Properties

Label 98.4.c.f.79.1
Level $98$
Weight $4$
Character 98.79
Analytic conductor $5.782$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.78218718056\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 98.79
Dual form 98.4.c.f.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(4.00000 + 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-7.00000 + 12.1244i) q^{5} +16.0000 q^{6} -8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(4.00000 + 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-7.00000 + 12.1244i) q^{5} +16.0000 q^{6} -8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +(14.0000 + 24.2487i) q^{10} +(14.0000 + 24.2487i) q^{11} +(16.0000 - 27.7128i) q^{12} -18.0000 q^{13} -112.000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(37.0000 + 64.0859i) q^{17} +(37.0000 + 64.0859i) q^{18} +(40.0000 - 69.2820i) q^{19} +56.0000 q^{20} +56.0000 q^{22} +(56.0000 - 96.9948i) q^{23} +(-32.0000 - 55.4256i) q^{24} +(-35.5000 - 61.4878i) q^{25} +(-18.0000 + 31.1769i) q^{26} -80.0000 q^{27} +190.000 q^{29} +(-112.000 + 193.990i) q^{30} +(36.0000 + 62.3538i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-112.000 + 193.990i) q^{33} +148.000 q^{34} +148.000 q^{36} +(173.000 - 299.645i) q^{37} +(-80.0000 - 138.564i) q^{38} +(-72.0000 - 124.708i) q^{39} +(56.0000 - 96.9948i) q^{40} -162.000 q^{41} -412.000 q^{43} +(56.0000 - 96.9948i) q^{44} +(-259.000 - 448.601i) q^{45} +(-112.000 - 193.990i) q^{46} +(12.0000 - 20.7846i) q^{47} -128.000 q^{48} -142.000 q^{50} +(-296.000 + 512.687i) q^{51} +(36.0000 + 62.3538i) q^{52} +(-159.000 - 275.396i) q^{53} +(-80.0000 + 138.564i) q^{54} -392.000 q^{55} +640.000 q^{57} +(190.000 - 329.090i) q^{58} +(-100.000 - 173.205i) q^{59} +(224.000 + 387.979i) q^{60} +(-99.0000 + 171.473i) q^{61} +144.000 q^{62} +64.0000 q^{64} +(126.000 - 218.238i) q^{65} +(224.000 + 387.979i) q^{66} +(358.000 + 620.074i) q^{67} +(148.000 - 256.344i) q^{68} +896.000 q^{69} +392.000 q^{71} +(148.000 - 256.344i) q^{72} +(269.000 + 465.922i) q^{73} +(-346.000 - 599.290i) q^{74} +(284.000 - 491.902i) q^{75} -320.000 q^{76} -288.000 q^{78} +(-120.000 + 207.846i) q^{79} +(-112.000 - 193.990i) q^{80} +(179.500 + 310.903i) q^{81} +(-162.000 + 280.592i) q^{82} +1072.00 q^{83} -1036.00 q^{85} +(-412.000 + 713.605i) q^{86} +(760.000 + 1316.36i) q^{87} +(-112.000 - 193.990i) q^{88} +(405.000 - 701.481i) q^{89} -1036.00 q^{90} -448.000 q^{92} +(-288.000 + 498.831i) q^{93} +(-24.0000 - 41.5692i) q^{94} +(560.000 + 969.948i) q^{95} +(-128.000 + 221.703i) q^{96} -1354.00 q^{97} -1036.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 8 q^{3} - 4 q^{4} - 14 q^{5} + 32 q^{6} - 16 q^{8} - 37 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 8 q^{3} - 4 q^{4} - 14 q^{5} + 32 q^{6} - 16 q^{8} - 37 q^{9} + 28 q^{10} + 28 q^{11} + 32 q^{12} - 36 q^{13} - 224 q^{15} - 16 q^{16} + 74 q^{17} + 74 q^{18} + 80 q^{19} + 112 q^{20} + 112 q^{22} + 112 q^{23} - 64 q^{24} - 71 q^{25} - 36 q^{26} - 160 q^{27} + 380 q^{29} - 224 q^{30} + 72 q^{31} + 32 q^{32} - 224 q^{33} + 296 q^{34} + 296 q^{36} + 346 q^{37} - 160 q^{38} - 144 q^{39} + 112 q^{40} - 324 q^{41} - 824 q^{43} + 112 q^{44} - 518 q^{45} - 224 q^{46} + 24 q^{47} - 256 q^{48} - 284 q^{50} - 592 q^{51} + 72 q^{52} - 318 q^{53} - 160 q^{54} - 784 q^{55} + 1280 q^{57} + 380 q^{58} - 200 q^{59} + 448 q^{60} - 198 q^{61} + 288 q^{62} + 128 q^{64} + 252 q^{65} + 448 q^{66} + 716 q^{67} + 296 q^{68} + 1792 q^{69} + 784 q^{71} + 296 q^{72} + 538 q^{73} - 692 q^{74} + 568 q^{75} - 640 q^{76} - 576 q^{78} - 240 q^{79} - 224 q^{80} + 359 q^{81} - 324 q^{82} + 2144 q^{83} - 2072 q^{85} - 824 q^{86} + 1520 q^{87} - 224 q^{88} + 810 q^{89} - 2072 q^{90} - 896 q^{92} - 576 q^{93} - 48 q^{94} + 1120 q^{95} - 256 q^{96} - 2708 q^{97} - 2072 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 4.00000 + 6.92820i 0.769800 + 1.33333i 0.937671 + 0.347524i \(0.112978\pi\)
−0.167871 + 0.985809i \(0.553689\pi\)
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −7.00000 + 12.1244i −0.626099 + 1.08444i 0.362228 + 0.932089i \(0.382016\pi\)
−0.988327 + 0.152346i \(0.951317\pi\)
\(6\) 16.0000 1.08866
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) −18.5000 + 32.0429i −0.685185 + 1.18678i
\(10\) 14.0000 + 24.2487i 0.442719 + 0.766812i
\(11\) 14.0000 + 24.2487i 0.383742 + 0.664660i 0.991594 0.129390i \(-0.0413020\pi\)
−0.607852 + 0.794050i \(0.707969\pi\)
\(12\) 16.0000 27.7128i 0.384900 0.666667i
\(13\) −18.0000 −0.384023 −0.192012 0.981393i \(-0.561501\pi\)
−0.192012 + 0.981393i \(0.561501\pi\)
\(14\) 0 0
\(15\) −112.000 −1.92789
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 37.0000 + 64.0859i 0.527872 + 0.914301i 0.999472 + 0.0324882i \(0.0103431\pi\)
−0.471600 + 0.881812i \(0.656324\pi\)
\(18\) 37.0000 + 64.0859i 0.484499 + 0.839177i
\(19\) 40.0000 69.2820i 0.482980 0.836547i −0.516829 0.856089i \(-0.672888\pi\)
0.999809 + 0.0195422i \(0.00622087\pi\)
\(20\) 56.0000 0.626099
\(21\) 0 0
\(22\) 56.0000 0.542693
\(23\) 56.0000 96.9948i 0.507687 0.879340i −0.492273 0.870441i \(-0.663834\pi\)
0.999960 0.00889936i \(-0.00283279\pi\)
\(24\) −32.0000 55.4256i −0.272166 0.471405i
\(25\) −35.5000 61.4878i −0.284000 0.491902i
\(26\) −18.0000 + 31.1769i −0.135773 + 0.235165i
\(27\) −80.0000 −0.570222
\(28\) 0 0
\(29\) 190.000 1.21662 0.608312 0.793698i \(-0.291847\pi\)
0.608312 + 0.793698i \(0.291847\pi\)
\(30\) −112.000 + 193.990i −0.681610 + 1.18058i
\(31\) 36.0000 + 62.3538i 0.208574 + 0.361261i 0.951266 0.308373i \(-0.0997845\pi\)
−0.742692 + 0.669634i \(0.766451\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) −112.000 + 193.990i −0.590809 + 1.02331i
\(34\) 148.000 0.746523
\(35\) 0 0
\(36\) 148.000 0.685185
\(37\) 173.000 299.645i 0.768676 1.33139i −0.169605 0.985512i \(-0.554249\pi\)
0.938281 0.345874i \(-0.112418\pi\)
\(38\) −80.0000 138.564i −0.341519 0.591528i
\(39\) −72.0000 124.708i −0.295621 0.512031i
\(40\) 56.0000 96.9948i 0.221359 0.383406i
\(41\) −162.000 −0.617077 −0.308538 0.951212i \(-0.599840\pi\)
−0.308538 + 0.951212i \(0.599840\pi\)
\(42\) 0 0
\(43\) −412.000 −1.46115 −0.730575 0.682833i \(-0.760748\pi\)
−0.730575 + 0.682833i \(0.760748\pi\)
\(44\) 56.0000 96.9948i 0.191871 0.332330i
\(45\) −259.000 448.601i −0.857988 1.48608i
\(46\) −112.000 193.990i −0.358989 0.621787i
\(47\) 12.0000 20.7846i 0.0372421 0.0645053i −0.846804 0.531906i \(-0.821476\pi\)
0.884046 + 0.467401i \(0.154809\pi\)
\(48\) −128.000 −0.384900
\(49\) 0 0
\(50\) −142.000 −0.401637
\(51\) −296.000 + 512.687i −0.812712 + 1.40766i
\(52\) 36.0000 + 62.3538i 0.0960058 + 0.166287i
\(53\) −159.000 275.396i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) −80.0000 + 138.564i −0.201604 + 0.349189i
\(55\) −392.000 −0.961041
\(56\) 0 0
\(57\) 640.000 1.48719
\(58\) 190.000 329.090i 0.430142 0.745027i
\(59\) −100.000 173.205i −0.220659 0.382193i 0.734349 0.678772i \(-0.237488\pi\)
−0.955008 + 0.296579i \(0.904154\pi\)
\(60\) 224.000 + 387.979i 0.481971 + 0.834799i
\(61\) −99.0000 + 171.473i −0.207798 + 0.359916i −0.951020 0.309128i \(-0.899963\pi\)
0.743223 + 0.669044i \(0.233296\pi\)
\(62\) 144.000 0.294968
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 126.000 218.238i 0.240437 0.416448i
\(66\) 224.000 + 387.979i 0.417765 + 0.723590i
\(67\) 358.000 + 620.074i 0.652786 + 1.13066i 0.982444 + 0.186558i \(0.0597332\pi\)
−0.329658 + 0.944100i \(0.606933\pi\)
\(68\) 148.000 256.344i 0.263936 0.457150i
\(69\) 896.000 1.56327
\(70\) 0 0
\(71\) 392.000 0.655237 0.327619 0.944810i \(-0.393754\pi\)
0.327619 + 0.944810i \(0.393754\pi\)
\(72\) 148.000 256.344i 0.242250 0.419589i
\(73\) 269.000 + 465.922i 0.431289 + 0.747014i 0.996985 0.0776001i \(-0.0247257\pi\)
−0.565696 + 0.824614i \(0.691392\pi\)
\(74\) −346.000 599.290i −0.543536 0.941432i
\(75\) 284.000 491.902i 0.437247 0.757333i
\(76\) −320.000 −0.482980
\(77\) 0 0
\(78\) −288.000 −0.418072
\(79\) −120.000 + 207.846i −0.170899 + 0.296006i −0.938735 0.344641i \(-0.888001\pi\)
0.767835 + 0.640647i \(0.221334\pi\)
\(80\) −112.000 193.990i −0.156525 0.271109i
\(81\) 179.500 + 310.903i 0.246228 + 0.426479i
\(82\) −162.000 + 280.592i −0.218170 + 0.377881i
\(83\) 1072.00 1.41768 0.708839 0.705370i \(-0.249219\pi\)
0.708839 + 0.705370i \(0.249219\pi\)
\(84\) 0 0
\(85\) −1036.00 −1.32200
\(86\) −412.000 + 713.605i −0.516594 + 0.894767i
\(87\) 760.000 + 1316.36i 0.936558 + 1.62217i
\(88\) −112.000 193.990i −0.135673 0.234993i
\(89\) 405.000 701.481i 0.482359 0.835470i −0.517436 0.855722i \(-0.673114\pi\)
0.999795 + 0.0202521i \(0.00644690\pi\)
\(90\) −1036.00 −1.21338
\(91\) 0 0
\(92\) −448.000 −0.507687
\(93\) −288.000 + 498.831i −0.321121 + 0.556197i
\(94\) −24.0000 41.5692i −0.0263342 0.0456121i
\(95\) 560.000 + 969.948i 0.604787 + 1.04752i
\(96\) −128.000 + 221.703i −0.136083 + 0.235702i
\(97\) −1354.00 −1.41730 −0.708649 0.705561i \(-0.750695\pi\)
−0.708649 + 0.705561i \(0.750695\pi\)
\(98\) 0 0
\(99\) −1036.00 −1.05174
\(100\) −142.000 + 245.951i −0.142000 + 0.245951i
\(101\) −679.000 1176.06i −0.668941 1.15864i −0.978201 0.207662i \(-0.933415\pi\)
0.309260 0.950978i \(-0.399919\pi\)
\(102\) 592.000 + 1025.37i 0.574674 + 0.995364i
\(103\) −416.000 + 720.533i −0.397958 + 0.689284i −0.993474 0.114060i \(-0.963614\pi\)
0.595516 + 0.803344i \(0.296948\pi\)
\(104\) 144.000 0.135773
\(105\) 0 0
\(106\) −636.000 −0.582772
\(107\) −222.000 + 384.515i −0.200575 + 0.347406i −0.948714 0.316136i \(-0.897614\pi\)
0.748139 + 0.663542i \(0.230948\pi\)
\(108\) 160.000 + 277.128i 0.142556 + 0.246914i
\(109\) −935.000 1619.47i −0.821622 1.42309i −0.904474 0.426529i \(-0.859736\pi\)
0.0828525 0.996562i \(-0.473597\pi\)
\(110\) −392.000 + 678.964i −0.339779 + 0.588515i
\(111\) 2768.00 2.36691
\(112\) 0 0
\(113\) 1378.00 1.14718 0.573590 0.819143i \(-0.305550\pi\)
0.573590 + 0.819143i \(0.305550\pi\)
\(114\) 640.000 1108.51i 0.525803 0.910717i
\(115\) 784.000 + 1357.93i 0.635725 + 1.10111i
\(116\) −380.000 658.179i −0.304156 0.526814i
\(117\) 333.000 576.773i 0.263127 0.455749i
\(118\) −400.000 −0.312059
\(119\) 0 0
\(120\) 896.000 0.681610
\(121\) 273.500 473.716i 0.205485 0.355910i
\(122\) 198.000 + 342.946i 0.146935 + 0.254499i
\(123\) −648.000 1122.37i −0.475026 0.822769i
\(124\) 144.000 249.415i 0.104287 0.180630i
\(125\) −756.000 −0.540950
\(126\) 0 0
\(127\) 1944.00 1.35828 0.679142 0.734007i \(-0.262352\pi\)
0.679142 + 0.734007i \(0.262352\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) −1648.00 2854.42i −1.12479 1.94820i
\(130\) −252.000 436.477i −0.170014 0.294473i
\(131\) −424.000 + 734.390i −0.282787 + 0.489801i −0.972070 0.234691i \(-0.924592\pi\)
0.689283 + 0.724492i \(0.257926\pi\)
\(132\) 896.000 0.590809
\(133\) 0 0
\(134\) 1432.00 0.923179
\(135\) 560.000 969.948i 0.357016 0.618369i
\(136\) −296.000 512.687i −0.186631 0.323254i
\(137\) 1483.00 + 2568.63i 0.924827 + 1.60185i 0.791840 + 0.610729i \(0.209123\pi\)
0.132987 + 0.991118i \(0.457543\pi\)
\(138\) 896.000 1551.92i 0.552700 0.957304i
\(139\) −2800.00 −1.70858 −0.854291 0.519795i \(-0.826008\pi\)
−0.854291 + 0.519795i \(0.826008\pi\)
\(140\) 0 0
\(141\) 192.000 0.114676
\(142\) 392.000 678.964i 0.231661 0.401249i
\(143\) −252.000 436.477i −0.147366 0.255245i
\(144\) −296.000 512.687i −0.171296 0.296694i
\(145\) −1330.00 + 2303.63i −0.761728 + 1.31935i
\(146\) 1076.00 0.609934
\(147\) 0 0
\(148\) −1384.00 −0.768676
\(149\) −255.000 + 441.673i −0.140204 + 0.242841i −0.927573 0.373641i \(-0.878109\pi\)
0.787369 + 0.616482i \(0.211443\pi\)
\(150\) −568.000 983.805i −0.309180 0.535516i
\(151\) −296.000 512.687i −0.159524 0.276304i 0.775173 0.631749i \(-0.217663\pi\)
−0.934697 + 0.355445i \(0.884329\pi\)
\(152\) −320.000 + 554.256i −0.170759 + 0.295764i
\(153\) −2738.00 −1.44676
\(154\) 0 0
\(155\) −1008.00 −0.522352
\(156\) −288.000 + 498.831i −0.147811 + 0.256015i
\(157\) −1343.00 2326.14i −0.682695 1.18246i −0.974155 0.225879i \(-0.927475\pi\)
0.291461 0.956583i \(-0.405859\pi\)
\(158\) 240.000 + 415.692i 0.120844 + 0.209308i
\(159\) 1272.00 2203.17i 0.634441 1.09888i
\(160\) −448.000 −0.221359
\(161\) 0 0
\(162\) 718.000 0.348219
\(163\) 506.000 876.418i 0.243147 0.421143i −0.718462 0.695566i \(-0.755154\pi\)
0.961609 + 0.274423i \(0.0884869\pi\)
\(164\) 324.000 + 561.184i 0.154269 + 0.267202i
\(165\) −1568.00 2715.86i −0.739810 1.28139i
\(166\) 1072.00 1856.76i 0.501225 0.868147i
\(167\) −544.000 −0.252072 −0.126036 0.992026i \(-0.540225\pi\)
−0.126036 + 0.992026i \(0.540225\pi\)
\(168\) 0 0
\(169\) −1873.00 −0.852526
\(170\) −1036.00 + 1794.40i −0.467397 + 0.809556i
\(171\) 1480.00 + 2563.44i 0.661862 + 1.14638i
\(172\) 824.000 + 1427.21i 0.365287 + 0.632696i
\(173\) 929.000 1609.08i 0.408269 0.707143i −0.586427 0.810002i \(-0.699466\pi\)
0.994696 + 0.102859i \(0.0327992\pi\)
\(174\) 3040.00 1.32449
\(175\) 0 0
\(176\) −448.000 −0.191871
\(177\) 800.000 1385.64i 0.339727 0.588424i
\(178\) −810.000 1402.96i −0.341079 0.590766i
\(179\) 150.000 + 259.808i 0.0626342 + 0.108486i 0.895642 0.444775i \(-0.146717\pi\)
−0.833008 + 0.553261i \(0.813383\pi\)
\(180\) −1036.00 + 1794.40i −0.428994 + 0.743039i
\(181\) 2358.00 0.968336 0.484168 0.874975i \(-0.339122\pi\)
0.484168 + 0.874975i \(0.339122\pi\)
\(182\) 0 0
\(183\) −1584.00 −0.639851
\(184\) −448.000 + 775.959i −0.179495 + 0.310894i
\(185\) 2422.00 + 4195.03i 0.962535 + 1.66716i
\(186\) 576.000 + 997.661i 0.227067 + 0.393291i
\(187\) −1036.00 + 1794.40i −0.405133 + 0.701710i
\(188\) −96.0000 −0.0372421
\(189\) 0 0
\(190\) 2240.00 0.855298
\(191\) −696.000 + 1205.51i −0.263669 + 0.456688i −0.967214 0.253962i \(-0.918266\pi\)
0.703545 + 0.710651i \(0.251599\pi\)
\(192\) 256.000 + 443.405i 0.0962250 + 0.166667i
\(193\) −889.000 1539.79i −0.331563 0.574284i 0.651256 0.758858i \(-0.274243\pi\)
−0.982818 + 0.184575i \(0.940909\pi\)
\(194\) −1354.00 + 2345.20i −0.501090 + 0.867914i
\(195\) 2016.00 0.740353
\(196\) 0 0
\(197\) 1214.00 0.439055 0.219528 0.975606i \(-0.429548\pi\)
0.219528 + 0.975606i \(0.429548\pi\)
\(198\) −1036.00 + 1794.40i −0.371845 + 0.644054i
\(199\) 520.000 + 900.666i 0.185235 + 0.320837i 0.943656 0.330929i \(-0.107362\pi\)
−0.758420 + 0.651766i \(0.774029\pi\)
\(200\) 284.000 + 491.902i 0.100409 + 0.173914i
\(201\) −2864.00 + 4960.59i −1.00503 + 1.74076i
\(202\) −2716.00 −0.946025
\(203\) 0 0
\(204\) 2368.00 0.812712
\(205\) 1134.00 1964.15i 0.386351 0.669180i
\(206\) 832.000 + 1441.07i 0.281399 + 0.487397i
\(207\) 2072.00 + 3588.81i 0.695720 + 1.20502i
\(208\) 144.000 249.415i 0.0480029 0.0831435i
\(209\) 2240.00 0.741359
\(210\) 0 0
\(211\) −3868.00 −1.26201 −0.631005 0.775779i \(-0.717357\pi\)
−0.631005 + 0.775779i \(0.717357\pi\)
\(212\) −636.000 + 1101.58i −0.206041 + 0.356873i
\(213\) 1568.00 + 2715.86i 0.504402 + 0.873650i
\(214\) 444.000 + 769.031i 0.141828 + 0.245653i
\(215\) 2884.00 4995.23i 0.914824 1.58452i
\(216\) 640.000 0.201604
\(217\) 0 0
\(218\) −3740.00 −1.16195
\(219\) −2152.00 + 3727.37i −0.664012 + 1.15010i
\(220\) 784.000 + 1357.93i 0.240260 + 0.416143i
\(221\) −666.000 1153.55i −0.202715 0.351113i
\(222\) 2768.00 4794.32i 0.836829 1.44943i
\(223\) −3968.00 −1.19156 −0.595778 0.803149i \(-0.703156\pi\)
−0.595778 + 0.803149i \(0.703156\pi\)
\(224\) 0 0
\(225\) 2627.00 0.778370
\(226\) 1378.00 2386.77i 0.405589 0.702501i
\(227\) −1968.00 3408.68i −0.575422 0.996660i −0.995996 0.0894015i \(-0.971505\pi\)
0.420574 0.907258i \(-0.361829\pi\)
\(228\) −1280.00 2217.03i −0.371799 0.643974i
\(229\) 2405.00 4165.58i 0.694004 1.20205i −0.276512 0.961011i \(-0.589178\pi\)
0.970515 0.241039i \(-0.0774883\pi\)
\(230\) 3136.00 0.899051
\(231\) 0 0
\(232\) −1520.00 −0.430142
\(233\) 1091.00 1889.67i 0.306754 0.531314i −0.670896 0.741551i \(-0.734090\pi\)
0.977650 + 0.210237i \(0.0674236\pi\)
\(234\) −666.000 1153.55i −0.186059 0.322263i
\(235\) 168.000 + 290.985i 0.0466345 + 0.0807734i
\(236\) −400.000 + 692.820i −0.110330 + 0.191096i
\(237\) −1920.00 −0.526234
\(238\) 0 0
\(239\) −3000.00 −0.811941 −0.405970 0.913886i \(-0.633066\pi\)
−0.405970 + 0.913886i \(0.633066\pi\)
\(240\) 896.000 1551.92i 0.240986 0.417399i
\(241\) 1021.00 + 1768.42i 0.272898 + 0.472673i 0.969603 0.244685i \(-0.0786845\pi\)
−0.696705 + 0.717358i \(0.745351\pi\)
\(242\) −547.000 947.432i −0.145300 0.251666i
\(243\) −2516.00 + 4357.84i −0.664204 + 1.15043i
\(244\) 792.000 0.207798
\(245\) 0 0
\(246\) −2592.00 −0.671788
\(247\) −720.000 + 1247.08i −0.185476 + 0.321253i
\(248\) −288.000 498.831i −0.0737420 0.127725i
\(249\) 4288.00 + 7427.03i 1.09133 + 1.89024i
\(250\) −756.000 + 1309.43i −0.191255 + 0.331263i
\(251\) 528.000 0.132777 0.0663886 0.997794i \(-0.478852\pi\)
0.0663886 + 0.997794i \(0.478852\pi\)
\(252\) 0 0
\(253\) 3136.00 0.779283
\(254\) 1944.00 3367.11i 0.480226 0.831776i
\(255\) −4144.00 7177.62i −1.01768 1.76267i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 2817.00 4879.19i 0.683734 1.18426i −0.290099 0.956997i \(-0.593688\pi\)
0.973833 0.227265i \(-0.0729785\pi\)
\(258\) −6592.00 −1.59070
\(259\) 0 0
\(260\) −1008.00 −0.240437
\(261\) −3515.00 + 6088.16i −0.833613 + 1.44386i
\(262\) 848.000 + 1468.78i 0.199960 + 0.346342i
\(263\) −84.0000 145.492i −0.0196945 0.0341119i 0.856010 0.516959i \(-0.172936\pi\)
−0.875705 + 0.482847i \(0.839603\pi\)
\(264\) 896.000 1551.92i 0.208883 0.361795i
\(265\) 4452.00 1.03202
\(266\) 0 0
\(267\) 6480.00 1.48528
\(268\) 1432.00 2480.30i 0.326393 0.565329i
\(269\) −655.000 1134.49i −0.148461 0.257142i 0.782198 0.623030i \(-0.214099\pi\)
−0.930659 + 0.365888i \(0.880765\pi\)
\(270\) −1120.00 1939.90i −0.252448 0.437253i
\(271\) −1104.00 + 1912.18i −0.247466 + 0.428623i −0.962822 0.270137i \(-0.912931\pi\)
0.715356 + 0.698760i \(0.246264\pi\)
\(272\) −1184.00 −0.263936
\(273\) 0 0
\(274\) 5932.00 1.30790
\(275\) 994.000 1721.66i 0.217965 0.377527i
\(276\) −1792.00 3103.84i −0.390818 0.676916i
\(277\) −2647.00 4584.74i −0.574162 0.994477i −0.996132 0.0878678i \(-0.971995\pi\)
0.421970 0.906610i \(-0.361339\pi\)
\(278\) −2800.00 + 4849.74i −0.604075 + 1.04629i
\(279\) −2664.00 −0.571647
\(280\) 0 0
\(281\) 3242.00 0.688262 0.344131 0.938922i \(-0.388174\pi\)
0.344131 + 0.938922i \(0.388174\pi\)
\(282\) 192.000 332.554i 0.0405441 0.0702244i
\(283\) −796.000 1378.71i −0.167199 0.289597i 0.770235 0.637760i \(-0.220139\pi\)
−0.937434 + 0.348163i \(0.886806\pi\)
\(284\) −784.000 1357.93i −0.163809 0.283726i
\(285\) −4480.00 + 7759.59i −0.931131 + 1.61277i
\(286\) −1008.00 −0.208407
\(287\) 0 0
\(288\) −1184.00 −0.242250
\(289\) −281.500 + 487.572i −0.0572970 + 0.0992413i
\(290\) 2660.00 + 4607.26i 0.538623 + 0.932922i
\(291\) −5416.00 9380.79i −1.09104 1.88973i
\(292\) 1076.00 1863.69i 0.215644 0.373507i
\(293\) 5022.00 1.00133 0.500663 0.865642i \(-0.333090\pi\)
0.500663 + 0.865642i \(0.333090\pi\)
\(294\) 0 0
\(295\) 2800.00 0.552618
\(296\) −1384.00 + 2397.16i −0.271768 + 0.470716i
\(297\) −1120.00 1939.90i −0.218818 0.379004i
\(298\) 510.000 + 883.346i 0.0991393 + 0.171714i
\(299\) −1008.00 + 1745.91i −0.194964 + 0.337687i
\(300\) −2272.00 −0.437247
\(301\) 0 0
\(302\) −1184.00 −0.225601
\(303\) 5432.00 9408.50i 1.02990 1.78384i
\(304\) 640.000 + 1108.51i 0.120745 + 0.209137i
\(305\) −1386.00 2400.62i −0.260204 0.450686i
\(306\) −2738.00 + 4742.36i −0.511507 + 0.885956i
\(307\) 9536.00 1.77280 0.886398 0.462924i \(-0.153200\pi\)
0.886398 + 0.462924i \(0.153200\pi\)
\(308\) 0 0
\(309\) −6656.00 −1.22539
\(310\) −1008.00 + 1745.91i −0.184679 + 0.319874i
\(311\) −484.000 838.313i −0.0882480 0.152850i 0.818523 0.574474i \(-0.194793\pi\)
−0.906771 + 0.421624i \(0.861460\pi\)
\(312\) 576.000 + 997.661i 0.104518 + 0.181030i
\(313\) 1529.00 2648.31i 0.276116 0.478246i −0.694300 0.719685i \(-0.744286\pi\)
0.970416 + 0.241439i \(0.0776194\pi\)
\(314\) −5372.00 −0.965476
\(315\) 0 0
\(316\) 960.000 0.170899
\(317\) 2493.00 4318.00i 0.441706 0.765057i −0.556110 0.831109i \(-0.687707\pi\)
0.997816 + 0.0660512i \(0.0210401\pi\)
\(318\) −2544.00 4406.34i −0.448618 0.777029i
\(319\) 2660.00 + 4607.26i 0.466870 + 0.808642i
\(320\) −448.000 + 775.959i −0.0782624 + 0.135554i
\(321\) −3552.00 −0.617612
\(322\) 0 0
\(323\) 5920.00 1.01981
\(324\) 718.000 1243.61i 0.123114 0.213239i
\(325\) 639.000 + 1106.78i 0.109063 + 0.188902i
\(326\) −1012.00 1752.84i −0.171931 0.297793i
\(327\) 7480.00 12955.7i 1.26497 2.19099i
\(328\) 1296.00 0.218170
\(329\) 0 0
\(330\) −6272.00 −1.04625
\(331\) −4306.00 + 7458.21i −0.715043 + 1.23849i 0.247900 + 0.968786i \(0.420259\pi\)
−0.962943 + 0.269705i \(0.913074\pi\)
\(332\) −2144.00 3713.52i −0.354420 0.613873i
\(333\) 6401.00 + 11086.9i 1.05337 + 1.82449i
\(334\) −544.000 + 942.236i −0.0891208 + 0.154362i
\(335\) −10024.0 −1.63483
\(336\) 0 0
\(337\) −10206.0 −1.64972 −0.824861 0.565336i \(-0.808747\pi\)
−0.824861 + 0.565336i \(0.808747\pi\)
\(338\) −1873.00 + 3244.13i −0.301414 + 0.522064i
\(339\) 5512.00 + 9547.06i 0.883100 + 1.52957i
\(340\) 2072.00 + 3588.81i 0.330500 + 0.572443i
\(341\) −1008.00 + 1745.91i −0.160077 + 0.277262i
\(342\) 5920.00 0.936014
\(343\) 0 0
\(344\) 3296.00 0.516594
\(345\) −6272.00 + 10863.4i −0.978763 + 1.69527i
\(346\) −1858.00 3218.15i −0.288690 0.500026i
\(347\) −1002.00 1735.51i −0.155015 0.268494i 0.778050 0.628203i \(-0.216209\pi\)
−0.933064 + 0.359709i \(0.882876\pi\)
\(348\) 3040.00 5265.43i 0.468279 0.811083i
\(349\) −1330.00 −0.203992 −0.101996 0.994785i \(-0.532523\pi\)
−0.101996 + 0.994785i \(0.532523\pi\)
\(350\) 0 0
\(351\) 1440.00 0.218979
\(352\) −448.000 + 775.959i −0.0678366 + 0.117496i
\(353\) 489.000 + 846.973i 0.0737304 + 0.127705i 0.900533 0.434787i \(-0.143176\pi\)
−0.826803 + 0.562492i \(0.809843\pi\)
\(354\) −1600.00 2771.28i −0.240223 0.416079i
\(355\) −2744.00 + 4752.75i −0.410243 + 0.710562i
\(356\) −3240.00 −0.482359
\(357\) 0 0
\(358\) 600.000 0.0885782
\(359\) 4840.00 8383.13i 0.711547 1.23244i −0.252729 0.967537i \(-0.581328\pi\)
0.964276 0.264899i \(-0.0853385\pi\)
\(360\) 2072.00 + 3588.81i 0.303344 + 0.525408i
\(361\) 229.500 + 397.506i 0.0334597 + 0.0579539i
\(362\) 2358.00 4084.18i 0.342358 0.592982i
\(363\) 4376.00 0.632728
\(364\) 0 0
\(365\) −7532.00 −1.08012
\(366\) −1584.00 + 2743.57i −0.226221 + 0.391827i
\(367\) −4328.00 7496.32i −0.615585 1.06622i −0.990282 0.139077i \(-0.955586\pi\)
0.374696 0.927148i \(-0.377747\pi\)
\(368\) 896.000 + 1551.92i 0.126922 + 0.219835i
\(369\) 2997.00 5190.96i 0.422812 0.732332i
\(370\) 9688.00 1.36123
\(371\) 0 0
\(372\) 2304.00 0.321121
\(373\) −2639.00 + 4570.88i −0.366333 + 0.634508i −0.988989 0.147988i \(-0.952720\pi\)
0.622656 + 0.782496i \(0.286054\pi\)
\(374\) 2072.00 + 3588.81i 0.286472 + 0.496184i
\(375\) −3024.00 5237.72i −0.416423 0.721266i
\(376\) −96.0000 + 166.277i −0.0131671 + 0.0228061i
\(377\) −3420.00 −0.467212
\(378\) 0 0
\(379\) 6340.00 0.859272 0.429636 0.903002i \(-0.358642\pi\)
0.429636 + 0.903002i \(0.358642\pi\)
\(380\) 2240.00 3879.79i 0.302394 0.523761i
\(381\) 7776.00 + 13468.4i 1.04561 + 1.81105i
\(382\) 1392.00 + 2411.01i 0.186442 + 0.322927i
\(383\) −3116.00 + 5397.07i −0.415718 + 0.720045i −0.995504 0.0947240i \(-0.969803\pi\)
0.579785 + 0.814769i \(0.303136\pi\)
\(384\) 1024.00 0.136083
\(385\) 0 0
\(386\) −3556.00 −0.468901
\(387\) 7622.00 13201.7i 1.00116 1.73406i
\(388\) 2708.00 + 4690.39i 0.354324 + 0.613708i
\(389\) 7405.00 + 12825.8i 0.965163 + 1.67171i 0.709177 + 0.705031i \(0.249067\pi\)
0.255986 + 0.966680i \(0.417600\pi\)
\(390\) 2016.00 3491.81i 0.261754 0.453372i
\(391\) 8288.00 1.07197
\(392\) 0 0
\(393\) −6784.00 −0.870757
\(394\) 1214.00 2102.71i 0.155230 0.268865i
\(395\) −1680.00 2909.85i −0.214000 0.370659i
\(396\) 2072.00 + 3588.81i 0.262934 + 0.455415i
\(397\) 2577.00 4463.49i 0.325783 0.564273i −0.655887 0.754859i \(-0.727705\pi\)
0.981671 + 0.190586i \(0.0610387\pi\)
\(398\) 2080.00 0.261962
\(399\) 0 0
\(400\) 1136.00 0.142000
\(401\) −1641.00 + 2842.30i −0.204358 + 0.353959i −0.949928 0.312469i \(-0.898844\pi\)
0.745570 + 0.666427i \(0.232177\pi\)
\(402\) 5728.00 + 9921.19i 0.710663 + 1.23091i
\(403\) −648.000 1122.37i −0.0800972 0.138732i
\(404\) −2716.00 + 4704.25i −0.334470 + 0.579320i
\(405\) −5026.00 −0.616652
\(406\) 0 0
\(407\) 9688.00 1.17989
\(408\) 2368.00 4101.50i 0.287337 0.497682i
\(409\) 2905.00 + 5031.61i 0.351205 + 0.608306i 0.986461 0.163996i \(-0.0524386\pi\)
−0.635256 + 0.772302i \(0.719105\pi\)
\(410\) −2268.00 3928.29i −0.273192 0.473182i
\(411\) −11864.0 + 20549.1i −1.42386 + 2.46620i
\(412\) 3328.00 0.397958
\(413\) 0 0
\(414\) 8288.00 0.983896
\(415\) −7504.00 + 12997.3i −0.887607 + 1.53738i
\(416\) −288.000 498.831i −0.0339432 0.0587913i
\(417\) −11200.0 19399.0i −1.31527 2.27811i
\(418\) 2240.00 3879.79i 0.262110 0.453988i
\(419\) −13560.0 −1.58102 −0.790512 0.612446i \(-0.790186\pi\)
−0.790512 + 0.612446i \(0.790186\pi\)
\(420\) 0 0
\(421\) −738.000 −0.0854345 −0.0427172 0.999087i \(-0.513601\pi\)
−0.0427172 + 0.999087i \(0.513601\pi\)
\(422\) −3868.00 + 6699.57i −0.446188 + 0.772820i
\(423\) 444.000 + 769.031i 0.0510355 + 0.0883961i
\(424\) 1272.00 + 2203.17i 0.145693 + 0.252347i
\(425\) 2627.00 4550.10i 0.299831 0.519323i
\(426\) 6272.00 0.713332
\(427\) 0 0
\(428\) 1776.00 0.200575
\(429\) 2016.00 3491.81i 0.226884 0.392975i
\(430\) −5768.00 9990.47i −0.646878 1.12043i
\(431\) −636.000 1101.58i −0.0710790 0.123112i 0.828295 0.560292i \(-0.189311\pi\)
−0.899374 + 0.437179i \(0.855978\pi\)
\(432\) 640.000 1108.51i 0.0712778 0.123457i
\(433\) 5062.00 0.561811 0.280906 0.959735i \(-0.409365\pi\)
0.280906 + 0.959735i \(0.409365\pi\)
\(434\) 0 0
\(435\) −21280.0 −2.34551
\(436\) −3740.00 + 6477.87i −0.410811 + 0.711545i
\(437\) −4480.00 7759.59i −0.490406 0.849408i
\(438\) 4304.00 + 7454.75i 0.469528 + 0.813246i
\(439\) 2820.00 4884.38i 0.306586 0.531023i −0.671027 0.741433i \(-0.734147\pi\)
0.977613 + 0.210410i \(0.0674800\pi\)
\(440\) 3136.00 0.339779
\(441\) 0 0
\(442\) −2664.00 −0.286682
\(443\) −6694.00 + 11594.3i −0.717927 + 1.24349i 0.243893 + 0.969802i \(0.421575\pi\)
−0.961820 + 0.273683i \(0.911758\pi\)
\(444\) −5536.00 9588.63i −0.591727 1.02490i
\(445\) 5670.00 + 9820.73i 0.604008 + 1.04617i
\(446\) −3968.00 + 6872.78i −0.421279 + 0.729676i
\(447\) −4080.00 −0.431717
\(448\) 0 0
\(449\) −3230.00 −0.339495 −0.169747 0.985488i \(-0.554295\pi\)
−0.169747 + 0.985488i \(0.554295\pi\)
\(450\) 2627.00 4550.10i 0.275195 0.476653i
\(451\) −2268.00 3928.29i −0.236798 0.410146i
\(452\) −2756.00 4773.53i −0.286795 0.496743i
\(453\) 2368.00 4101.50i 0.245603 0.425398i
\(454\) −7872.00 −0.813769
\(455\) 0 0
\(456\) −5120.00 −0.525803
\(457\) 5323.00 9219.71i 0.544857 0.943719i −0.453759 0.891124i \(-0.649917\pi\)
0.998616 0.0525950i \(-0.0167492\pi\)
\(458\) −4810.00 8331.16i −0.490735 0.849978i
\(459\) −2960.00 5126.87i −0.301004 0.521355i
\(460\) 3136.00 5431.71i 0.317863 0.550554i
\(461\) −7282.00 −0.735698 −0.367849 0.929886i \(-0.619906\pi\)
−0.367849 + 0.929886i \(0.619906\pi\)
\(462\) 0 0
\(463\) 12688.0 1.27357 0.636783 0.771043i \(-0.280265\pi\)
0.636783 + 0.771043i \(0.280265\pi\)
\(464\) −1520.00 + 2632.72i −0.152078 + 0.263407i
\(465\) −4032.00 6983.63i −0.402107 0.696469i
\(466\) −2182.00 3779.33i −0.216908 0.375696i
\(467\) −1408.00 + 2438.73i −0.139517 + 0.241651i −0.927314 0.374285i \(-0.877888\pi\)
0.787797 + 0.615935i \(0.211222\pi\)
\(468\) −2664.00 −0.263127
\(469\) 0 0
\(470\) 672.000 0.0659512
\(471\) 10744.0 18609.2i 1.05108 1.82052i
\(472\) 800.000 + 1385.64i 0.0780148 + 0.135126i
\(473\) −5768.00 9990.47i −0.560704 0.971168i
\(474\) −1920.00 + 3325.54i −0.186052 + 0.322251i
\(475\) −5680.00 −0.548666
\(476\) 0 0
\(477\) 11766.0 1.12941
\(478\) −3000.00 + 5196.15i −0.287064 + 0.497210i
\(479\) −1580.00 2736.64i −0.150714 0.261044i 0.780776 0.624811i \(-0.214824\pi\)
−0.931490 + 0.363766i \(0.881491\pi\)
\(480\) −1792.00 3103.84i −0.170403 0.295146i
\(481\) −3114.00 + 5393.61i −0.295190 + 0.511283i
\(482\) 4084.00 0.385936
\(483\) 0 0
\(484\) −2188.00 −0.205485
\(485\) 9478.00 16416.4i 0.887369 1.53697i
\(486\) 5032.00 + 8715.68i 0.469663 + 0.813480i
\(487\) 7088.00 + 12276.8i 0.659523 + 1.14233i 0.980739 + 0.195322i \(0.0625752\pi\)
−0.321216 + 0.947006i \(0.604091\pi\)
\(488\) 792.000 1371.78i 0.0734675 0.127249i
\(489\) 8096.00 0.748699
\(490\) 0 0
\(491\) −11268.0 −1.03568 −0.517839 0.855478i \(-0.673263\pi\)
−0.517839 + 0.855478i \(0.673263\pi\)
\(492\) −2592.00 + 4489.48i −0.237513 + 0.411385i
\(493\) 7030.00 + 12176.3i 0.642222 + 1.11236i
\(494\) 1440.00 + 2494.15i 0.131151 + 0.227160i
\(495\) 7252.00 12560.8i 0.658491 1.14054i
\(496\) −1152.00 −0.104287
\(497\) 0 0
\(498\) 17152.0 1.54337
\(499\) 2230.00 3862.47i 0.200057 0.346509i −0.748489 0.663147i \(-0.769221\pi\)
0.948547 + 0.316638i \(0.102554\pi\)
\(500\) 1512.00 + 2618.86i 0.135237 + 0.234238i
\(501\) −2176.00 3768.94i −0.194045 0.336096i
\(502\) 528.000 914.523i 0.0469438 0.0813091i
\(503\) 1512.00 0.134029 0.0670147 0.997752i \(-0.478653\pi\)
0.0670147 + 0.997752i \(0.478653\pi\)
\(504\) 0 0
\(505\) 19012.0 1.67529
\(506\) 3136.00 5431.71i 0.275518 0.477212i
\(507\) −7492.00 12976.5i −0.656275 1.13670i
\(508\) −3888.00 6734.21i −0.339571 0.588154i
\(509\) −5895.00 + 10210.4i −0.513342 + 0.889135i 0.486538 + 0.873660i \(0.338260\pi\)
−0.999880 + 0.0154756i \(0.995074\pi\)
\(510\) −16576.0 −1.43921
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) −3200.00 + 5542.56i −0.275406 + 0.477018i
\(514\) −5634.00 9758.37i −0.483473 0.837400i
\(515\) −5824.00 10087.5i −0.498323 0.863120i
\(516\) −6592.00 + 11417.7i −0.562397 + 0.974099i
\(517\) 672.000 0.0571654
\(518\) 0 0
\(519\) 14864.0 1.25714
\(520\) −1008.00 + 1745.91i −0.0850072 + 0.147237i
\(521\) 681.000 + 1179.53i 0.0572652 + 0.0991862i 0.893237 0.449586i \(-0.148429\pi\)
−0.835972 + 0.548773i \(0.815095\pi\)
\(522\) 7030.00 + 12176.3i 0.589454 + 1.02096i
\(523\) 3484.00 6034.47i 0.291290 0.504529i −0.682825 0.730582i \(-0.739249\pi\)
0.974115 + 0.226053i \(0.0725822\pi\)
\(524\) 3392.00 0.282787
\(525\) 0 0
\(526\) −336.000 −0.0278523
\(527\) −2664.00 + 4614.18i −0.220200 + 0.381398i
\(528\) −1792.00 3103.84i −0.147702 0.255828i
\(529\) −188.500 326.492i −0.0154927 0.0268342i
\(530\) 4452.00 7711.09i 0.364873 0.631978i
\(531\) 7400.00 0.604770
\(532\) 0 0
\(533\) 2916.00 0.236972
\(534\) 6480.00 11223.7i 0.525126 0.909544i
\(535\) −3108.00 5383.21i −0.251160 0.435022i
\(536\) −2864.00 4960.59i −0.230795 0.399748i
\(537\) −1200.00 + 2078.46i −0.0964317 + 0.167025i
\(538\) −2620.00 −0.209956
\(539\) 0 0
\(540\) −4480.00 −0.357016
\(541\) −3531.00 + 6115.87i −0.280609 + 0.486029i −0.971535 0.236896i \(-0.923870\pi\)
0.690926 + 0.722926i \(0.257203\pi\)
\(542\) 2208.00 + 3824.37i 0.174985 + 0.303082i
\(543\) 9432.00 + 16336.7i 0.745425 + 1.29111i
\(544\) −1184.00 + 2050.75i −0.0933154 + 0.161627i
\(545\) 26180.0 2.05767
\(546\) 0 0
\(547\) −8196.00 −0.640650 −0.320325 0.947308i \(-0.603792\pi\)
−0.320325 + 0.947308i \(0.603792\pi\)
\(548\) 5932.00 10274.5i 0.462413 0.800923i
\(549\) −3663.00 6344.50i −0.284760 0.493218i
\(550\) −1988.00 3443.32i −0.154125 0.266952i
\(551\) 7600.00 13163.6i 0.587606 1.01776i
\(552\) −7168.00 −0.552700
\(553\) 0 0
\(554\) −10588.0 −0.811987
\(555\) −19376.0 + 33560.2i −1.48192 + 2.56676i
\(556\) 5600.00 + 9699.48i 0.427146 + 0.739838i
\(557\) 3733.00 + 6465.75i 0.283972 + 0.491854i 0.972359 0.233490i \(-0.0750145\pi\)
−0.688388 + 0.725343i \(0.741681\pi\)
\(558\) −2664.00 + 4614.18i −0.202108 + 0.350061i
\(559\) 7416.00 0.561115
\(560\) 0 0
\(561\) −16576.0 −1.24749
\(562\) 3242.00 5615.31i 0.243337 0.421472i
\(563\) 12484.0 + 21622.9i 0.934526 + 1.61865i 0.775478 + 0.631375i \(0.217509\pi\)
0.159048 + 0.987271i \(0.449158\pi\)
\(564\) −384.000 665.108i −0.0286690 0.0496562i
\(565\) −9646.00 + 16707.4i −0.718248 + 1.24404i
\(566\) −3184.00 −0.236455
\(567\) 0 0
\(568\) −3136.00 −0.231661
\(569\) −7125.00 + 12340.9i −0.524948 + 0.909237i 0.474630 + 0.880186i \(0.342582\pi\)
−0.999578 + 0.0290514i \(0.990751\pi\)
\(570\) 8960.00 + 15519.2i 0.658409 + 1.14040i
\(571\) −3186.00 5518.31i −0.233503 0.404438i 0.725334 0.688397i \(-0.241685\pi\)
−0.958836 + 0.283959i \(0.908352\pi\)
\(572\) −1008.00 + 1745.91i −0.0736829 + 0.127622i
\(573\) −11136.0 −0.811890
\(574\) 0 0
\(575\) −7952.00 −0.576733
\(576\) −1184.00 + 2050.75i −0.0856481 + 0.148347i
\(577\) −4183.00 7245.17i −0.301803 0.522739i 0.674741 0.738055i \(-0.264255\pi\)
−0.976545 + 0.215316i \(0.930922\pi\)
\(578\) 563.000 + 975.145i 0.0405151 + 0.0701742i
\(579\) 7112.00 12318.3i 0.510474 0.884167i
\(580\) 10640.0 0.761728
\(581\) 0 0
\(582\) −21664.0 −1.54296
\(583\) 4452.00 7711.09i 0.316266 0.547789i
\(584\) −2152.00 3727.37i −0.152484 0.264109i
\(585\) 4662.00 + 8074.82i 0.329487 + 0.570688i
\(586\) 5022.00 8698.36i 0.354022 0.613184i
\(587\) −20384.0 −1.43328 −0.716642 0.697441i \(-0.754322\pi\)
−0.716642 + 0.697441i \(0.754322\pi\)
\(588\) 0 0
\(589\) 5760.00 0.402948
\(590\) 2800.00 4849.74i 0.195380 0.338408i
\(591\) 4856.00 + 8410.84i 0.337985 + 0.585407i
\(592\) 2768.00 + 4794.32i 0.192169 + 0.332847i
\(593\) 4689.00 8121.59i 0.324712 0.562417i −0.656742 0.754115i \(-0.728066\pi\)
0.981454 + 0.191698i \(0.0613993\pi\)
\(594\) −4480.00 −0.309456
\(595\) 0 0
\(596\) 2040.00 0.140204
\(597\) −4160.00 + 7205.33i −0.285188 + 0.493961i
\(598\) 2016.00 + 3491.81i 0.137860 + 0.238781i
\(599\) 4500.00 + 7794.23i 0.306953 + 0.531659i 0.977694 0.210033i \(-0.0673571\pi\)
−0.670741 + 0.741692i \(0.734024\pi\)
\(600\) −2272.00 + 3935.22i −0.154590 + 0.267758i
\(601\) −7562.00 −0.513245 −0.256623 0.966512i \(-0.582610\pi\)
−0.256623 + 0.966512i \(0.582610\pi\)
\(602\) 0 0
\(603\) −26492.0 −1.78912
\(604\) −1184.00 + 2050.75i −0.0797620 + 0.138152i
\(605\) 3829.00 + 6632.02i 0.257307 + 0.445670i
\(606\) −10864.0 18817.0i −0.728251 1.26137i
\(607\) −1488.00 + 2577.29i −0.0994993 + 0.172338i −0.911478 0.411350i \(-0.865057\pi\)
0.811978 + 0.583688i \(0.198391\pi\)
\(608\) 2560.00 0.170759
\(609\) 0 0
\(610\) −5544.00 −0.367984
\(611\) −216.000 + 374.123i −0.0143018 + 0.0247715i
\(612\) 5476.00 + 9484.71i 0.361690 + 0.626465i
\(613\) −2139.00 3704.86i −0.140935 0.244107i 0.786914 0.617063i \(-0.211678\pi\)
−0.927849 + 0.372956i \(0.878344\pi\)
\(614\) 9536.00 16516.8i 0.626778 1.08561i
\(615\) 18144.0 1.18965
\(616\) 0 0
\(617\) 18794.0 1.22629 0.613143 0.789972i \(-0.289905\pi\)
0.613143 + 0.789972i \(0.289905\pi\)
\(618\) −6656.00 + 11528.5i −0.433242 + 0.750397i
\(619\) 9020.00 + 15623.1i 0.585694 + 1.01445i 0.994789 + 0.101959i \(0.0325112\pi\)
−0.409095 + 0.912492i \(0.634155\pi\)
\(620\) 2016.00 + 3491.81i 0.130588 + 0.226185i
\(621\) −4480.00 + 7759.59i −0.289495 + 0.501420i
\(622\) −1936.00 −0.124801
\(623\) 0 0
\(624\) 2304.00 0.147811
\(625\) 9729.50 16852.0i 0.622688 1.07853i
\(626\) −3058.00 5296.61i −0.195243 0.338171i
\(627\) 8960.00 + 15519.2i 0.570698 + 0.988479i
\(628\) −5372.00 + 9304.58i −0.341347 + 0.591231i
\(629\) 25604.0 1.62305
\(630\) 0 0
\(631\) −21688.0 −1.36828 −0.684141 0.729350i \(-0.739823\pi\)
−0.684141 + 0.729350i \(0.739823\pi\)
\(632\) 960.000 1662.77i 0.0604221 0.104654i
\(633\) −15472.0 26798.3i −0.971496 1.68268i
\(634\) −4986.00 8636.01i −0.312333 0.540977i
\(635\) −13608.0 + 23569.7i −0.850420 + 1.47297i
\(636\) −10176.0 −0.634441
\(637\) 0 0
\(638\) 10640.0 0.660253
\(639\) −7252.00 + 12560.8i −0.448959 + 0.777619i
\(640\) 896.000 + 1551.92i 0.0553399 + 0.0958514i
\(641\) 5279.00 + 9143.50i 0.325285 + 0.563411i 0.981570 0.191102i \(-0.0612063\pi\)
−0.656285 + 0.754513i \(0.727873\pi\)
\(642\) −3552.00 + 6152.24i −0.218359 + 0.378208i
\(643\) 26152.0 1.60394 0.801971 0.597363i \(-0.203785\pi\)
0.801971 + 0.597363i \(0.203785\pi\)
\(644\) 0 0
\(645\) 46144.0 2.81693
\(646\) 5920.00 10253.7i 0.360556 0.624502i
\(647\) 12792.0 + 22156.4i 0.777288 + 1.34630i 0.933499 + 0.358579i \(0.116739\pi\)
−0.156211 + 0.987724i \(0.549928\pi\)
\(648\) −1436.00 2487.22i −0.0870546 0.150783i
\(649\) 2800.00 4849.74i 0.169352 0.293327i
\(650\) 2556.00 0.154238
\(651\) 0 0
\(652\) −4048.00 −0.243147
\(653\) −7599.00 + 13161.9i −0.455393 + 0.788764i −0.998711 0.0507630i \(-0.983835\pi\)
0.543317 + 0.839527i \(0.317168\pi\)
\(654\) −14960.0 25911.5i −0.894468 1.54926i
\(655\) −5936.00 10281.5i −0.354105 0.613328i
\(656\) 1296.00 2244.74i 0.0771346 0.133601i
\(657\) −19906.0 −1.18205
\(658\) 0 0
\(659\) −6100.00 −0.360580 −0.180290 0.983613i \(-0.557704\pi\)
−0.180290 + 0.983613i \(0.557704\pi\)
\(660\) −6272.00 + 10863.4i −0.369905 + 0.640694i
\(661\) −1159.00 2007.45i −0.0681995 0.118125i 0.829909 0.557898i \(-0.188392\pi\)
−0.898109 + 0.439773i \(0.855059\pi\)
\(662\) 8612.00 + 14916.4i 0.505612 + 0.875745i
\(663\) 5328.00 9228.37i 0.312100 0.540573i
\(664\) −8576.00 −0.501225
\(665\) 0 0
\(666\) 25604.0 1.48969
\(667\) 10640.0 18429.0i 0.617665 1.06983i
\(668\) 1088.00 + 1884.47i 0.0630179 + 0.109150i
\(669\) −15872.0 27491.1i −0.917260 1.58874i
\(670\) −10024.0 + 17362.1i −0.578001 + 1.00113i
\(671\) −5544.00 −0.318962
\(672\) 0 0
\(673\) −10222.0 −0.585482 −0.292741 0.956192i \(-0.594567\pi\)
−0.292741 + 0.956192i \(0.594567\pi\)
\(674\) −10206.0 + 17677.3i −0.583265 + 1.01024i
\(675\) 2840.00 + 4919.02i 0.161943 + 0.280494i
\(676\) 3746.00 + 6488.26i 0.213132 + 0.369155i
\(677\) 12717.0 22026.5i 0.721941 1.25044i −0.238280 0.971197i \(-0.576584\pi\)
0.960221 0.279242i \(-0.0900831\pi\)
\(678\) 22048.0 1.24889
\(679\) 0 0
\(680\) 8288.00 0.467397
\(681\) 15744.0 27269.4i 0.885920 1.53446i
\(682\) 2016.00 + 3491.81i 0.113192 + 0.196053i
\(683\) 4266.00 + 7388.93i 0.238996 + 0.413952i 0.960426 0.278534i \(-0.0898485\pi\)
−0.721431 + 0.692487i \(0.756515\pi\)
\(684\) 5920.00 10253.7i 0.330931 0.573189i
\(685\) −41524.0 −2.31613
\(686\) 0 0
\(687\) 38480.0 2.13698
\(688\) 3296.00 5708.84i 0.182644 0.316348i
\(689\) 2862.00 + 4957.13i 0.158249 + 0.274095i
\(690\) 12544.0 + 21726.8i 0.692090 + 1.19873i
\(691\) 10336.0 17902.5i 0.569030 0.985589i −0.427632 0.903953i \(-0.640652\pi\)
0.996662 0.0816365i \(-0.0260146\pi\)
\(692\) −7432.00 −0.408269
\(693\) 0 0
\(694\) −4008.00 −0.219224
\(695\) 19600.0 33948.2i 1.06974 1.85285i
\(696\) −6080.00 10530.9i −0.331123 0.573522i
\(697\) −5994.00 10381.9i −0.325737 0.564194i
\(698\) −1330.00 + 2303.63i −0.0721221 + 0.124919i
\(699\) 17456.0 0.944559
\(700\) 0 0
\(701\) −21458.0 −1.15614 −0.578072 0.815985i \(-0.696195\pi\)
−0.578072 + 0.815985i \(0.696195\pi\)
\(702\) 1440.00 2494.15i 0.0774207 0.134097i
\(703\) −13840.0 23971.6i −0.742511 1.28607i
\(704\) 896.000 + 1551.92i 0.0479677 + 0.0830825i
\(705\) −1344.00 + 2327.88i −0.0717985 + 0.124359i
\(706\) 1956.00 0.104271
\(707\) 0 0
\(708\) −6400.00 −0.339727
\(709\) 4925.00 8530.35i 0.260878 0.451853i −0.705598 0.708613i \(-0.749321\pi\)
0.966475 + 0.256759i \(0.0826547\pi\)
\(710\) 5488.00 + 9505.49i 0.290086 + 0.502443i
\(711\) −4440.00 7690.31i −0.234196 0.405639i
\(712\) −3240.00 + 5611.84i −0.170540 + 0.295383i
\(713\) 8064.00 0.423561
\(714\) 0 0
\(715\) 7056.00 0.369062
\(716\) 600.000 1039.23i 0.0313171 0.0542428i
\(717\) −12000.0 20784.6i −0.625032 1.08259i
\(718\) −9680.00 16766.3i −0.503140 0.871464i
\(719\) −9420.00 + 16315.9i −0.488605 + 0.846288i −0.999914 0.0131086i \(-0.995827\pi\)
0.511309 + 0.859397i \(0.329161\pi\)
\(720\) 8288.00 0.428994
\(721\) 0 0
\(722\) 918.000 0.0473191
\(723\) −8168.00 + 14147.4i −0.420154 + 0.727728i
\(724\) −4716.00 8168.35i −0.242084 0.419302i
\(725\) −6745.00 11682.7i −0.345521 0.598461i
\(726\) 4376.00 7579.45i 0.223703 0.387465i
\(727\) −37504.0 −1.91327 −0.956634 0.291291i \(-0.905915\pi\)
−0.956634 + 0.291291i \(0.905915\pi\)
\(728\) 0 0
\(729\) −30563.0 −1.55276
\(730\) −7532.00 + 13045.8i −0.381879 + 0.661434i
\(731\) −15244.0 26403.4i −0.771299 1.33593i
\(732\) 3168.00 + 5487.14i 0.159963 + 0.277063i
\(733\) 6669.00 11551.0i 0.336051 0.582057i −0.647635 0.761950i \(-0.724242\pi\)
0.983686 + 0.179894i \(0.0575753\pi\)
\(734\) −17312.0 −0.870569
\(735\) 0 0
\(736\) 3584.00 0.179495
\(737\) −10024.0 + 17362.1i −0.501002 + 0.867762i
\(738\) −5994.00 10381.9i −0.298973 0.517837i
\(739\) −8550.00 14809.0i −0.425598 0.737157i 0.570878 0.821035i \(-0.306603\pi\)
−0.996476 + 0.0838776i \(0.973270\pi\)
\(740\) 9688.00 16780.1i 0.481268 0.833580i
\(741\) −11520.0 −0.571117
\(742\) 0 0
\(743\) −19632.0 −0.969352 −0.484676 0.874694i \(-0.661062\pi\)
−0.484676 + 0.874694i \(0.661062\pi\)
\(744\) 2304.00 3990.65i 0.113533 0.196645i
\(745\) −3570.00 6183.42i −0.175563 0.304085i
\(746\) 5278.00 + 9141.76i 0.259037 + 0.448665i
\(747\) −19832.0 + 34350.0i −0.971372 + 1.68247i
\(748\) 8288.00 0.405133
\(749\) 0 0
\(750\) −12096.0 −0.588911
\(751\) −16956.0 + 29368.7i −0.823879 + 1.42700i 0.0788938 + 0.996883i \(0.474861\pi\)
−0.902773 + 0.430117i \(0.858472\pi\)
\(752\) 192.000 + 332.554i 0.00931053 + 0.0161263i
\(753\) 2112.00 + 3658.09i 0.102212 + 0.177036i
\(754\) −3420.00 + 5923.61i −0.165184 + 0.286108i
\(755\) 8288.00 0.399512
\(756\) 0 0
\(757\) −31386.0 −1.50693 −0.753463 0.657490i \(-0.771618\pi\)
−0.753463 + 0.657490i \(0.771618\pi\)
\(758\) 6340.00 10981.2i 0.303798 0.526194i
\(759\) 12544.0 + 21726.8i 0.599892 + 1.03904i
\(760\) −4480.00 7759.59i −0.213825 0.370355i
\(761\) −17279.0 + 29928.1i −0.823079 + 1.42561i 0.0802993 + 0.996771i \(0.474412\pi\)
−0.903378 + 0.428844i \(0.858921\pi\)
\(762\) 31104.0 1.47871
\(763\) 0 0
\(764\) 5568.00 0.263669
\(765\) 19166.0 33196.5i 0.905815 1.56892i
\(766\) 6232.00 + 10794.1i 0.293957 + 0.509149i
\(767\) 1800.00 + 3117.69i 0.0847382 + 0.146771i
\(768\) 1024.00 1773.62i 0.0481125 0.0833333i
\(769\) −39130.0 −1.83493 −0.917467 0.397812i \(-0.869769\pi\)
−0.917467 + 0.397812i \(0.869769\pi\)
\(770\) 0 0
\(771\) 45072.0 2.10535
\(772\) −3556.00 + 6159.17i −0.165781 + 0.287142i
\(773\) −12991.0 22501.1i −0.604468 1.04697i −0.992135 0.125170i \(-0.960052\pi\)
0.387667 0.921799i \(-0.373281\pi\)
\(774\) −15244.0 26403.4i −0.707925 1.22616i
\(775\) 2556.00 4427.12i 0.118470 0.205196i
\(776\) 10832.0 0.501090
\(777\) 0 0