
\(586\) −180.662 104.305i −0.308297 0.177996i
\(587\) 833.001i 1.41908i −0.704665 0.709541i \(-0.748903\pi\)
0.704665 0.709541i \(-0.251097\pi\)
\(588\) −169.610 + 6.67408i −0.288452 + 0.0113505i
\(589\) −6.00955 −0.0102030
\(590\) 79.8970 138.386i 0.135419 0.234552i
\(591\) −280.008 + 161.663i −0.473787 + 0.273541i
\(592\) 19.5073 + 33.7876i 0.0329515 + 0.0570736i
\(593\) 270.842 + 156.371i 0.456731 + 0.263694i 0.710669 0.703527i \(-0.248392\pi\)
−0.253938 + 0.967221i \(0.581726\pi\)
\(594\) 3.86857i 0.00651274i
\(595\) −144.997 501.478i −0.243693 0.842820i
\(596\) 288.161 0.483491
\(597\) −99.8454 + 172.937i −0.167245 + 0.289677i
\(598\) 57.1996 33.0242i 0.0956514 0.0552244i
\(599\) −107.121 185.540i −0.178834 0.309749i 0.762648 0.646814i \(-0.223899\pi\)
−0.941481 + 0.337065i \(0.890566\pi\)
\(600\) −21.2132 12.2474i −0.0353553 0.0204124i
\(601\) 176.849i 0.294257i 0.989117 + 0.147129i \(0.0470031\pi\)
−0.989117 + 0.147129i \(0.952997\pi\)
\(602\) −445.474 110.023i −0.739991 0.182763i
\(603\) −26.2169 −0.0434774
\(604\) −93.5125 + 161.968i −0.154822 + 0.268160i
\(605\) 233.779 134.972i 0.386411 0.223095i
\(606\) −118.488 205.228i −0.195525 0.338660i
\(607\) 32.1304 + 18.5505i 0.0529331 + 0.0305609i 0.526233 0.850340i \(-0.323604\pi\)
−0.473300 + 0.880901i \(0.656937\pi\)
\(608\) 17.9716i 0.0295586i
\(609\) 490.586 + 471.661i 0.805559 + 0.774484i
\(610\) −326.656 −0.535501
\(611\) −133.605 + 231.411i −0.218666 + 0.378741i
\(612\) 173.295 100.052i 0.283161 0.163483i
\(613\) 449.860 + 779.180i 0.733866 + 1.27109i 0.955219 + 0.295899i \(0.0956192\pi\)
−0.221353 + 0.975194i \(0.571047\pi\)
\(614\) −460.516 265.879i −0.750027 0.433028i
\(615\) 15.7777i 0.0256547i
\(616\) −7.22389 + 7.51374i −0.0117271 + 0.0121976i
\(617\) −626.244 −1.01498 −0.507491 0.861657i \(-0.669427\pi\)
−0.507491 + 0.861657i \(0.669427\pi\)
\(618\) 128.307 222.234i 0.207617 0.359602i
\(619\) −776.375 + 448.240i −1.25424 + 0.724136i −0.971949 0.235193i \(-0.924428\pi\)
−0.282291 + 0.959329i \(0.591094\pi\)
\(620\) 4.22975 + 7.32614i 0.00682217 + 0.0118164i
\(621\) −49.7658 28.7323i −0.0801382 0.0462678i
\(622\) 551.298i 0.886331i
\(623\) 114.560 463.843i 0.183885 0.744532i
\(624\) 29.2583 0.0468883
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) 175.207 101.156i 0.279884 0.161591i
\(627\) −1.44843 2.50875i −0.00231009 0.00400120i
\(628\) 296.571 + 171.225i 0.472247 + 0.272652i
\(629\) 325.290i 0.517153i
\(630\) −63.7947 + 18.4456i −0.101261 + 0.0292787i
\(631\) −500.730 −0.793550 −0.396775 0.917916i \(-0.629871\pi\)
−0.396775 + 0.917916i \(0.629871\pi\)
\(632\) 187.093 324.054i 0.296033 0.512744i
\(633\) −209.149 + 120.752i −0.330409 + 0.190762i
\(634\) −271.843 470.846i −0.428774 0.742659i
\(635\) −157.581 90.9793i −0.248159 0.143275i
\(636\) 161.154i 0.253387i
\(637\) −110.431 175.000i −0.173362 0.274726i
\(638\) 41.7893 0.0655005
\(639\) 43.5912 75.5021i 0.0682178 0.118157i
\(640\) −21.9089 + 12.6491i −0.0342327 + 0.0197642i
\(641\) −310.289 537.436i −0.484070 0.838434i 0.515763 0.856732i \(-0.327509\pi\)
−0.999833 + 0.0182978i \(0.994175\pi\)
\(642\) −264.326 152.609i −0.411722 0.237708i
\(643\) 1127.93i 1.75417i 0.480334 + 0.877086i \(0.340516\pi\)
−0.480334 + 0.877086i \(0.659484\pi\)
\(644\) 43.0051 + 148.735i 0.0667782 + 0.230954i
\(645\) −179.520 −0.278326
\(646\) 74.9206 129.766i 0.115976 0.200877i
\(647\) −117.130 + 67.6248i −0.181035 + 0.104521i −0.587779 0.809022i \(-0.699997\pi\)
0.406744 + 0.913542i \(0.366664\pi\)
\(648\) −12.7279 22.0454i −0.0196419 0.0340207i
\(649\) −23.0380 13.3010i −0.0354977 0.0204946i
\(650\) 29.8616i 0.0459409i
\(651\) 22.2654 + 5.49912i 0.0342018 + 0.00844719i
\(652\) 186.026 0.285316
\(653\) 195.145 338.001i 0.298843 0.517612i −0.677028 0.735957i \(-0.736733\pi\)
0.975872 + 0.218345i \(0.0700658\pi\)
\(654\) −179.482 + 103.624i −0.274437 + 0.158446i
\(655\) 269.028 + 465.971i 0.410730 + 0.711406i
\(656\) 14.1120 + 8.14755i 0.0215121 + 0.0124200i
\(657\) 50.1988i 0.0764061i
\(658\) −451.542 434.123i −0.686233 0.659761i
\(659\) −864.853 −1.31237 −0.656186 0.754599i \(-0.727831\pi\)
−0.656186 + 0.754599i \(0.727831\pi\)
\(660\) −2.03892 + 3.53150i −0.00308927 + 0.00535076i
\(661\) −873.134 + 504.104i −1.32093 + 0.762638i −0.983877 0.178848i \(-0.942763\pi\)
−0.337052 + 0.941486i \(0.609430\pi\)
\(662\) −137.113 237.487i −0.207120 0.358742i
\(663\) 211.263 + 121.973i 0.318647 + 0.183971i
\(664\) 35.3094i 0.0531768i
\(665\) −34.4644 + 35.8472i −0.0518261 + 0.0539055i
\(666\) 41.3812 0.0621339
\(667\) 310.374 537.584i 0.465328 0.805973i
\(668\) −181.849 + 104.991i −0.272230 + 0.157172i
\(669\) −223.482 387.083i −0.334054 0.578599i
\(670\) 23.9326 + 13.8175i 0.0357203 + 0.0206231i
\(671\) 54.3806i 0.0810441i
\(672\) −16.4452 + 66.5850i −0.0244720 + 0.0990848i
\(673\) −109.959 −0.163386 −0.0816928 0.996658i \(-0.526033\pi\)
−0.0816928 + 0.996658i \(0.526033\pi\)
\(674\) −88.7259 + 153.678i −0.131641 + 0.228009i
\(675\) −22.5000 + 12.9904i −0.0333333 + 0.0192450i
\(676\) −151.166 261.827i −0.223618 0.387318i
\(677\) 146.213 + 84.4163i 0.215972 + 0.124692i 0.604084 0.796921i \(-0.293539\pi\)
−0.388112 + 0.921612i \(0.626872\pi\)
\(678\) 284.731i 0.419957i
\(679\) −1003.85 + 290.253i −1.47842 + 0.427471i
\(680\) −210.928 −0.310188
\(681\) −286.682 + 496.548i −0.420973 + 0.729146i
\(682\) 1.21963 0.704155i 0.00178832 0.00103248i
\(683\) 218.065 + 377.700i 0.319276 + 0.553002i 0.980337 0.197330i \(-0.0632271\pi\)
−0.661061 + 0.750332i \(0.729894\pi\)
\(684\) −16.5080 9.53090i −0.0241345 0.0139341i
\(685\) 522.482i 0.762748i
\(686\) 460.329 152.954i 0.671034 0.222965i
\(687\) −423.033 −0.615768
\(688\) −92.7038 + 160.568i −0.134744 + 0.233383i
\(689\) −170.141 + 98.2309i −0.246939 + 0.142570i
\(690\) 30.2865 + 52.4578i 0.0438935 + 0.0760258i
\(691\) −59.2770 34.2236i −0.0857843 0.0495276i 0.456494 0.889726i \(-0.349105\pi\)
−0.542279 + 0.840199i \(0.682438\pi\)
\(692\) 408.314i 0.590049i
\(693\) 3.07076 + 10.6203i 0.00443112 + 0.0153251i
\(694\) −712.193 −1.02622
\(695\) −236.454 + 409.551i −0.340222 + 0.589282i
\(696\) 238.140 137.490i 0.342156 0.197544i
\(697\) 67.9314 + 117.661i 0.0974625 + 0.168810i
\(698\) 58.5039 + 33.7772i 0.0838164 + 0.0483914i
\(699\) 366.311i 0.524050i
\(700\) 67.9580 + 16.7843i 0.0970828 + 0.0239776i
\(701\) 1283.41 1.83083 0.915414 0.402514i \(-0.131864\pi\)
0.915414 + 0.402514i \(0.131864\pi\)
\(702\) 15.5165 26.8754i 0.0221033 0.0382841i
\(703\) 26.8355 15.4935i 0.0381728 0.0220391i
\(704\) 2.10578 + 3.64732i 0.00299117 + 0.00518086i
\(705\) −212.227 122.530i −0.301032 0.173801i
\(706\) 46.5422i 0.0659238i
\(707\) 488.188 + 469.356i 0.690507 + 0.663870i
\(708\) −175.046 −0.247240
\(709\) −86.2000 + 149.303i −0.121580 + 0.210582i −0.920391 0.391000i \(-0.872129\pi\)
0.798811 + 0.601582i \(0.205463\pi\)
\(710\) −79.5862 + 45.9491i −0.112093 + 0.0647171i
\(711\) −198.442 343.712i −0.279103 0.483420i
\(712\) −167.189 96.5264i −0.234815 0.135571i
\(713\) 20.9194i 0.0293399i
\(714\) −396.325 + 412.227i −0.555077 + 0.577349i
\(715\) −4.97126 −0.00695282
\(716\) 195.899 339.307i 0.273602 0.473892i
\(717\) −516.201 + 298.029i −0.719946 + 0.415661i
\(718\) −189.361 327.983i −0.263734 0.456801i
\(719\) −435.015 251.156i −0.605028 0.349313i 0.165989 0.986128i \(-0.446918\pi\)
−0.771017 + 0.636815i \(0.780252\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −175.836 + 711.943i −0.243878 + 0.987439i
\(722\) 496.257 0.687337
\(723\) 148.392 257.023i 0.205245 0.355495i
\(724\) −206.168 + 119.031i −0.284763 + 0.164408i
\(725\) −140.326 243.051i −0.193552 0.335243i
\(726\) −256.092 147.855i −0.352744 0.203657i
\(727\) 748.693i 1.02984i 0.857238 + 0.514920i \(0.172178\pi\)
−0.857238 + 0.514920i \(0.827822\pi\)
\(728\) −80.3223 + 23.2244i −0.110333 + 0.0319017i
\(729\) −27.0000 −0.0370370
\(730\) −26.4571 + 45.8251i −0.0362426 + 0.0627741i
\(731\) −1338.76 + 772.931i −1.83140 + 1.05736i
\(732\) 178.917 + 309.893i 0.244422 + 0.423351i
\(733\) −812.761 469.248i −1.10881 0.640175i −0.170293 0.985394i \(-0.554471\pi\)
−0.938522 + 0.345219i \(0.887805\pi\)
\(734\) 224.468i 0.305814i
\(735\) 160.493 101.277i 0.218358 0.137792i
\(736\) 62.5596 0.0849994
\(737\) 2.30029 3.98422i 0.00312116 0.00540600i
\(738\) 14.9680 8.64178i 0.0202818 0.0117097i
\(739\) −106.820 185.018i −0.144547 0.250363i 0.784657 0.619931i \(-0.212839\pi\)
−0.929204 + 0.369567i \(0.879506\pi\)
\(740\) −37.7757 21.8098i −0.0510482 0.0294727i
\(741\) 23.2381i 0.0313605i
\(742\) −127.919 442.413i −0.172398 0.596244i
\(743\) 544.013 0.732184 0.366092 0.930579i \(-0.380696\pi\)
0.366092 + 0.930579i \(0.380696\pi\)
\(744\) 4.63346 8.02538i 0.00622776 0.0107868i
\(745\) −279.010 + 161.087i −0.374511 + 0.216224i
\(746\) −292.985 507.465i −0.392742 0.680249i
\(747\) −32.4337 18.7256i −0.0434187 0.0250678i
\(748\) 35.1146i 0.0469446i
\(749\) 846.786 + 209.140i 1.13056 + 0.279225i
\(750\) 27.3861 0.0365148
\(751\) −294.705 + 510.443i −0.392416 + 0.679685i −0.992768 0.120051i \(-0.961694\pi\)
0.600351 + 0.799736i \(0.295027\pi\)
\(752\) −219.187 + 126.548i −0.291473 + 0.168282i
\(753\) 283.656 + 491.307i 0.376702 + 0.652467i
\(754\) 290.316 + 167.614i 0.385034 + 0.222299i
\(755\) 209.100i 0.276954i
\(756\) 52.4408 + 50.4179i 0.0693662 + 0.0666903i
\(757\) −448.997 −0.593127 −0.296564 0.955013i \(-0.595841\pi\)
−0.296564 + 0.955013i \(0.595841\pi\)
\(758\) 51.4774 89.1614i 0.0679121 0.117627i
\(759\) 8.73300 5.04200i 0.0115059 0.00664295i
\(760\) 10.0464 + 17.4010i 0.0132190 + 0.0228960i
\(761\) 371.914 + 214.725i 0.488718 + 0.282161i 0.724042 0.689756i \(-0.242282\pi\)
−0.235325 + 0.971917i \(0.575615\pi\)
\(762\) 199.326i 0.261582i
\(763\) 410.475 426.944i 0.537975 0.559560i
\(764\) −131.463 −0.172072
\(765\) −111.861 + 193.749i −0.146224 + 0.253267i
\(766\) 349.070 201.536i 0.455705 0.263101i
\(767\) −106.699 184.807i −0.139112 0.240948i
\(768\) 24.0000 + 13.8564i 0.0312500 + 0.0180422i
\(769\) 32.5790i 0.0423655i −0.999776 0.0211827i \(-0.993257\pi\)
0.999776 0.0211827i \(-0.00674318\pi\)
\(770\) 2.79419