Properties

Label 1050.3.q.e.199.4
Level $1050$
Weight $3$
Character 1050.199
Analytic conductor $28.610$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.4
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.e.649.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.72455 - 1.94434i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.72455 - 1.94434i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.263223 - 0.455915i) q^{11} +(-1.73205 - 3.00000i) q^{12} +4.22307 q^{13} +(9.61071 - 2.37366i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-16.6753 + 28.8825i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-2.75133 + 1.58848i) q^{19} +(-8.74014 + 8.40298i) q^{21} +0.744507i q^{22} +(9.57744 - 5.52954i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-5.17218 + 2.98616i) q^{26} -5.19615 q^{27} +(-10.0922 + 9.70292i) q^{28} +56.1302 q^{29} +(-1.63817 - 0.945800i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-0.455915 - 0.789668i) q^{33} -47.1649i q^{34} -6.00000 q^{36} +(8.44690 - 4.87682i) q^{37} +(2.24645 - 3.89097i) q^{38} +(3.65729 - 6.33460i) q^{39} +4.07377i q^{41} +(4.76263 - 16.4717i) q^{42} +46.3519i q^{43} +(-0.526446 - 0.911831i) q^{44} +(-7.81995 + 13.5445i) q^{46} +(-31.6370 - 54.7969i) q^{47} -6.92820 q^{48} +(41.4391 + 26.1496i) q^{49} +(28.8825 + 50.0259i) q^{51} +(4.22307 - 7.31457i) q^{52} +(40.2885 + 23.2606i) q^{53} +(6.36396 - 3.67423i) q^{54} +(5.49942 - 19.0199i) q^{56} +5.50267i q^{57} +(-68.7452 + 39.6900i) q^{58} +(43.7614 + 25.2657i) q^{59} +(89.4583 - 51.6488i) q^{61} +2.67513 q^{62} +(5.03529 + 20.3874i) q^{63} -8.00000 q^{64} +(1.11676 + 0.644762i) q^{66} +(7.56816 + 4.36948i) q^{67} +(33.3506 + 57.7649i) q^{68} -19.1549i q^{69} +29.0608 q^{71} +(7.34847 - 4.24264i) q^{72} +(-8.36647 + 14.4912i) q^{73} +(-6.89686 + 11.9457i) q^{74} +6.35393i q^{76} +(-2.65651 + 2.55403i) q^{77} +10.3444i q^{78} +(-66.1473 - 114.571i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-2.88059 - 4.98933i) q^{82} -12.4838 q^{83} +(5.81425 + 23.5413i) q^{84} +(-32.7757 - 56.7692i) q^{86} +(48.6102 - 84.1953i) q^{87} +(1.28952 + 0.744507i) q^{88} +(59.1101 - 34.1272i) q^{89} +(-28.3982 - 8.21107i) q^{91} -22.1182i q^{92} +(-2.83740 + 1.63817i) q^{93} +(77.4945 + 44.7415i) q^{94} +(8.48528 - 4.89898i) q^{96} -149.281 q^{97} +(-69.2429 - 2.72468i) q^{98} -1.57934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 + 0.707107i −0.612372 + 0.353553i
\(3\) 0.866025 1.50000i 0.288675 0.500000i
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −6.72455 1.94434i −0.960650 0.277762i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) 0.263223 0.455915i 0.0239293 0.0414468i −0.853813 0.520580i \(-0.825716\pi\)
0.877742 + 0.479133i \(0.159049\pi\)
\(12\) −1.73205 3.00000i −0.144338 0.250000i
\(13\) 4.22307 0.324851 0.162426 0.986721i \(-0.448068\pi\)
0.162426 + 0.986721i \(0.448068\pi\)
\(14\) 9.61071 2.37366i 0.686479 0.169547i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −16.6753 + 28.8825i −0.980900 + 1.69897i −0.321997 + 0.946741i \(0.604354\pi\)
−0.658903 + 0.752228i \(0.728979\pi\)
\(18\) 3.67423 + 2.12132i 0.204124 + 0.117851i
\(19\) −2.75133 + 1.58848i −0.144807 + 0.0836044i −0.570653 0.821191i \(-0.693310\pi\)
0.425846 + 0.904796i \(0.359977\pi\)
\(20\) 0 0
\(21\) −8.74014 + 8.40298i −0.416197 + 0.400142i
\(22\) 0.744507i 0.0338412i
\(23\) 9.57744 5.52954i 0.416410 0.240415i −0.277130 0.960832i \(-0.589383\pi\)
0.693540 + 0.720418i \(0.256050\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −5.17218 + 2.98616i −0.198930 + 0.114852i
\(27\) −5.19615 −0.192450
\(28\) −10.0922 + 9.70292i −0.360437 + 0.346533i
\(29\) 56.1302 1.93552 0.967762 0.251866i \(-0.0810442\pi\)
0.967762 + 0.251866i \(0.0810442\pi\)
\(30\) 0 0
\(31\) −1.63817 0.945800i −0.0528443 0.0305097i 0.473345 0.880877i \(-0.343046\pi\)
−0.526189 + 0.850367i \(0.676380\pi\)
\(32\) 4.89898 + 2.82843i 0.153093 + 0.0883883i
\(33\) −0.455915 0.789668i −0.0138156 0.0239293i
\(34\) 47.1649i 1.38720i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 8.44690 4.87682i 0.228294 0.131806i −0.381491 0.924373i \(-0.624589\pi\)
0.609785 + 0.792567i \(0.291256\pi\)
\(38\) 2.24645 3.89097i 0.0591172 0.102394i
\(39\) 3.65729 6.33460i 0.0937765 0.162426i
\(40\) 0 0
\(41\) 4.07377i 0.0993603i 0.998765 + 0.0496802i \(0.0158202\pi\)
−0.998765 + 0.0496802i \(0.984180\pi\)
\(42\) 4.76263 16.4717i 0.113396 0.392184i
\(43\) 46.3519i 1.07795i 0.842322 + 0.538975i \(0.181188\pi\)
−0.842322 + 0.538975i \(0.818812\pi\)
\(44\) −0.526446 0.911831i −0.0119647 0.0207234i
\(45\) 0 0
\(46\) −7.81995 + 13.5445i −0.169999 + 0.294447i
\(47\) −31.6370 54.7969i −0.673127 1.16589i −0.977012 0.213182i \(-0.931617\pi\)
0.303885 0.952709i \(-0.401716\pi\)
\(48\) −6.92820 −0.144338
\(49\) 41.4391 + 26.1496i 0.845696 + 0.533665i
\(50\) 0 0
\(51\) 28.8825 + 50.0259i 0.566323 + 0.980900i
\(52\) 4.22307 7.31457i 0.0812129 0.140665i
\(53\) 40.2885 + 23.2606i 0.760160 + 0.438878i 0.829353 0.558725i \(-0.188709\pi\)
−0.0691934 + 0.997603i \(0.522043\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 5.49942 19.0199i 0.0982038 0.339641i
\(57\) 5.50267i 0.0965380i
\(58\) −68.7452 + 39.6900i −1.18526 + 0.684311i
\(59\) 43.7614 + 25.2657i 0.741719 + 0.428231i 0.822694 0.568485i \(-0.192470\pi\)
−0.0809752 + 0.996716i \(0.525803\pi\)
\(60\) 0 0
\(61\) 89.4583 51.6488i 1.46653 0.846702i 0.467231 0.884135i \(-0.345252\pi\)
0.999299 + 0.0374335i \(0.0119182\pi\)
\(62\) 2.67513 0.0431472
\(63\) 5.03529 + 20.3874i 0.0799252 + 0.323609i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 1.11676 + 0.644762i 0.0169206 + 0.00976912i
\(67\) 7.56816 + 4.36948i 0.112958 + 0.0652161i 0.555414 0.831574i \(-0.312560\pi\)
−0.442457 + 0.896790i \(0.645893\pi\)
\(68\) 33.3506 + 57.7649i 0.490450 + 0.849484i
\(69\) 19.1549i 0.277607i
\(70\) 0 0
\(71\) 29.0608 0.409307 0.204653 0.978835i \(-0.434393\pi\)
0.204653 + 0.978835i \(0.434393\pi\)
\(72\) 7.34847 4.24264i 0.102062 0.0589256i
\(73\) −8.36647 + 14.4912i −0.114609 + 0.198509i −0.917623 0.397451i \(-0.869895\pi\)
0.803014 + 0.595960i \(0.203228\pi\)
\(74\) −6.89686 + 11.9457i −0.0932008 + 0.161429i
\(75\) 0 0
\(76\) 6.35393i 0.0836044i
\(77\) −2.65651 + 2.55403i −0.0345001 + 0.0331692i
\(78\) 10.3444i 0.132620i
\(79\) −66.1473 114.571i −0.837308 1.45026i −0.892137 0.451764i \(-0.850795\pi\)
0.0548297 0.998496i \(-0.482538\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −2.88059 4.98933i −0.0351292 0.0608455i
\(83\) −12.4838 −0.150407 −0.0752033 0.997168i \(-0.523961\pi\)
−0.0752033 + 0.997168i \(0.523961\pi\)
\(84\) 5.81425 + 23.5413i 0.0692173 + 0.280254i
\(85\) 0 0
\(86\) −32.7757 56.7692i −0.381113 0.660107i
\(87\) 48.6102 84.1953i 0.558738 0.967762i
\(88\) 1.28952 + 0.744507i 0.0146537 + 0.00846030i
\(89\) 59.1101 34.1272i 0.664158 0.383452i −0.129701 0.991553i \(-0.541402\pi\)
0.793860 + 0.608101i \(0.208069\pi\)
\(90\) 0 0
\(91\) −28.3982 8.21107i −0.312068 0.0902315i
\(92\) 22.1182i 0.240415i
\(93\) −2.83740 + 1.63817i −0.0305097 + 0.0176148i
\(94\) 77.4945 + 44.7415i 0.824409 + 0.475973i
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) −149.281 −1.53898 −0.769490 0.638659i \(-0.779490\pi\)
−0.769490 + 0.638659i \(0.779490\pi\)
\(98\) −69.2429 2.72468i −0.706560 0.0278029i
\(99\) −1.57934 −0.0159529
\(100\) 0 0
\(101\) 83.7839 + 48.3726i 0.829543 + 0.478937i 0.853696 0.520771i \(-0.174356\pi\)
−0.0241531 + 0.999708i \(0.507689\pi\)
\(102\) −70.7473 40.8460i −0.693601 0.400451i
\(103\) 52.3811 + 90.7268i 0.508555 + 0.880843i 0.999951 + 0.00990642i \(0.00315336\pi\)
−0.491396 + 0.870936i \(0.663513\pi\)
\(104\) 11.9446i 0.114852i
\(105\) 0 0
\(106\) −65.7908 −0.620668
\(107\) 107.911 62.3022i 1.00851 0.582263i 0.0977548 0.995211i \(-0.468834\pi\)
0.910755 + 0.412947i \(0.135501\pi\)
\(108\) −5.19615 + 9.00000i −0.0481125 + 0.0833333i
\(109\) 42.3042 73.2731i 0.388112 0.672230i −0.604083 0.796921i \(-0.706461\pi\)
0.992196 + 0.124691i \(0.0397940\pi\)
\(110\) 0 0
\(111\) 16.8938i 0.152196i
\(112\) 6.71372 + 27.1832i 0.0599439 + 0.242707i
\(113\) 116.241i 1.02868i −0.857586 0.514340i \(-0.828037\pi\)
0.857586 0.514340i \(-0.171963\pi\)
\(114\) −3.89097 6.73936i −0.0341313 0.0591172i
\(115\) 0 0
\(116\) 56.1302 97.2204i 0.483881 0.838107i
\(117\) −6.33460 10.9719i −0.0541419 0.0937765i
\(118\) −71.4621 −0.605611
\(119\) 168.291 161.799i 1.41421 1.35966i
\(120\) 0 0
\(121\) 60.3614 + 104.549i 0.498855 + 0.864042i
\(122\) −73.0424 + 126.513i −0.598708 + 1.03699i
\(123\) 6.11066 + 3.52799i 0.0496802 + 0.0286829i
\(124\) −3.27635 + 1.89160i −0.0264222 + 0.0152548i
\(125\) 0 0
\(126\) −20.5830 21.4089i −0.163357 0.169912i
\(127\) 81.3744i 0.640743i 0.947292 + 0.320372i \(0.103808\pi\)
−0.947292 + 0.320372i \(0.896192\pi\)
\(128\) 9.79796 5.65685i 0.0765466 0.0441942i
\(129\) 69.5278 + 40.1419i 0.538975 + 0.311178i
\(130\) 0 0
\(131\) 208.389 120.313i 1.59075 0.918421i 0.597574 0.801814i \(-0.296131\pi\)
0.993178 0.116608i \(-0.0372020\pi\)
\(132\) −1.82366 −0.0138156
\(133\) 21.5900 5.33231i 0.162331 0.0400926i
\(134\) −12.3588 −0.0922295
\(135\) 0 0
\(136\) −81.6919 47.1649i −0.600676 0.346800i
\(137\) 202.357 + 116.831i 1.47706 + 0.852778i 0.999664 0.0259125i \(-0.00824914\pi\)
0.477391 + 0.878691i \(0.341582\pi\)
\(138\) 13.5445 + 23.4598i 0.0981489 + 0.169999i
\(139\) 211.491i 1.52152i 0.649033 + 0.760760i \(0.275174\pi\)
−0.649033 + 0.760760i \(0.724826\pi\)
\(140\) 0 0
\(141\) −109.594 −0.777261
\(142\) −35.5920 + 20.5491i −0.250648 + 0.144712i
\(143\) 1.11161 1.92536i 0.00777348 0.0134641i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 23.6640i 0.162082i
\(147\) 75.1117 39.5125i 0.510964 0.268792i
\(148\) 19.5073i 0.131806i
\(149\) 72.0402 + 124.777i 0.483491 + 0.837431i 0.999820 0.0189590i \(-0.00603520\pi\)
−0.516329 + 0.856390i \(0.672702\pi\)
\(150\) 0 0
\(151\) −46.7563 + 80.9842i −0.309644 + 0.536319i −0.978285 0.207267i \(-0.933543\pi\)
0.668640 + 0.743586i \(0.266877\pi\)
\(152\) −4.49291 7.78195i −0.0295586 0.0511970i
\(153\) 100.052 0.653933
\(154\) 1.44757 5.00647i 0.00939982 0.0325095i
\(155\) 0 0
\(156\) −7.31457 12.6692i −0.0468883 0.0812129i
\(157\) −85.6127 + 148.286i −0.545304 + 0.944494i 0.453284 + 0.891366i \(0.350252\pi\)
−0.998588 + 0.0531280i \(0.983081\pi\)
\(158\) 162.027 + 93.5464i 1.02549 + 0.592066i
\(159\) 69.7817 40.2885i 0.438878 0.253387i
\(160\) 0 0
\(161\) −75.1553 + 18.5619i −0.466803 + 0.115291i
\(162\) 12.7279i 0.0785674i
\(163\) 80.5515 46.5064i 0.494181 0.285316i −0.232126 0.972686i \(-0.574568\pi\)
0.726307 + 0.687370i \(0.241235\pi\)
\(164\) 7.05598 + 4.07377i 0.0430243 + 0.0248401i
\(165\) 0 0
\(166\) 15.2894 8.82735i 0.0921049 0.0531768i
\(167\) 104.991 0.628688 0.314344 0.949309i \(-0.398216\pi\)
0.314344 + 0.949309i \(0.398216\pi\)
\(168\) −23.7672 24.7208i −0.141471 0.147148i
\(169\) −151.166 −0.894472
\(170\) 0 0
\(171\) 8.25400 + 4.76545i 0.0482690 + 0.0278681i
\(172\) 80.2838 + 46.3519i 0.466766 + 0.269488i
\(173\) 102.079 + 176.805i 0.590049 + 1.02200i 0.994225 + 0.107314i \(0.0342251\pi\)
−0.404176 + 0.914681i \(0.632442\pi\)
\(174\) 137.490i 0.790174i
\(175\) 0 0
\(176\) −2.10578 −0.0119647
\(177\) 75.7970 43.7614i 0.428231 0.247240i
\(178\) −48.2632 + 83.5943i −0.271141 + 0.469631i
\(179\) −97.9495 + 169.653i −0.547204 + 0.947785i 0.451261 + 0.892392i \(0.350974\pi\)
−0.998465 + 0.0553926i \(0.982359\pi\)
\(180\) 0 0
\(181\) 119.031i 0.657632i 0.944394 + 0.328816i \(0.106650\pi\)
−0.944394 + 0.328816i \(0.893350\pi\)
\(182\) 40.5867 10.0241i 0.223004 0.0550776i
\(183\) 178.917i 0.977687i
\(184\) 15.6399 + 27.0891i 0.0849994 + 0.147223i
\(185\) 0 0
\(186\) 2.31673 4.01269i 0.0124555 0.0215736i
\(187\) 8.77864 + 15.2050i 0.0469446 + 0.0813104i
\(188\) −126.548 −0.673127
\(189\) 34.9418 + 10.1031i 0.184877 + 0.0534554i
\(190\) 0 0
\(191\) 32.8657 + 56.9250i 0.172072 + 0.298037i 0.939144 0.343524i \(-0.111621\pi\)
−0.767072 + 0.641561i \(0.778287\pi\)
\(192\) −6.92820 + 12.0000i −0.0360844 + 0.0625000i
\(193\) 83.8919 + 48.4350i 0.434673 + 0.250959i 0.701335 0.712831i \(-0.252588\pi\)
−0.266662 + 0.963790i \(0.585921\pi\)
\(194\) 182.831 105.558i 0.942429 0.544112i
\(195\) 0 0
\(196\) 86.7315 45.6251i 0.442508 0.232781i
\(197\) 186.672i 0.947574i −0.880640 0.473787i \(-0.842887\pi\)
0.880640 0.473787i \(-0.157113\pi\)
\(198\) 1.93428 1.11676i 0.00976912 0.00564020i
\(199\) −99.8454 57.6458i −0.501736 0.289677i 0.227694 0.973733i \(-0.426881\pi\)
−0.729430 + 0.684055i \(0.760215\pi\)
\(200\) 0 0
\(201\) 13.1084 7.56816i 0.0652161 0.0376525i
\(202\) −136.818 −0.677319
\(203\) −377.450 109.136i −1.85936 0.537616i
\(204\) 115.530 0.566323
\(205\) 0 0
\(206\) −128.307 74.0781i −0.622850 0.359602i
\(207\) −28.7323 16.5886i −0.138803 0.0801382i
\(208\) −8.44614 14.6291i −0.0406064 0.0703324i
\(209\) 1.67250i 0.00800239i
\(210\) 0 0
\(211\) 139.433 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(212\) 80.5769 46.5211i 0.380080 0.219439i
\(213\) 25.1674 43.5912i 0.118157 0.204653i
\(214\) −88.1086 + 152.609i −0.411722 + 0.713124i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 9.17703 + 9.54524i 0.0422905 + 0.0439873i
\(218\) 119.654i 0.548874i
\(219\) 14.4912 + 25.0994i 0.0661697 + 0.114609i
\(220\) 0 0
\(221\) −70.4209 + 121.973i −0.318647 + 0.551912i
\(222\) 11.9457 + 20.6906i 0.0538095 + 0.0932008i
\(223\) 258.055 1.15720 0.578599 0.815612i \(-0.303600\pi\)
0.578599 + 0.815612i \(0.303600\pi\)
\(224\) −27.4440 28.5452i −0.122518 0.127434i
\(225\) 0 0
\(226\) 82.1947 + 142.365i 0.363693 + 0.629935i
\(227\) 165.516 286.682i 0.729146 1.26292i −0.228099 0.973638i \(-0.573251\pi\)
0.957245 0.289280i \(-0.0934158\pi\)
\(228\) 9.53090 + 5.50267i 0.0418022 + 0.0241345i
\(229\) −211.516 + 122.119i −0.923653 + 0.533271i −0.884799 0.465974i \(-0.845704\pi\)
−0.0388541 + 0.999245i \(0.512371\pi\)
\(230\) 0 0
\(231\) 1.53044 + 6.19662i 0.00662529 + 0.0268252i
\(232\) 158.760i 0.684311i
\(233\) 183.155 105.745i 0.786074 0.453840i −0.0525044 0.998621i \(-0.516720\pi\)
0.838579 + 0.544781i \(0.183387\pi\)
\(234\) 15.5165 + 8.95848i 0.0663100 + 0.0382841i
\(235\) 0 0
\(236\) 87.5228 50.5313i 0.370859 0.214116i
\(237\) −229.141 −0.966840
\(238\) −91.7044 + 317.162i −0.385313 + 1.33262i
\(239\) −344.134 −1.43989 −0.719946 0.694030i \(-0.755833\pi\)
−0.719946 + 0.694030i \(0.755833\pi\)
\(240\) 0 0
\(241\) −148.392 85.6742i −0.615735 0.355495i 0.159472 0.987203i \(-0.449021\pi\)
−0.775207 + 0.631708i \(0.782354\pi\)
\(242\) −147.855 85.3639i −0.610970 0.352744i
\(243\) 7.79423 + 13.5000i 0.0320750 + 0.0555556i
\(244\) 206.595i 0.846702i
\(245\) 0 0
\(246\) −9.97867 −0.0405637
\(247\) −11.6191 + 6.70827i −0.0470408 + 0.0271590i
\(248\) 2.67513 4.63346i 0.0107868 0.0186833i
\(249\) −10.8112 + 18.7256i −0.0434187 + 0.0752033i
\(250\) 0 0
\(251\) 327.538i 1.30493i 0.757818 + 0.652467i \(0.226266\pi\)
−0.757818 + 0.652467i \(0.773734\pi\)
\(252\) 40.3473 + 11.6660i 0.160108 + 0.0462937i
\(253\) 5.82200i 0.0230119i
\(254\) −57.5404 99.6629i −0.226537 0.392374i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 110.179 + 190.836i 0.428713 + 0.742552i 0.996759 0.0804442i \(-0.0256339\pi\)
−0.568046 + 0.822997i \(0.692301\pi\)
\(258\) −113.538 −0.440072
\(259\) −66.2837 + 16.3708i −0.255922 + 0.0632077i
\(260\) 0 0
\(261\) −84.1953 145.831i −0.322587 0.558738i
\(262\) −170.149 + 294.706i −0.649422 + 1.12483i
\(263\) −115.350 66.5976i −0.438594 0.253223i 0.264407 0.964411i \(-0.414824\pi\)
−0.703001 + 0.711189i \(0.748157\pi\)
\(264\) 2.23352 1.28952i 0.00846030 0.00488456i
\(265\) 0 0
\(266\) −22.6718 + 21.7972i −0.0852322 + 0.0819443i
\(267\) 118.220i 0.442772i
\(268\) 15.1363 8.73896i 0.0564788 0.0326080i
\(269\) 22.9633 + 13.2578i 0.0853653 + 0.0492857i 0.542075 0.840330i \(-0.317639\pi\)
−0.456710 + 0.889616i \(0.650972\pi\)
\(270\) 0 0
\(271\) −92.6776 + 53.5074i −0.341984 + 0.197444i −0.661149 0.750255i \(-0.729931\pi\)
0.319165 + 0.947699i \(0.396598\pi\)
\(272\) 133.402 0.490450
\(273\) −36.9102 + 35.4864i −0.135202 + 0.129987i
\(274\) −330.447 −1.20601
\(275\) 0 0
\(276\) −33.1772 19.1549i −0.120207 0.0694017i
\(277\) 381.381 + 220.191i 1.37683 + 0.794912i 0.991776 0.127983i \(-0.0408503\pi\)
0.385052 + 0.922895i \(0.374184\pi\)
\(278\) −149.547 259.023i −0.537939 0.931737i
\(279\) 5.67480i 0.0203398i
\(280\) 0 0
\(281\) 322.069 1.14615 0.573076 0.819502i \(-0.305750\pi\)
0.573076 + 0.819502i \(0.305750\pi\)
\(282\) 134.224 77.4945i 0.475973 0.274803i
\(283\) 34.2665 59.3514i 0.121083 0.209722i −0.799112 0.601182i \(-0.794697\pi\)
0.920195 + 0.391460i \(0.128030\pi\)
\(284\) 29.0608 50.3347i 0.102327 0.177235i
\(285\) 0 0
\(286\) 3.14410i 0.0109934i
\(287\) 7.92079 27.3943i 0.0275986 0.0954505i
\(288\) 16.9706i 0.0589256i
\(289\) −411.631 712.966i −1.42433 2.46701i
\(290\) 0 0
\(291\) −129.281 + 223.922i −0.444265 + 0.769490i
\(292\) 16.7329 + 28.9823i 0.0573046 + 0.0992545i
\(293\) 147.510 0.503448 0.251724 0.967799i \(-0.419003\pi\)
0.251724 + 0.967799i \(0.419003\pi\)
\(294\) −64.0531 + 101.505i −0.217868 + 0.345254i
\(295\) 0 0
\(296\) 13.7937 + 23.8914i 0.0466004 + 0.0807143i
\(297\) −1.36775 + 2.36901i −0.00460521 + 0.00797645i
\(298\) −176.462 101.880i −0.592153 0.341880i
\(299\) 40.4462 23.3516i 0.135272 0.0780991i
\(300\) 0 0
\(301\) 90.1237 311.695i 0.299414 1.03553i
\(302\) 132.247i 0.437903i
\(303\) 145.118 83.7839i 0.478937 0.276514i
\(304\) 11.0053 + 6.35393i 0.0362018 + 0.0209011i
\(305\) 0 0
\(306\) −122.538 + 70.7473i −0.400451 + 0.231200i
\(307\) −376.010 −1.22479 −0.612394 0.790553i \(-0.709793\pi\)
−0.612394 + 0.790553i \(0.709793\pi\)
\(308\) 1.76720 + 7.15524i 0.00573767 + 0.0232313i
\(309\) 181.454 0.587228
\(310\) 0 0
\(311\) −337.599 194.913i −1.08553 0.626730i −0.153146 0.988204i \(-0.548941\pi\)
−0.932383 + 0.361473i \(0.882274\pi\)
\(312\) 17.9170 + 10.3444i 0.0574262 + 0.0331550i
\(313\) −71.5282 123.890i −0.228524 0.395816i 0.728847 0.684677i \(-0.240057\pi\)
−0.957371 + 0.288861i \(0.906723\pi\)
\(314\) 242.149i 0.771176i
\(315\) 0 0
\(316\) −264.589 −0.837308
\(317\) −332.938 + 192.222i −1.05028 + 0.606378i −0.922727 0.385454i \(-0.874045\pi\)
−0.127551 + 0.991832i \(0.540712\pi\)
\(318\) −56.9765 + 98.6862i −0.179171 + 0.310334i
\(319\) 14.7747 25.5906i 0.0463158 0.0802214i
\(320\) 0 0
\(321\) 215.821i 0.672340i
\(322\) 78.9208 75.8764i 0.245096 0.235641i
\(323\) 105.954i 0.328030i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −65.7700 + 113.917i −0.201749 + 0.349439i
\(327\) −73.2731 126.913i −0.224077 0.388112i
\(328\) −11.5224 −0.0351292
\(329\) 106.201 + 429.997i 0.322799 + 1.30698i
\(330\) 0 0
\(331\) −96.9539 167.929i −0.292912 0.507338i 0.681585 0.731739i \(-0.261291\pi\)
−0.974497 + 0.224400i \(0.927958\pi\)
\(332\) −12.4838 + 21.6225i −0.0376017 + 0.0651280i
\(333\) −25.3407 14.6305i −0.0760982 0.0439353i
\(334\) −128.587 + 74.2397i −0.384991 + 0.222275i
\(335\) 0 0
\(336\) 46.5890 + 13.4708i 0.138658 + 0.0400916i
\(337\) 125.477i 0.372337i −0.982518 0.186168i \(-0.940393\pi\)
0.982518 0.186168i \(-0.0596070\pi\)
\(338\) 185.139 106.890i 0.547750 0.316243i
\(339\) −174.361 100.668i −0.514340 0.296954i
\(340\) 0 0
\(341\) −0.862410 + 0.497912i −0.00252906 + 0.00146015i
\(342\) −13.4787 −0.0394115
\(343\) −227.816 256.416i −0.664186 0.747568i
\(344\) −131.103 −0.381113
\(345\) 0 0
\(346\) −250.040 144.361i −0.722660 0.417228i
\(347\) −436.128 251.798i −1.25685 0.725644i −0.284391 0.958708i \(-0.591791\pi\)
−0.972461 + 0.233065i \(0.925125\pi\)
\(348\) −97.2204 168.391i −0.279369 0.483881i
\(349\) 47.7682i 0.136872i −0.997656 0.0684358i \(-0.978199\pi\)
0.997656 0.0684358i \(-0.0218008\pi\)
\(350\) 0 0
\(351\) −21.9437 −0.0625177
\(352\) 2.57905 1.48901i 0.00732684 0.00423015i
\(353\) −16.4552 + 28.5012i −0.0466152 + 0.0807399i −0.888392 0.459087i \(-0.848177\pi\)
0.841776 + 0.539826i \(0.181510\pi\)
\(354\) −61.8880 + 107.193i −0.174825 + 0.302805i
\(355\) 0 0
\(356\) 136.509i 0.383452i
\(357\) −96.9543 392.559i −0.271581 1.09960i
\(358\) 277.043i 0.773863i
\(359\) 133.898 + 231.919i 0.372976 + 0.646013i 0.990022 0.140914i \(-0.0450040\pi\)
−0.617046 + 0.786927i \(0.711671\pi\)
\(360\) 0 0
\(361\) −175.453 + 303.894i −0.486021 + 0.841812i
\(362\) −84.1679 145.783i −0.232508 0.402716i
\(363\) 209.098 0.576028
\(364\) −42.6202 + 40.9761i −0.117089 + 0.112572i
\(365\) 0 0
\(366\) 126.513 + 219.127i 0.345665 + 0.598708i
\(367\) −79.3613 + 137.458i −0.216243 + 0.374545i −0.953657 0.300897i \(-0.902714\pi\)
0.737413 + 0.675442i \(0.236047\pi\)
\(368\) −38.3098 22.1182i −0.104103 0.0601037i
\(369\) 10.5840 6.11066i 0.0286829 0.0165601i
\(370\) 0 0
\(371\) −225.695 234.751i −0.608343 0.632752i
\(372\) 6.55270i 0.0176148i
\(373\) 358.832 207.172i 0.962017 0.555421i 0.0652235 0.997871i \(-0.479224\pi\)
0.896793 + 0.442450i \(0.145891\pi\)
\(374\) −21.5032 12.4149i −0.0574951 0.0331948i
\(375\) 0 0
\(376\) 154.989 89.4829i 0.412205 0.237986i
\(377\) 237.042 0.628758
\(378\) −49.9387 + 12.3339i −0.132113 + 0.0326293i
\(379\) 72.8000 0.192084 0.0960422 0.995377i \(-0.469382\pi\)
0.0960422 + 0.995377i \(0.469382\pi\)
\(380\) 0 0
\(381\) 122.062 + 70.4723i 0.320372 + 0.184967i
\(382\) −80.5042 46.4791i −0.210744 0.121673i
\(383\) −142.507 246.830i −0.372082 0.644464i 0.617804 0.786332i \(-0.288023\pi\)
−0.989886 + 0.141868i \(0.954689\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −136.995 −0.354909
\(387\) 120.426 69.5278i 0.311178 0.179658i
\(388\) −149.281 + 258.562i −0.384745 + 0.666398i
\(389\) −48.5692 + 84.1242i −0.124856 + 0.216258i −0.921677 0.387959i \(-0.873180\pi\)
0.796820 + 0.604216i \(0.206514\pi\)
\(390\) 0 0
\(391\) 368.827i 0.943291i
\(392\) −73.9622 + 117.207i −0.188679 + 0.298999i
\(393\) 416.777i 1.06050i
\(394\) 131.997 + 228.626i 0.335018 + 0.580268i
\(395\) 0 0
\(396\) −1.57934 + 2.73549i −0.00398822 + 0.00690781i
\(397\) 395.852 + 685.636i 0.997108 + 1.72704i 0.564371 + 0.825522i \(0.309119\pi\)
0.432737 + 0.901520i \(0.357548\pi\)
\(398\) 163.047 0.409665
\(399\) 10.6990 37.0030i 0.0268146 0.0927392i
\(400\) 0 0
\(401\) −251.613 435.807i −0.627464 1.08680i −0.988059 0.154077i \(-0.950759\pi\)
0.360594 0.932723i \(-0.382574\pi\)
\(402\) −10.7030 + 18.5381i −0.0266244 + 0.0461147i
\(403\) −6.91812 3.99418i −0.0171666 0.00991112i
\(404\) 167.568 96.7453i 0.414772 0.239468i
\(405\) 0 0
\(406\) 539.451 133.234i 1.32870 0.328162i
\(407\) 5.13476i 0.0126161i
\(408\) −141.495 + 81.6919i −0.346800 + 0.200225i
\(409\) −649.395 374.928i −1.58776 0.916696i −0.993675 0.112296i \(-0.964180\pi\)
−0.594088 0.804400i \(-0.702487\pi\)
\(410\) 0 0
\(411\) 350.492 202.357i 0.852778 0.492352i
\(412\) 209.525 0.508555
\(413\) −245.151 254.987i −0.593585 0.617402i
\(414\) 46.9197 0.113333
\(415\) 0 0
\(416\) 20.6887 + 11.9446i 0.0497325 + 0.0287131i
\(417\) 317.237 + 183.157i 0.760760 + 0.439225i
\(418\) −1.18264 2.04839i −0.00282927 0.00490044i
\(419\) 465.759i 1.11160i 0.831317 + 0.555799i \(0.187587\pi\)
−0.831317 + 0.555799i \(0.812413\pi\)
\(420\) 0 0
\(421\) 345.980 0.821805 0.410902 0.911679i \(-0.365214\pi\)
0.410902 + 0.911679i \(0.365214\pi\)
\(422\) −170.770 + 98.5939i −0.404667 + 0.233635i
\(423\) −94.9110 + 164.391i −0.224376 + 0.388630i
\(424\) −65.7908 + 113.953i −0.155167 + 0.268757i
\(425\) 0 0
\(426\) 71.1841i 0.167099i
\(427\) −701.990 + 173.378i −1.64400 + 0.406037i
\(428\) 249.209i 0.582263i
\(429\) −1.92536 3.33482i −0.00448802 0.00777348i
\(430\) 0 0
\(431\) −247.300 + 428.336i −0.573782 + 0.993819i 0.422391 + 0.906414i \(0.361191\pi\)
−0.996173 + 0.0874056i \(0.972142\pi\)
\(432\) 10.3923 + 18.0000i 0.0240563 + 0.0416667i
\(433\) −730.022 −1.68596 −0.842981 0.537943i \(-0.819201\pi\)
−0.842981 + 0.537943i \(0.819201\pi\)
\(434\) −17.9890 5.20135i −0.0414494 0.0119847i
\(435\) 0 0
\(436\) −84.6085 146.546i −0.194056 0.336115i
\(437\) −17.5672 + 30.4272i −0.0401994 + 0.0696275i
\(438\) −35.4959 20.4936i −0.0810410 0.0467890i
\(439\) 321.631 185.694i 0.732645 0.422993i −0.0867437 0.996231i \(-0.527646\pi\)
0.819389 + 0.573238i \(0.194313\pi\)
\(440\) 0 0
\(441\) 5.77993 146.886i 0.0131064 0.333076i
\(442\) 199.180i 0.450635i
\(443\) 353.951 204.354i 0.798987 0.461295i −0.0441299 0.999026i \(-0.514052\pi\)
0.843117 + 0.537731i \(0.180718\pi\)
\(444\) −29.2609 16.8938i −0.0659029 0.0380491i
\(445\) 0 0
\(446\) −316.052 + 182.473i −0.708636 + 0.409131i
\(447\) 249.555 0.558288
\(448\) 53.7964 + 15.5547i 0.120081 + 0.0347203i
\(449\) −725.469 −1.61574 −0.807872 0.589358i \(-0.799381\pi\)
−0.807872 + 0.589358i \(0.799381\pi\)
\(450\) 0 0
\(451\) 1.85730 + 1.07231i 0.00411817 + 0.00237763i
\(452\) −201.335 116.241i −0.445432 0.257170i
\(453\) 80.9842 + 140.269i 0.178773 + 0.309644i
\(454\) 468.150i 1.03117i
\(455\) 0 0
\(456\) −15.5639 −0.0341313
\(457\) −347.736 + 200.765i −0.760909 + 0.439311i −0.829622 0.558325i \(-0.811444\pi\)
0.0687128 + 0.997636i \(0.478111\pi\)
\(458\) 172.702 299.129i 0.377080 0.653121i
\(459\) 86.6474 150.078i 0.188774 0.326967i
\(460\) 0 0
\(461\) 653.050i 1.41659i 0.705915 + 0.708297i \(0.250536\pi\)
−0.705915 + 0.708297i \(0.749464\pi\)
\(462\) −6.25607 6.50709i −0.0135413 0.0140846i
\(463\) 869.580i 1.87814i −0.343722 0.939072i \(-0.611688\pi\)
0.343722 0.939072i \(-0.388312\pi\)
\(464\) −112.260 194.441i −0.241941 0.419053i
\(465\) 0 0
\(466\) −149.546 + 259.021i −0.320913 + 0.555838i
\(467\) −369.601 640.168i −0.791437 1.37081i −0.925077 0.379779i \(-0.876000\pi\)
0.133641 0.991030i \(-0.457333\pi\)
\(468\) −25.3384 −0.0541419
\(469\) −42.3967 44.0978i −0.0903981 0.0940252i
\(470\) 0 0
\(471\) 148.286 + 256.838i 0.314831 + 0.545304i
\(472\) −71.4621 + 123.776i −0.151403 + 0.262237i
\(473\) 21.1325 + 12.2009i 0.0446777 + 0.0257947i
\(474\) 280.639 162.027i 0.592066 0.341829i
\(475\) 0 0
\(476\) −111.953 453.288i −0.235196 0.952285i
\(477\) 139.563i 0.292586i
\(478\) 421.476 243.339i 0.881750 0.509078i
\(479\) 525.006 + 303.112i 1.09605 + 0.632802i 0.935180 0.354174i \(-0.115238\pi\)
0.160866 + 0.986976i \(0.448571\pi\)
\(480\) 0 0
\(481\) 35.6718 20.5951i 0.0741618 0.0428173i
\(482\) 242.323 0.502745
\(483\) −37.2435 + 128.808i −0.0771088 + 0.266683i
\(484\) 241.446 0.498855
\(485\) 0 0
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) 562.549 + 324.788i 1.15513 + 0.666916i 0.950133 0.311846i \(-0.100947\pi\)
0.205000 + 0.978762i \(0.434281\pi\)
\(488\) 146.085 + 253.026i 0.299354 + 0.518497i
\(489\) 161.103i 0.329454i
\(490\) 0 0
\(491\) 266.629 0.543033 0.271516 0.962434i \(-0.412475\pi\)
0.271516 + 0.962434i \(0.412475\pi\)
\(492\) 12.2213 7.05598i 0.0248401 0.0143414i
\(493\) −935.988 + 1621.18i −1.89856 + 3.28839i
\(494\) 9.48693 16.4318i 0.0192043 0.0332628i
\(495\) 0 0
\(496\) 7.56640i 0.0152548i
\(497\) −195.421 56.5039i −0.393200 0.113690i
\(498\) 30.5788i 0.0614033i
\(499\) −340.553 589.855i −0.682471 1.18207i −0.974225 0.225581i \(-0.927572\pi\)
0.291754 0.956493i \(-0.405761\pi\)
\(500\) 0 0
\(501\) 90.9247 157.486i 0.181487 0.314344i
\(502\) −231.604 401.151i −0.461364 0.799105i
\(503\) −453.326 −0.901245 −0.450622 0.892715i \(-0.648798\pi\)
−0.450622 + 0.892715i \(0.648798\pi\)
\(504\) −57.6643 + 14.2419i −0.114413 + 0.0282578i
\(505\) 0 0
\(506\) 4.11678 + 7.13047i 0.00813592 + 0.0140918i
\(507\) −130.913 + 226.749i −0.258212 + 0.447236i
\(508\) 140.945 + 81.3744i 0.277450 + 0.160186i
\(509\) 43.5300 25.1321i 0.0855206 0.0493754i −0.456630 0.889657i \(-0.650944\pi\)
0.542150 + 0.840281i \(0.317610\pi\)
\(510\) 0 0
\(511\) 84.4364 81.1792i 0.165238 0.158863i
\(512\) 22.6274i 0.0441942i
\(513\) 14.2963 8.25400i 0.0278681 0.0160897i
\(514\) −269.883 155.817i −0.525064 0.303146i
\(515\) 0 0
\(516\) 139.056 80.2838i 0.269488 0.155589i
\(517\) −33.3103 −0.0644300
\(518\) 69.6048 66.9197i 0.134372 0.129189i
\(519\) 353.610 0.681330
\(520\) 0 0
\(521\) −89.2971 51.5557i −0.171396 0.0989553i 0.411848 0.911252i \(-0.364883\pi\)
−0.583244 + 0.812297i \(0.698217\pi\)
\(522\) 206.236 + 119.070i 0.395087 + 0.228104i
\(523\) −183.434 317.716i −0.350733 0.607488i 0.635645 0.771982i \(-0.280734\pi\)
−0.986378 + 0.164494i \(0.947401\pi\)
\(524\) 481.253i 0.918421i
\(525\) 0 0
\(526\) 188.366 0.358111
\(527\) 54.6341 31.5430i 0.103670 0.0598539i
\(528\) −1.82366 + 3.15867i −0.00345390 + 0.00598234i
\(529\) −203.348 + 352.210i −0.384402 + 0.665803i
\(530\) 0 0
\(531\) 151.594i 0.285488i
\(532\) 12.3542 42.7273i 0.0232222 0.0803145i
\(533\) 17.2038i 0.0322773i
\(534\) 83.5943 + 144.790i 0.156544 + 0.271141i
\(535\) 0 0
\(536\) −12.3588 + 21.4060i −0.0230574 + 0.0399365i
\(537\) 169.653 + 293.848i 0.315928 + 0.547204i
\(538\) −37.4988 −0.0697005
\(539\) 22.8297 12.0096i 0.0423557 0.0222812i
\(540\) 0 0
\(541\) 266.559 + 461.693i 0.492714 + 0.853407i 0.999965 0.00839227i \(-0.00267137\pi\)
−0.507250 + 0.861799i \(0.669338\pi\)
\(542\) 75.6709 131.066i 0.139614 0.241819i
\(543\) 178.547 + 103.084i 0.328816 + 0.189842i
\(544\) −163.384 + 94.3297i −0.300338 + 0.173400i
\(545\) 0 0
\(546\) 20.1129 69.5612i 0.0368369 0.127401i
\(547\) 69.6218i 0.127279i −0.997973 0.0636396i \(-0.979729\pi\)
0.997973 0.0636396i \(-0.0202708\pi\)
\(548\) 404.713 233.661i 0.738528 0.426389i
\(549\) −268.375 154.946i −0.488843 0.282234i
\(550\) 0 0
\(551\) −154.433 + 89.1619i −0.280277 + 0.161818i
\(552\) 54.1782 0.0981489
\(553\) 222.047 + 899.048i 0.401532 + 1.62576i
\(554\) −622.793 −1.12418
\(555\) 0 0
\(556\) 366.314 + 211.491i 0.658838 + 0.380380i
\(557\) 14.6033 + 8.43122i 0.0262178 + 0.0151368i 0.513052 0.858358i \(-0.328515\pi\)
−0.486834 + 0.873495i \(0.661848\pi\)
\(558\) −4.01269 6.95018i −0.00719120 0.0124555i
\(559\) 195.747i 0.350174i
\(560\) 0 0
\(561\) 30.4101 0.0542069
\(562\) −394.452 + 227.737i −0.701872 + 0.405226i
\(563\) −457.892 + 793.093i −0.813308 + 1.40869i 0.0972290 + 0.995262i \(0.469002\pi\)
−0.910537 + 0.413428i \(0.864331\pi\)
\(564\) −109.594 + 189.822i −0.194315 + 0.336564i
\(565\) 0 0
\(566\) 96.9204i 0.171237i
\(567\) 45.4151 43.6632i 0.0800971 0.0770073i
\(568\) 82.1963i 0.144712i
\(569\) 203.828 + 353.040i 0.358221 + 0.620456i 0.987664 0.156590i \(-0.0500502\pi\)
−0.629443 + 0.777047i \(0.716717\pi\)
\(570\) 0 0
\(571\) 447.910 775.803i 0.784431 1.35867i −0.144908 0.989445i \(-0.546289\pi\)
0.929339 0.369229i \(-0.120378\pi\)
\(572\) −2.22322 3.85072i −0.00388674 0.00673203i
\(573\) 113.850 0.198691
\(574\) 9.66974 + 39.1519i 0.0168462 + 0.0682088i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 340.703 590.115i 0.590473 1.02273i −0.403695 0.914893i \(-0.632274\pi\)
0.994169 0.107836i \(-0.0343922\pi\)
\(578\) 1008.29 + 582.134i 1.74444 + 1.00715i
\(579\) 145.305 83.8919i 0.250959 0.144891i
\(580\) 0 0
\(581\) 83.9476 + 24.2726i 0.144488 + 0.0417773i
\(582\) 365.662i 0.628286i
\(583\) 21.2097 12.2454i 0.0363802 0.0210041i
\(584\) −40.9872 23.6640i −0.0701835 0.0405205i
\(585\) 0 0
\(586\) −180.662 + 104.305i −0.308297 + 0.177996i
\(587\) 833.001 1.41908 0.709541 0.704665i \(-0.248903\pi\)
0.709541 + 0.704665i \(0.248903\pi\)
\(588\) 6.67408 169.610i 0.0113505 0.288452i
\(589\) 6.00955 0.0102030
\(590\) 0 0
\(591\) −280.008 161.663i −0.473787 0.273541i
\(592\) −33.7876 19.5073i −0.0570736 0.0329515i
\(593\) 156.371 + 270.842i 0.263694 + 0.456731i 0.967221 0.253938i \(-0.0817258\pi\)
−0.703527 + 0.710669i \(0.748392\pi\)
\(594\) 3.86857i 0.00651274i
\(595\) 0 0
\(596\) 288.161 0.483491
\(597\) −172.937 + 99.8454i −0.289677 + 0.167245i
\(598\) −33.0242 + 57.1996i −0.0552244 + 0.0956514i
\(599\) 107.121 185.540i 0.178834 0.309749i −0.762648 0.646814i \(-0.776101\pi\)
0.941481 + 0.337065i \(0.109434\pi\)
\(600\) 0 0
\(601\) 176.849i 0.294257i −0.989117 0.147129i \(-0.952997\pi\)
0.989117 0.147129i \(-0.0470031\pi\)
\(602\) 110.023 + 445.474i 0.182763 + 0.739991i
\(603\) 26.2169i 0.0434774i
\(604\) 93.5125 + 161.968i 0.154822 + 0.268160i
\(605\) 0 0
\(606\) −118.488 + 205.228i −0.195525 + 0.338660i
\(607\) −18.5505 32.1304i −0.0305609 0.0529331i 0.850340 0.526233i \(-0.176396\pi\)
−0.880901 + 0.473300i \(0.843063\pi\)
\(608\) −17.9716 −0.0295586
\(609\) −490.586 + 471.661i −0.805559 + 0.774484i
\(610\) 0 0
\(611\) −133.605 231.411i −0.218666 0.378741i
\(612\) 100.052 173.295i 0.163483 0.283161i
\(613\) 779.180 + 449.860i 1.27109 + 0.733866i 0.975194 0.221353i \(-0.0710475\pi\)
0.295899 + 0.955219i \(0.404381\pi\)
\(614\) 460.516 265.879i 0.750027 0.433028i
\(615\) 0 0
\(616\) −7.22389 7.51374i −0.0117271 0.0121976i
\(617\) 626.244i 1.01498i 0.861657 + 0.507491i \(0.169427\pi\)
−0.861657 + 0.507491i \(0.830573\pi\)
\(618\) −222.234 + 128.307i −0.359602 + 0.207617i
\(619\) 776.375 + 448.240i 1.25424 + 0.724136i 0.971949 0.235193i \(-0.0755722\pi\)
0.282291 + 0.959329i \(0.408906\pi\)
\(620\) 0 0
\(621\) −49.7658 + 28.7323i −0.0801382 + 0.0462678i
\(622\) 551.298 0.886331
\(623\) −463.843 + 114.560i −0.744532 + 0.183885i
\(624\) −29.2583 −0.0468883
\(625\) 0 0
\(626\) 175.207 + 101.156i 0.279884 + 0.161591i
\(627\) 2.50875 + 1.44843i 0.00400120 + 0.00231009i
\(628\) 171.225 + 296.571i 0.272652 + 0.472247i
\(629\) 325.290i 0.517153i
\(630\) 0 0
\(631\) −500.730 −0.793550 −0.396775 0.917916i \(-0.629871\pi\)
−0.396775 + 0.917916i \(0.629871\pi\)
\(632\) 324.054 187.093i 0.512744 0.296033i
\(633\) 120.752 209.149i 0.190762 0.330409i
\(634\) 271.843 470.846i 0.428774 0.742659i
\(635\) 0 0
\(636\) 161.154i 0.253387i
\(637\) 175.000 + 110.431i 0.274726 + 0.173362i
\(638\) 41.7893i 0.0655005i
\(639\) −43.5912 75.5021i −0.0682178 0.118157i
\(640\) 0 0
\(641\) −310.289 + 537.436i −0.484070 + 0.838434i −0.999833 0.0182978i \(-0.994175\pi\)
0.515763 + 0.856732i \(0.327509\pi\)
\(642\) 152.609 + 264.326i 0.237708 + 0.411722i
\(643\) 1127.93 1.75417 0.877086 0.480334i \(-0.159484\pi\)
0.877086 + 0.480334i \(0.159484\pi\)
\(644\) −43.0051 + 148.735i −0.0667782 + 0.230954i
\(645\) 0 0
\(646\) 74.9206 + 129.766i 0.115976 + 0.200877i
\(647\) −67.6248 + 117.130i −0.104521 + 0.181035i −0.913542 0.406744i \(-0.866664\pi\)
0.809022 + 0.587779i \(0.199997\pi\)
\(648\) −22.0454 12.7279i −0.0340207 0.0196419i
\(649\) 23.0380 13.3010i 0.0354977 0.0204946i
\(650\) 0 0
\(651\) 22.2654 5.49912i 0.0342018 0.00844719i
\(652\) 186.026i 0.285316i
\(653\) −338.001 + 195.145i −0.517612 + 0.298843i −0.735957 0.677028i \(-0.763267\pi\)
0.218345 + 0.975872i \(0.429934\pi\)
\(654\) 179.482 + 103.624i 0.274437 + 0.158446i
\(655\) 0 0
\(656\) 14.1120 8.14755i 0.0215121 0.0124200i
\(657\) 50.1988 0.0764061
\(658\) −434.123 451.542i −0.659761 0.686233i
\(659\) 864.853 1.31237 0.656186 0.754599i \(-0.272169\pi\)
0.656186 + 0.754599i \(0.272169\pi\)
\(660\) 0 0
\(661\) −873.134 504.104i −1.32093 0.762638i −0.337052 0.941486i \(-0.609430\pi\)
−0.983877 + 0.178848i \(0.942763\pi\)
\(662\) 237.487 + 137.113i 0.358742 + 0.207120i
\(663\) 121.973 + 211.263i 0.183971 + 0.318647i
\(664\) 35.3094i 0.0531768i
\(665\) 0 0
\(666\) 41.3812 0.0621339
\(667\) 537.584 310.374i 0.805973 0.465328i
\(668\) 104.991 181.849i 0.157172 0.272230i
\(669\) 223.482 387.083i 0.334054 0.578599i
\(670\) 0 0
\(671\) 54.3806i 0.0810441i
\(672\) −66.5850 + 16.4452i −0.0990848 + 0.0244720i
\(673\) 109.959i 0.163386i −0.996658 0.0816928i \(-0.973967\pi\)
0.996658 0.0816928i \(-0.0260327\pi\)
\(674\) 88.7259 + 153.678i 0.131641 + 0.228009i
\(675\) 0 0
\(676\) −151.166 + 261.827i −0.223618 + 0.387318i
\(677\) −84.4163 146.213i −0.124692 0.215972i 0.796921 0.604084i \(-0.206461\pi\)
−0.921612 + 0.388112i \(0.873128\pi\)
\(678\) 284.731 0.419957
\(679\) 1003.85 + 290.253i 1.47842 + 0.427471i
\(680\) 0 0
\(681\) −286.682 496.548i −0.420973 0.729146i
\(682\) 0.704155 1.21963i 0.00103248 0.00178832i
\(683\) 377.700 + 218.065i 0.553002 + 0.319276i 0.750332 0.661061i \(-0.229894\pi\)
−0.197330 + 0.980337i \(0.563227\pi\)
\(684\) 16.5080 9.53090i 0.0241345 0.0139341i
\(685\) 0 0
\(686\) 460.329 + 152.954i 0.671034 + 0.222965i
\(687\) 423.033i 0.615768i
\(688\) 160.568 92.7038i 0.233383 0.134744i
\(689\) 170.141 + 98.2309i 0.246939 + 0.142570i
\(690\) 0 0
\(691\) −59.2770 + 34.2236i −0.0857843 + 0.0495276i −0.542279 0.840199i \(-0.682438\pi\)
0.456494 + 0.889726i \(0.349105\pi\)
\(692\) 408.314 0.590049
\(693\) 10.6203 + 3.07076i 0.0153251 + 0.00443112i
\(694\) 712.193 1.02622
\(695\) 0 0
\(696\) 238.140 + 137.490i 0.342156 + 0.197544i
\(697\) −117.661 67.9314i −0.168810 0.0974625i
\(698\) 33.7772 + 58.5039i 0.0483914 + 0.0838164i
\(699\) 366.311i 0.524050i
\(700\) 0 0
\(701\) 1283.41 1.83083 0.915414 0.402514i \(-0.131864\pi\)
0.915414 + 0.402514i \(0.131864\pi\)
\(702\) 26.8754 15.5165i 0.0382841 0.0221033i
\(703\) −15.4935 + 26.8355i −0.0220391 + 0.0381728i
\(704\) −2.10578 + 3.64732i −0.00299117 + 0.00518086i
\(705\) 0 0
\(706\) 46.5422i 0.0659238i
\(707\) −469.356 488.188i −0.663870 0.690507i
\(708\) 175.046i 0.247240i
\(709\) 86.2000 + 149.303i 0.121580 + 0.210582i 0.920391 0.391000i \(-0.127871\pi\)
−0.798811 + 0.601582i \(0.794537\pi\)
\(710\) 0 0
\(711\) −198.442 + 343.712i −0.279103 + 0.483420i
\(712\) 96.5264 + 167.189i 0.135571 + 0.234815i
\(713\) −20.9194 −0.0293399
\(714\) 396.325 + 412.227i 0.555077 + 0.577349i
\(715\) 0 0
\(716\) 195.899 + 339.307i 0.273602 + 0.473892i
\(717\) −298.029 + 516.201i −0.415661 + 0.719946i
\(718\) −327.983 189.361i −0.456801 0.263734i
\(719\) 435.015 251.156i 0.605028 0.349313i −0.165989 0.986128i \(-0.553082\pi\)
0.771017 + 0.636815i \(0.219748\pi\)
\(720\) 0 0
\(721\) −175.836 711.943i −0.243878 0.987439i
\(722\) 496.257i 0.687337i
\(723\) −257.023 + 148.392i −0.355495 + 0.205245i
\(724\) 206.168 + 119.031i 0.284763 + 0.164408i
\(725\) 0 0
\(726\) −256.092 + 147.855i −0.352744 + 0.203657i
\(727\) −748.693 −1.02984 −0.514920 0.857238i \(-0.672178\pi\)
−0.514920 + 0.857238i \(0.672178\pi\)
\(728\) 23.2244 80.3223i 0.0319017 0.110333i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −1338.76 772.931i −1.83140 1.05736i
\(732\) −309.893 178.917i −0.423351 0.244422i
\(733\) −469.248 812.761i −0.640175 1.10881i −0.985394 0.170293i \(-0.945529\pi\)
0.345219 0.938522i \(-0.387805\pi\)
\(734\) 224.468i 0.305814i
\(735\) 0 0
\(736\) 62.5596 0.0849994
\(737\) 3.98422 2.30029i 0.00540600 0.00312116i
\(738\) −8.64178 + 14.9680i −0.0117097 + 0.0202818i
\(739\) 106.820 185.018i 0.144547 0.250363i −0.784657 0.619931i \(-0.787161\pi\)
0.929204 + 0.369567i \(0.120494\pi\)
\(740\) 0 0
\(741\) 23.2381i 0.0313605i
\(742\) 442.413 + 127.919i 0.596244 + 0.172398i
\(743\) 544.013i 0.732184i 0.930579 + 0.366092i \(0.119304\pi\)
−0.930579 + 0.366092i \(0.880696\pi\)
\(744\) −4.63346 8.02538i −0.00622776 0.0107868i
\(745\) 0 0
\(746\) −292.985 + 507.465i −0.392742 + 0.680249i
\(747\) 18.7256 + 32.4337i 0.0250678 + 0.0434187i
\(748\) 35.1146 0.0469446
\(749\) −846.786 + 209.140i −1.13056 + 0.279225i
\(750\) 0 0
\(751\) −294.705 510.443i −0.392416 0.679685i 0.600351 0.799736i \(-0.295027\pi\)
−0.992768 + 0.120051i \(0.961694\pi\)
\(752\) −126.548 + 219.187i −0.168282 + 0.291473i
\(753\) 491.307 + 283.656i 0.652467 + 0.376702i
\(754\) −290.316 + 167.614i −0.385034 + 0.222299i
\(755\) 0 0
\(756\) 52.4408 50.4179i 0.0693662 0.0666903i
\(757\) 448.997i 0.593127i 0.955013 + 0.296564i \(0.0958406\pi\)
−0.955013 + 0.296564i \(0.904159\pi\)
\(758\) −89.1614 + 51.4774i −0.117627 + 0.0679121i
\(759\) −8.73300 5.04200i −0.0115059 0.00664295i
\(760\) 0 0
\(761\) 371.914 214.725i 0.488718 0.282161i −0.235325 0.971917i \(-0.575615\pi\)
0.724042 + 0.689756i \(0.242282\pi\)
\(762\) −199.326 −0.261582
\(763\) −426.944 + 410.475i −0.559560 + 0.537975i
\(764\) 131.463 0.172072
\(765\) 0 0
\(766\) 349.070 + 201.536i 0.455705 + 0.263101i
\(767\) 184.807 + 106.699i 0.240948 + 0.139112i
\(768\) 13.8564 + 24.0000i 0.0180422 + 0.0312500i
\(769\) 32.5790i 0.0423655i −0.999776 0.0211827i \(-0.993257\pi\)
0.999776 0.0211827i \(-0.00674318\pi\)
\(770\) 0 0
\(771\) 381.672 0.495035
\(772\) 167.784 96.8700i 0.217337 0.125479i
\(773\) −621.768 + 1076.93i −0.804357 + 1.39319i 0.112367 + 0.993667i \(0.464157\pi\)
−0.916724 + 0.399520i \(0.869177\pi\)
\(774\) −98.3272 + 170.308i −0.127038 + 0.220036i
\(775\) 0 0
\(776\) 422.231i 0.544112i
\(777\) −32.8472 + 113.603i −0.0422744 + 0.146207i
\(778\) 137.374i 0.176574i
\(779\) −6.47112 11.2083i −0.00830696 0.0143881i
\(780\) 0 0
\(781\) 7.64946 13.2493i 0.00979444 0.0169645i
\(782\) −260.800 451.719i −0.333504 0.577645i
\(783\) −291.661