Properties

Label 98.4.c.d.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.d.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 \(-0.887022\pi\)
0.167871 0.985809i \(-0.446311\pi\)
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 7.00000 12.1244i 0.626099 1.08444i −0.362228 0.932089i \(-0.617984\pi\)
0.988327 0.152346i \(-0.0486828\pi\)
\(6\) −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 \(-0.438499\pi\)
0.192012 + 0.981393i \(0.438499\pi\)
\(14\) 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 \(-0.989657\pi\)
0.471600 0.881812i \(-0.343676\pi\)
\(18\) 37.0000 + 64.0859i 0.484499 + 0.839177i
\(19\) −40.0000 + 69.2820i −0.482980 + 0.836547i −0.999809 0.0195422i \(-0.993779\pi\)
0.516829 + 0.856089i \(0.327112\pi\)
\(20\) −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 0.742692 0.669634i \(-0.233549\pi\)
−0.951266 + 0.308373i \(0.900216\pi\)
\(32\) 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 \(-0.400160\pi\)
0.308538 + 0.951212i \(0.400160\pi\)
\(42\) 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 −0.884046 0.467401i \(-0.845191\pi\)
0.846804 + 0.531906i \(0.178524\pi\)
\(48\) 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 0.955008 0.296579i \(-0.0958458\pi\)
−0.734349 + 0.678772i \(0.762512\pi\)
\(60\) 224.000 + 387.979i 0.481971 + 0.834799i
\(61\) 99.0000 171.473i 0.207798 0.359916i −0.743223 0.669044i \(-0.766704\pi\)
0.951020 + 0.309128i \(0.100037\pi\)
\(62\) −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 0.565696 0.824614i \(-0.308608\pi\)
−0.996985 + 0.0776001i \(0.975274\pi\)
\(74\) −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 \(-0.750781\pi\)
−0.708839 + 0.705370i \(0.750781\pi\)
\(84\) 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 −0.999795 0.0202521i \(-0.993553\pi\)
0.517436 + 0.855722i \(0.326886\pi\)
\(90\) 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 \(-0.249305\pi\)
0.708649 + 0.705561i \(0.249305\pi\)
\(98\) 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 \(0.0665854\pi\)
−0.309260 + 0.950978i \(0.600081\pi\)
\(102\) 592.000 + 1025.37i 0.574674 + 0.995364i
\(103\) 416.000 720.533i 0.397958 0.689284i −0.595516 0.803344i \(-0.703052\pi\)
0.993474 + 0.114060i \(0.0363856\pi\)
\(104\) −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 −0.689283 0.724492i \(-0.742074\pi\)
0.972070 + 0.234691i \(0.0754078\pi\)
\(132\) −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 \(-0.173992\pi\)
0.854291 + 0.519795i \(0.173992\pi\)
\(140\) 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 \(0.0725254\pi\)
−0.291461 + 0.956583i \(0.594141\pi\)
\(158\) 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 \(-0.459775\pi\)
0.126036 + 0.992026i \(0.459775\pi\)
\(168\) 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 −0.994696 0.102859i \(-0.967201\pi\)
0.586427 + 0.810002i \(0.300534\pi\)
\(174\) −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 \(-0.660878\pi\)
−0.484168 + 0.874975i \(0.660878\pi\)
\(182\) 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 0.758420 0.651766i \(-0.225971\pi\)
−0.943656 + 0.330929i \(0.892638\pi\)
\(200\) 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 \(-0.296844\pi\)
0.595778 + 0.803149i \(0.296844\pi\)
\(224\) 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 \(0.0284954\pi\)
−0.420574 + 0.907258i \(0.638171\pi\)
\(228\) −1280.00 2217.03i −0.371799 0.643974i
\(229\) −2405.00 + 4165.58i −0.694004 + 1.20205i 0.276512 + 0.961011i \(0.410822\pi\)
−0.970515 + 0.241039i \(0.922512\pi\)
\(230\) −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 0.696705 0.717358i \(-0.254649\pi\)
−0.969603 + 0.244685i \(0.921315\pi\)
\(242\) −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 \(-0.521148\pi\)
−0.0663886 + 0.997794i \(0.521148\pi\)
\(252\) 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 \(0.406312\pi\)
−0.973833 + 0.227265i \(0.927022\pi\)
\(258\) 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 0.930659 0.365888i \(-0.119235\pi\)
−0.782198 + 0.623030i \(0.785901\pi\)
\(270\) −1120.00 1939.90i −0.252448 0.437253i
\(271\) 1104.00 1912.18i 0.247466 0.428623i −0.715356 0.698760i \(-0.753736\pi\)
0.962822 + 0.270137i \(0.0870689\pi\)
\(272\) 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 0.937434 0.348163i \(-0.113194\pi\)
−0.770235 + 0.637760i \(0.779861\pi\)
\(284\) −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 \(-0.666910\pi\)
−0.500663 + 0.865642i \(0.666910\pi\)
\(294\) 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 \(-0.846800\pi\)
−0.886398 + 0.462924i \(0.846800\pi\)
\(308\) 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 0.906771 0.421624i \(-0.138540\pi\)
−0.818523 + 0.574474i \(0.805207\pi\)
\(312\) 576.000 + 997.661i 0.104518 + 0.181030i
\(313\) −1529.00 + 2648.31i −0.276116 + 0.478246i −0.970416 0.241439i \(-0.922381\pi\)
0.694300 + 0.719685i \(0.255714\pi\)
\(314\) 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 \(-0.467477\pi\)
0.101996 + 0.994785i \(0.467477\pi\)
\(350\) 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 0.826803 0.562492i \(-0.190157\pi\)
−0.900533 + 0.434787i \(0.856824\pi\)
\(354\) −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 \(0.0444136\pi\)
−0.374696 + 0.927148i \(0.622253\pi\)
\(368\) 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 −0.579785 0.814769i \(-0.696864\pi\)
0.995504 + 0.0947240i \(0.0301968\pi\)
\(384\) −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 −0.981671 0.190586i \(-0.938961\pi\)
0.655887 + 0.754859i \(0.272295\pi\)
\(398\) −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 0.635256 0.772302i \(-0.280895\pi\)
−0.986461 + 0.163996i \(0.947561\pi\)
\(410\) −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 \(-0.209814\pi\)
0.790512 + 0.612446i \(0.209814\pi\)
\(420\) 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 \(-0.590635\pi\)
−0.280906 + 0.959735i \(0.590635\pi\)
\(434\) 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 −0.977613 0.210410i \(-0.932520\pi\)
0.671027 + 0.741433i \(0.265853\pi\)
\(440\) −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 \(-0.380094\pi\)
0.367849 + 0.929886i \(0.380094\pi\)
\(462\) 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 −0.787797 0.615935i \(-0.788778\pi\)
0.927314 + 0.374285i \(0.122112\pi\)
\(468\) 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 0.931490 0.363766i \(-0.118509\pi\)
−0.780776 + 0.624811i \(0.785176\pi\)
\(480\) −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 \(-0.521347\pi\)
−0.0670147 + 0.997752i \(0.521347\pi\)
\(504\) 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 \(-0.661740\pi\)
0.999880 0.0154756i \(-0.00492624\pi\)
\(510\) 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 0.835972 0.548773i \(-0.184905\pi\)
−0.893237 + 0.449586i \(0.851571\pi\)
\(522\) 7030.00 + 12176.3i 0.589454 + 1.02096i
\(523\) −3484.00 + 6034.47i −0.291290 + 0.504529i −0.974115 0.226053i \(-0.927418\pi\)
0.682825 + 0.730582i \(0.260751\pi\)
\(524\) −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 \(-0.782491\pi\)
−0.159048 0.987271i \(-0.550842\pi\)
\(564\) −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 0.976545 0.215316i \(-0.0690780\pi\)
−0.674741 + 0.738055i \(0.735745\pi\)
\(578\) 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 \(-0.245678\pi\)
0.716642 + 0.697441i \(0.245678\pi\)
\(588\) 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 −0.981454 0.191698i \(-0.938601\pi\)
0.656742 + 0.754115i \(0.271934\pi\)
\(594\) 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 \(-0.417390\pi\)
0.256623 + 0.966512i \(0.417390\pi\)
\(602\) 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 −0.811978 0.583688i \(-0.801609\pi\)
0.911478 + 0.411350i \(0.134943\pi\)
\(608\) −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 \(-0.967489\pi\)
0.409095 0.912492i \(-0.365845\pi\)
\(620\) 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 \(-0.796215\pi\)
−0.801971 + 0.597363i \(0.796215\pi\)
\(644\) 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 \(-0.883261\pi\)
0.156211 0.987724i \(-0.450072\pi\)
\(648\) −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 0.898109 0.439773i \(-0.144941\pi\)
−0.829909 + 0.557898i \(0.811608\pi\)
\(662\) 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 \(0.423416\pi\)
−0.960221 + 0.279242i \(0.909917\pi\)
\(678\) −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 \(0.359348\pi\)
−0.996662 + 0.0816365i \(0.973985\pi\)
\(692\) 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 −0.511309 0.859397i \(-0.670839\pi\)
0.999914 + 0.0131086i \(0.00417273\pi\)
\(720\) −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 \(-0.0940849\pi\)
0.956634 + 0.291291i \(0.0940849\pi\)
\(728\) 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 −0.983686 0.179894i \(-0.942425\pi\)
0.647635 + 0.761950i \(0.275758\pi\)
\(734\) 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 \(-0.525588\pi\)
0.903378 0.428844i \(-0.141079\pi\)
\(762\) −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 \(-0.130231\pi\)
0.917467 + 0.397812i \(0.130231\pi\)
\(770\) 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 \(0.0399476\pi\)
−0.387667 + 0.921799i \(0.626719\pi\)
\(774\) −15244.0 26403.4i −0.707925 1.22616i
\(775\) −2556.00 + 4427.12i −0.118470 + 0.205196i
\(776\) −10832.0