Properties

Label 22.3.b.a.21.2
Level $22$
Weight $3$
Character 22.21
Analytic conductor $0.599$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 22.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.599456581593\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
Defining polynomial: \( x^{2} + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 21.2
Root \(1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 22.21
Dual form 22.3.b.a.21.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{5} +1.41421i q^{6} -8.48528i q^{7} -2.82843i q^{8} -8.00000 q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{5} +1.41421i q^{6} -8.48528i q^{7} -2.82843i q^{8} -8.00000 q^{9} -1.41421i q^{10} +(7.00000 + 8.48528i) q^{11} -2.00000 q^{12} +8.48528i q^{13} +12.0000 q^{14} -1.00000 q^{15} +4.00000 q^{16} +25.4558i q^{17} -11.3137i q^{18} -25.4558i q^{19} +2.00000 q^{20} -8.48528i q^{21} +(-12.0000 + 9.89949i) q^{22} +17.0000 q^{23} -2.82843i q^{24} -24.0000 q^{25} -12.0000 q^{26} -17.0000 q^{27} +16.9706i q^{28} -33.9411i q^{29} -1.41421i q^{30} +17.0000 q^{31} +5.65685i q^{32} +(7.00000 + 8.48528i) q^{33} -36.0000 q^{34} +8.48528i q^{35} +16.0000 q^{36} +47.0000 q^{37} +36.0000 q^{38} +8.48528i q^{39} +2.82843i q^{40} +8.48528i q^{41} +12.0000 q^{42} +16.9706i q^{43} +(-14.0000 - 16.9706i) q^{44} +8.00000 q^{45} +24.0416i q^{46} -58.0000 q^{47} +4.00000 q^{48} -23.0000 q^{49} -33.9411i q^{50} +25.4558i q^{51} -16.9706i q^{52} +2.00000 q^{53} -24.0416i q^{54} +(-7.00000 - 8.48528i) q^{55} -24.0000 q^{56} -25.4558i q^{57} +48.0000 q^{58} -55.0000 q^{59} +2.00000 q^{60} -84.8528i q^{61} +24.0416i q^{62} +67.8823i q^{63} -8.00000 q^{64} -8.48528i q^{65} +(-12.0000 + 9.89949i) q^{66} +89.0000 q^{67} -50.9117i q^{68} +17.0000 q^{69} -12.0000 q^{70} -7.00000 q^{71} +22.6274i q^{72} +127.279i q^{73} +66.4680i q^{74} -24.0000 q^{75} +50.9117i q^{76} +(72.0000 - 59.3970i) q^{77} -12.0000 q^{78} -33.9411i q^{79} -4.00000 q^{80} +55.0000 q^{81} -12.0000 q^{82} -33.9411i q^{83} +16.9706i q^{84} -25.4558i q^{85} -24.0000 q^{86} -33.9411i q^{87} +(24.0000 - 19.7990i) q^{88} -97.0000 q^{89} +11.3137i q^{90} +72.0000 q^{91} -34.0000 q^{92} +17.0000 q^{93} -82.0244i q^{94} +25.4558i q^{95} +5.65685i q^{96} -121.000 q^{97} -32.5269i q^{98} +(-56.0000 - 67.8823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - 4 q^{4} - 2 q^{5} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} - 4 q^{4} - 2 q^{5} - 16 q^{9} + 14 q^{11} - 4 q^{12} + 24 q^{14} - 2 q^{15} + 8 q^{16} + 4 q^{20} - 24 q^{22} + 34 q^{23} - 48 q^{25} - 24 q^{26} - 34 q^{27} + 34 q^{31} + 14 q^{33} - 72 q^{34} + 32 q^{36} + 94 q^{37} + 72 q^{38} + 24 q^{42} - 28 q^{44} + 16 q^{45} - 116 q^{47} + 8 q^{48} - 46 q^{49} + 4 q^{53} - 14 q^{55} - 48 q^{56} + 96 q^{58} - 110 q^{59} + 4 q^{60} - 16 q^{64} - 24 q^{66} + 178 q^{67} + 34 q^{69} - 24 q^{70} - 14 q^{71} - 48 q^{75} + 144 q^{77} - 24 q^{78} - 8 q^{80} + 110 q^{81} - 24 q^{82} - 48 q^{86} + 48 q^{88} - 194 q^{89} + 144 q^{91} - 68 q^{92} + 34 q^{93} - 242 q^{97} - 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(-1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 1.00000 0.333333 0.166667 0.986013i \(-0.446700\pi\)
0.166667 + 0.986013i \(0.446700\pi\)
\(4\) −2.00000 −0.500000
\(5\) −1.00000 −0.200000 −0.100000 0.994987i \(-0.531884\pi\)
−0.100000 + 0.994987i \(0.531884\pi\)
\(6\) 1.41421i 0.235702i
\(7\) 8.48528i 1.21218i −0.795395 0.606092i \(-0.792737\pi\)
0.795395 0.606092i \(-0.207263\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −8.00000 −0.888889
\(10\) 1.41421i 0.141421i
\(11\) 7.00000 + 8.48528i 0.636364 + 0.771389i
\(12\) −2.00000 −0.166667
\(13\) 8.48528i 0.652714i 0.945247 + 0.326357i \(0.105821\pi\)
−0.945247 + 0.326357i \(0.894179\pi\)
\(14\) 12.0000 0.857143
\(15\) −1.00000 −0.0666667
\(16\) 4.00000 0.250000
\(17\) 25.4558i 1.49740i 0.662908 + 0.748701i \(0.269322\pi\)
−0.662908 + 0.748701i \(0.730678\pi\)
\(18\) 11.3137i 0.628539i
\(19\) 25.4558i 1.33978i −0.742460 0.669891i \(-0.766341\pi\)
0.742460 0.669891i \(-0.233659\pi\)
\(20\) 2.00000 0.100000
\(21\) 8.48528i 0.404061i
\(22\) −12.0000 + 9.89949i −0.545455 + 0.449977i
\(23\) 17.0000 0.739130 0.369565 0.929205i \(-0.379507\pi\)
0.369565 + 0.929205i \(0.379507\pi\)
\(24\) 2.82843i 0.117851i
\(25\) −24.0000 −0.960000
\(26\) −12.0000 −0.461538
\(27\) −17.0000 −0.629630
\(28\) 16.9706i 0.606092i
\(29\) 33.9411i 1.17038i −0.810895 0.585192i \(-0.801019\pi\)
0.810895 0.585192i \(-0.198981\pi\)
\(30\) 1.41421i 0.0471405i
\(31\) 17.0000 0.548387 0.274194 0.961675i \(-0.411589\pi\)
0.274194 + 0.961675i \(0.411589\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 7.00000 + 8.48528i 0.212121 + 0.257130i
\(34\) −36.0000 −1.05882
\(35\) 8.48528i 0.242437i
\(36\) 16.0000 0.444444
\(37\) 47.0000 1.27027 0.635135 0.772401i \(-0.280944\pi\)
0.635135 + 0.772401i \(0.280944\pi\)
\(38\) 36.0000 0.947368
\(39\) 8.48528i 0.217571i
\(40\) 2.82843i 0.0707107i
\(41\) 8.48528i 0.206958i 0.994632 + 0.103479i \(0.0329975\pi\)
−0.994632 + 0.103479i \(0.967003\pi\)
\(42\) 12.0000 0.285714
\(43\) 16.9706i 0.394664i 0.980337 + 0.197332i \(0.0632277\pi\)
−0.980337 + 0.197332i \(0.936772\pi\)
\(44\) −14.0000 16.9706i −0.318182 0.385695i
\(45\) 8.00000 0.177778
\(46\) 24.0416i 0.522644i
\(47\) −58.0000 −1.23404 −0.617021 0.786946i \(-0.711661\pi\)
−0.617021 + 0.786946i \(0.711661\pi\)
\(48\) 4.00000 0.0833333
\(49\) −23.0000 −0.469388
\(50\) 33.9411i 0.678823i
\(51\) 25.4558i 0.499134i
\(52\) 16.9706i 0.326357i
\(53\) 2.00000 0.0377358 0.0188679 0.999822i \(-0.493994\pi\)
0.0188679 + 0.999822i \(0.493994\pi\)
\(54\) 24.0416i 0.445215i
\(55\) −7.00000 8.48528i −0.127273 0.154278i
\(56\) −24.0000 −0.428571
\(57\) 25.4558i 0.446594i
\(58\) 48.0000 0.827586
\(59\) −55.0000 −0.932203 −0.466102 0.884731i \(-0.654342\pi\)
−0.466102 + 0.884731i \(0.654342\pi\)
\(60\) 2.00000 0.0333333
\(61\) 84.8528i 1.39103i −0.718512 0.695515i \(-0.755176\pi\)
0.718512 0.695515i \(-0.244824\pi\)
\(62\) 24.0416i 0.387768i
\(63\) 67.8823i 1.07750i
\(64\) −8.00000 −0.125000
\(65\) 8.48528i 0.130543i
\(66\) −12.0000 + 9.89949i −0.181818 + 0.149992i
\(67\) 89.0000 1.32836 0.664179 0.747573i \(-0.268781\pi\)
0.664179 + 0.747573i \(0.268781\pi\)
\(68\) 50.9117i 0.748701i
\(69\) 17.0000 0.246377
\(70\) −12.0000 −0.171429
\(71\) −7.00000 −0.0985915 −0.0492958 0.998784i \(-0.515698\pi\)
−0.0492958 + 0.998784i \(0.515698\pi\)
\(72\) 22.6274i 0.314270i
\(73\) 127.279i 1.74355i 0.489906 + 0.871775i \(0.337031\pi\)
−0.489906 + 0.871775i \(0.662969\pi\)
\(74\) 66.4680i 0.898217i
\(75\) −24.0000 −0.320000
\(76\) 50.9117i 0.669891i
\(77\) 72.0000 59.3970i 0.935065 0.771389i
\(78\) −12.0000 −0.153846
\(79\) 33.9411i 0.429634i −0.976654 0.214817i \(-0.931084\pi\)
0.976654 0.214817i \(-0.0689156\pi\)
\(80\) −4.00000 −0.0500000
\(81\) 55.0000 0.679012
\(82\) −12.0000 −0.146341
\(83\) 33.9411i 0.408929i −0.978874 0.204465i \(-0.934455\pi\)
0.978874 0.204465i \(-0.0655453\pi\)
\(84\) 16.9706i 0.202031i
\(85\) 25.4558i 0.299481i
\(86\) −24.0000 −0.279070
\(87\) 33.9411i 0.390128i
\(88\) 24.0000 19.7990i 0.272727 0.224989i
\(89\) −97.0000 −1.08989 −0.544944 0.838473i \(-0.683449\pi\)
−0.544944 + 0.838473i \(0.683449\pi\)
\(90\) 11.3137i 0.125708i
\(91\) 72.0000 0.791209
\(92\) −34.0000 −0.369565
\(93\) 17.0000 0.182796
\(94\) 82.0244i 0.872600i
\(95\) 25.4558i 0.267956i
\(96\) 5.65685i 0.0589256i
\(97\) −121.000 −1.24742 −0.623711 0.781655i \(-0.714376\pi\)
−0.623711 + 0.781655i \(0.714376\pi\)
\(98\) 32.5269i 0.331907i
\(99\) −56.0000 67.8823i −0.565657 0.685679i
\(100\) 48.0000 0.480000
\(101\) 8.48528i 0.0840127i −0.999117 0.0420063i \(-0.986625\pi\)
0.999117 0.0420063i \(-0.0133750\pi\)
\(102\) −36.0000 −0.352941
\(103\) −82.0000 −0.796117 −0.398058 0.917360i \(-0.630316\pi\)
−0.398058 + 0.917360i \(0.630316\pi\)
\(104\) 24.0000 0.230769
\(105\) 8.48528i 0.0808122i
\(106\) 2.82843i 0.0266833i
\(107\) 76.3675i 0.713715i 0.934159 + 0.356858i \(0.116152\pi\)
−0.934159 + 0.356858i \(0.883848\pi\)
\(108\) 34.0000 0.314815
\(109\) 152.735i 1.40124i 0.713535 + 0.700620i \(0.247093\pi\)
−0.713535 + 0.700620i \(0.752907\pi\)
\(110\) 12.0000 9.89949i 0.109091 0.0899954i
\(111\) 47.0000 0.423423
\(112\) 33.9411i 0.303046i
\(113\) −1.00000 −0.00884956 −0.00442478 0.999990i \(-0.501408\pi\)
−0.00442478 + 0.999990i \(0.501408\pi\)
\(114\) 36.0000 0.315789
\(115\) −17.0000 −0.147826
\(116\) 67.8823i 0.585192i
\(117\) 67.8823i 0.580190i
\(118\) 77.7817i 0.659167i
\(119\) 216.000 1.81513
\(120\) 2.82843i 0.0235702i
\(121\) −23.0000 + 118.794i −0.190083 + 0.981768i
\(122\) 120.000 0.983607
\(123\) 8.48528i 0.0689860i
\(124\) −34.0000 −0.274194
\(125\) 49.0000 0.392000
\(126\) −96.0000 −0.761905
\(127\) 25.4558i 0.200440i −0.994965 0.100220i \(-0.968045\pi\)
0.994965 0.100220i \(-0.0319546\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 16.9706i 0.131555i
\(130\) 12.0000 0.0923077
\(131\) 93.3381i 0.712505i −0.934390 0.356252i \(-0.884054\pi\)
0.934390 0.356252i \(-0.115946\pi\)
\(132\) −14.0000 16.9706i −0.106061 0.128565i
\(133\) −216.000 −1.62406
\(134\) 125.865i 0.939291i
\(135\) 17.0000 0.125926
\(136\) 72.0000 0.529412
\(137\) 167.000 1.21898 0.609489 0.792794i \(-0.291375\pi\)
0.609489 + 0.792794i \(0.291375\pi\)
\(138\) 24.0416i 0.174215i
\(139\) 93.3381i 0.671497i −0.941952 0.335749i \(-0.891011\pi\)
0.941952 0.335749i \(-0.108989\pi\)
\(140\) 16.9706i 0.121218i
\(141\) −58.0000 −0.411348
\(142\) 9.89949i 0.0697148i
\(143\) −72.0000 + 59.3970i −0.503497 + 0.415363i
\(144\) −32.0000 −0.222222
\(145\) 33.9411i 0.234077i
\(146\) −180.000 −1.23288
\(147\) −23.0000 −0.156463
\(148\) −94.0000 −0.635135
\(149\) 161.220i 1.08202i 0.841018 + 0.541008i \(0.181957\pi\)
−0.841018 + 0.541008i \(0.818043\pi\)
\(150\) 33.9411i 0.226274i
\(151\) 288.500i 1.91059i −0.295649 0.955297i \(-0.595536\pi\)
0.295649 0.955297i \(-0.404464\pi\)
\(152\) −72.0000 −0.473684
\(153\) 203.647i 1.33102i
\(154\) 84.0000 + 101.823i 0.545455 + 0.661191i
\(155\) −17.0000 −0.109677
\(156\) 16.9706i 0.108786i
\(157\) −1.00000 −0.00636943 −0.00318471 0.999995i \(-0.501014\pi\)
−0.00318471 + 0.999995i \(0.501014\pi\)
\(158\) 48.0000 0.303797
\(159\) 2.00000 0.0125786
\(160\) 5.65685i 0.0353553i
\(161\) 144.250i 0.895961i
\(162\) 77.7817i 0.480134i
\(163\) 110.000 0.674847 0.337423 0.941353i \(-0.390445\pi\)
0.337423 + 0.941353i \(0.390445\pi\)
\(164\) 16.9706i 0.103479i
\(165\) −7.00000 8.48528i −0.0424242 0.0514259i
\(166\) 48.0000 0.289157
\(167\) 110.309i 0.660531i 0.943888 + 0.330265i \(0.107138\pi\)
−0.943888 + 0.330265i \(0.892862\pi\)
\(168\) −24.0000 −0.142857
\(169\) 97.0000 0.573964
\(170\) 36.0000 0.211765
\(171\) 203.647i 1.19092i
\(172\) 33.9411i 0.197332i
\(173\) 16.9706i 0.0980957i 0.998796 + 0.0490479i \(0.0156187\pi\)
−0.998796 + 0.0490479i \(0.984381\pi\)
\(174\) 48.0000 0.275862
\(175\) 203.647i 1.16370i
\(176\) 28.0000 + 33.9411i 0.159091 + 0.192847i
\(177\) −55.0000 −0.310734
\(178\) 137.179i 0.770667i
\(179\) 209.000 1.16760 0.583799 0.811898i \(-0.301566\pi\)
0.583799 + 0.811898i \(0.301566\pi\)
\(180\) −16.0000 −0.0888889
\(181\) 119.000 0.657459 0.328729 0.944424i \(-0.393380\pi\)
0.328729 + 0.944424i \(0.393380\pi\)
\(182\) 101.823i 0.559469i
\(183\) 84.8528i 0.463677i
\(184\) 48.0833i 0.261322i
\(185\) −47.0000 −0.254054
\(186\) 24.0416i 0.129256i
\(187\) −216.000 + 178.191i −1.15508 + 0.952893i
\(188\) 116.000 0.617021
\(189\) 144.250i 0.763226i
\(190\) −36.0000 −0.189474
\(191\) −319.000 −1.67016 −0.835079 0.550131i \(-0.814578\pi\)
−0.835079 + 0.550131i \(0.814578\pi\)
\(192\) −8.00000 −0.0416667
\(193\) 16.9706i 0.0879304i −0.999033 0.0439652i \(-0.986001\pi\)
0.999033 0.0439652i \(-0.0139991\pi\)
\(194\) 171.120i 0.882061i
\(195\) 8.48528i 0.0435143i
\(196\) 46.0000 0.234694
\(197\) 101.823i 0.516870i −0.966029 0.258435i \(-0.916793\pi\)
0.966029 0.258435i \(-0.0832068\pi\)
\(198\) 96.0000 79.1960i 0.484848 0.399980i
\(199\) 182.000 0.914573 0.457286 0.889319i \(-0.348821\pi\)
0.457286 + 0.889319i \(0.348821\pi\)
\(200\) 67.8823i 0.339411i
\(201\) 89.0000 0.442786
\(202\) 12.0000 0.0594059
\(203\) −288.000 −1.41872
\(204\) 50.9117i 0.249567i
\(205\) 8.48528i 0.0413916i
\(206\) 115.966i 0.562939i
\(207\) −136.000 −0.657005
\(208\) 33.9411i 0.163178i
\(209\) 216.000 178.191i 1.03349 0.852588i
\(210\) −12.0000 −0.0571429
\(211\) 118.794i 0.563004i −0.959561 0.281502i \(-0.909167\pi\)
0.959561 0.281502i \(-0.0908327\pi\)
\(212\) −4.00000 −0.0188679
\(213\) −7.00000 −0.0328638
\(214\) −108.000 −0.504673
\(215\) 16.9706i 0.0789328i
\(216\) 48.0833i 0.222608i
\(217\) 144.250i 0.664746i
\(218\) −216.000 −0.990826
\(219\) 127.279i 0.581184i
\(220\) 14.0000 + 16.9706i 0.0636364 + 0.0771389i
\(221\) −216.000 −0.977376
\(222\) 66.4680i 0.299406i
\(223\) −31.0000 −0.139013 −0.0695067 0.997581i \(-0.522143\pi\)
−0.0695067 + 0.997581i \(0.522143\pi\)
\(224\) 48.0000 0.214286
\(225\) 192.000 0.853333
\(226\) 1.41421i 0.00625758i
\(227\) 93.3381i 0.411181i 0.978638 + 0.205591i \(0.0659115\pi\)
−0.978638 + 0.205591i \(0.934089\pi\)
\(228\) 50.9117i 0.223297i
\(229\) −73.0000 −0.318777 −0.159389 0.987216i \(-0.550952\pi\)
−0.159389 + 0.987216i \(0.550952\pi\)
\(230\) 24.0416i 0.104529i
\(231\) 72.0000 59.3970i 0.311688 0.257130i
\(232\) −96.0000 −0.413793
\(233\) 203.647i 0.874020i −0.899457 0.437010i \(-0.856037\pi\)
0.899457 0.437010i \(-0.143963\pi\)
\(234\) 96.0000 0.410256
\(235\) 58.0000 0.246809
\(236\) 110.000 0.466102
\(237\) 33.9411i 0.143211i
\(238\) 305.470i 1.28349i
\(239\) 288.500i 1.20711i 0.797321 + 0.603556i \(0.206250\pi\)
−0.797321 + 0.603556i \(0.793750\pi\)
\(240\) −4.00000 −0.0166667
\(241\) 118.794i 0.492921i 0.969153 + 0.246460i \(0.0792675\pi\)
−0.969153 + 0.246460i \(0.920732\pi\)
\(242\) −168.000 32.5269i −0.694215 0.134409i
\(243\) 208.000 0.855967
\(244\) 169.706i 0.695515i
\(245\) 23.0000 0.0938776
\(246\) −12.0000 −0.0487805
\(247\) 216.000 0.874494
\(248\) 48.0833i 0.193884i
\(249\) 33.9411i 0.136310i
\(250\) 69.2965i 0.277186i
\(251\) 65.0000 0.258964 0.129482 0.991582i \(-0.458669\pi\)
0.129482 + 0.991582i \(0.458669\pi\)
\(252\) 135.765i 0.538748i
\(253\) 119.000 + 144.250i 0.470356 + 0.570157i
\(254\) 36.0000 0.141732
\(255\) 25.4558i 0.0998268i
\(256\) 16.0000 0.0625000
\(257\) 170.000 0.661479 0.330739 0.943722i \(-0.392702\pi\)
0.330739 + 0.943722i \(0.392702\pi\)
\(258\) −24.0000 −0.0930233
\(259\) 398.808i 1.53980i
\(260\) 16.9706i 0.0652714i
\(261\) 271.529i 1.04034i
\(262\) 132.000 0.503817
\(263\) 313.955i 1.19375i −0.802335 0.596873i \(-0.796409\pi\)
0.802335 0.596873i \(-0.203591\pi\)
\(264\) 24.0000 19.7990i 0.0909091 0.0749962i
\(265\) −2.00000 −0.00754717
\(266\) 305.470i 1.14838i
\(267\) −97.0000 −0.363296
\(268\) −178.000 −0.664179
\(269\) −430.000 −1.59851 −0.799257 0.600990i \(-0.794773\pi\)
−0.799257 + 0.600990i \(0.794773\pi\)
\(270\) 24.0416i 0.0890431i
\(271\) 381.838i 1.40900i 0.709706 + 0.704498i \(0.248828\pi\)
−0.709706 + 0.704498i \(0.751172\pi\)
\(272\) 101.823i 0.374351i
\(273\) 72.0000 0.263736
\(274\) 236.174i 0.861948i
\(275\) −168.000 203.647i −0.610909 0.740534i
\(276\) −34.0000 −0.123188
\(277\) 84.8528i 0.306328i −0.988201 0.153164i \(-0.951054\pi\)
0.988201 0.153164i \(-0.0489463\pi\)
\(278\) 132.000 0.474820
\(279\) −136.000 −0.487455
\(280\) 24.0000 0.0857143
\(281\) 135.765i 0.483148i −0.970382 0.241574i \(-0.922336\pi\)
0.970382 0.241574i \(-0.0776636\pi\)
\(282\) 82.0244i 0.290867i
\(283\) 67.8823i 0.239867i −0.992782 0.119933i \(-0.961732\pi\)
0.992782 0.119933i \(-0.0382681\pi\)
\(284\) 14.0000 0.0492958
\(285\) 25.4558i 0.0893188i
\(286\) −84.0000 101.823i −0.293706 0.356026i
\(287\) 72.0000 0.250871
\(288\) 45.2548i 0.157135i
\(289\) −359.000 −1.24221
\(290\) −48.0000 −0.165517
\(291\) −121.000 −0.415808
\(292\) 254.558i 0.871775i
\(293\) 517.602i 1.76656i 0.468846 + 0.883280i \(0.344670\pi\)
−0.468846 + 0.883280i \(0.655330\pi\)
\(294\) 32.5269i 0.110636i
\(295\) 55.0000 0.186441
\(296\) 132.936i 0.449108i
\(297\) −119.000 144.250i −0.400673 0.485690i
\(298\) −228.000 −0.765101
\(299\) 144.250i 0.482441i
\(300\) 48.0000 0.160000
\(301\) 144.000 0.478405
\(302\) 408.000 1.35099
\(303\) 8.48528i 0.0280042i
\(304\) 101.823i 0.334945i
\(305\) 84.8528i 0.278206i
\(306\) 288.000 0.941176
\(307\) 25.4558i 0.0829181i 0.999140 + 0.0414590i \(0.0132006\pi\)
−0.999140 + 0.0414590i \(0.986799\pi\)
\(308\) −144.000 + 118.794i −0.467532 + 0.385695i
\(309\) −82.0000 −0.265372
\(310\) 24.0416i 0.0775536i
\(311\) −154.000 −0.495177 −0.247588 0.968865i \(-0.579638\pi\)
−0.247588 + 0.968865i \(0.579638\pi\)
\(312\) 24.0000 0.0769231
\(313\) 95.0000 0.303514 0.151757 0.988418i \(-0.451507\pi\)
0.151757 + 0.988418i \(0.451507\pi\)
\(314\) 1.41421i 0.00450386i
\(315\) 67.8823i 0.215499i
\(316\) 67.8823i 0.214817i
\(317\) 23.0000 0.0725552 0.0362776 0.999342i \(-0.488450\pi\)
0.0362776 + 0.999342i \(0.488450\pi\)
\(318\) 2.82843i 0.00889442i
\(319\) 288.000 237.588i 0.902821 0.744790i
\(320\) 8.00000 0.0250000
\(321\) 76.3675i 0.237905i
\(322\) 204.000 0.633540
\(323\) 648.000 2.00619
\(324\) −110.000 −0.339506
\(325\) 203.647i 0.626605i
\(326\) 155.563i 0.477189i
\(327\) 152.735i 0.467080i
\(328\) 24.0000 0.0731707
\(329\) 492.146i 1.49589i
\(330\) 12.0000 9.89949i 0.0363636 0.0299985i
\(331\) 185.000 0.558912 0.279456 0.960158i \(-0.409846\pi\)
0.279456 + 0.960158i \(0.409846\pi\)
\(332\) 67.8823i 0.204465i
\(333\) −376.000 −1.12913
\(334\) −156.000 −0.467066
\(335\) −89.0000 −0.265672
\(336\) 33.9411i 0.101015i
\(337\) 8.48528i 0.0251789i 0.999921 + 0.0125894i \(0.00400745\pi\)
−0.999921 + 0.0125894i \(0.995993\pi\)
\(338\) 137.179i 0.405854i
\(339\) −1.00000 −0.00294985
\(340\) 50.9117i 0.149740i
\(341\) 119.000 + 144.250i 0.348974 + 0.423020i
\(342\) −288.000 −0.842105
\(343\) 220.617i 0.643199i
\(344\) 48.0000 0.139535
\(345\) −17.0000 −0.0492754
\(346\) −24.0000 −0.0693642
\(347\) 212.132i 0.611332i 0.952139 + 0.305666i \(0.0988790\pi\)
−0.952139 + 0.305666i \(0.901121\pi\)
\(348\) 67.8823i 0.195064i
\(349\) 263.044i 0.753707i −0.926273 0.376853i \(-0.877006\pi\)
0.926273 0.376853i \(-0.122994\pi\)
\(350\) −288.000 −0.822857
\(351\) 144.250i 0.410968i
\(352\) −48.0000 + 39.5980i −0.136364 + 0.112494i
\(353\) 167.000 0.473088 0.236544 0.971621i \(-0.423985\pi\)
0.236544 + 0.971621i \(0.423985\pi\)
\(354\) 77.7817i 0.219722i
\(355\) 7.00000 0.0197183
\(356\) 194.000 0.544944
\(357\) 216.000 0.605042
\(358\) 295.571i 0.825616i
\(359\) 636.396i 1.77269i −0.463024 0.886346i \(-0.653236\pi\)
0.463024 0.886346i \(-0.346764\pi\)
\(360\) 22.6274i 0.0628539i
\(361\) −287.000 −0.795014
\(362\) 168.291i 0.464893i
\(363\) −23.0000 + 118.794i −0.0633609 + 0.327256i
\(364\) −144.000 −0.395604
\(365\) 127.279i 0.348710i
\(366\) 120.000 0.327869
\(367\) −607.000 −1.65395 −0.826975 0.562238i \(-0.809940\pi\)
−0.826975 + 0.562238i \(0.809940\pi\)
\(368\) 68.0000 0.184783
\(369\) 67.8823i 0.183963i
\(370\) 66.4680i 0.179643i
\(371\) 16.9706i 0.0457428i
\(372\) −34.0000 −0.0913978
\(373\) 347.897i 0.932698i −0.884601 0.466349i \(-0.845569\pi\)
0.884601 0.466349i \(-0.154431\pi\)
\(374\) −252.000 305.470i −0.673797 0.816765i
\(375\) 49.0000 0.130667
\(376\) 164.049i 0.436300i
\(377\) 288.000 0.763926
\(378\) −204.000 −0.539683
\(379\) −295.000 −0.778364 −0.389182 0.921161i \(-0.627242\pi\)
−0.389182 + 0.921161i \(0.627242\pi\)
\(380\) 50.9117i 0.133978i
\(381\) 25.4558i 0.0668132i
\(382\) 451.134i 1.18098i
\(383\) 377.000 0.984334 0.492167 0.870501i \(-0.336205\pi\)
0.492167 + 0.870501i \(0.336205\pi\)
\(384\) 11.3137i 0.0294628i
\(385\) −72.0000 + 59.3970i −0.187013 + 0.154278i
\(386\) 24.0000 0.0621762
\(387\) 135.765i 0.350813i
\(388\) 242.000 0.623711
\(389\) −121.000 −0.311054 −0.155527 0.987832i \(-0.549708\pi\)
−0.155527 + 0.987832i \(0.549708\pi\)
\(390\) 12.0000 0.0307692
\(391\) 432.749i 1.10678i
\(392\) 65.0538i 0.165954i
\(393\) 93.3381i 0.237502i
\(394\) 144.000 0.365482
\(395\) 33.9411i 0.0859269i
\(396\) 112.000 + 135.765i 0.282828 + 0.342840i
\(397\) 578.000 1.45592 0.727960 0.685620i \(-0.240469\pi\)
0.727960 + 0.685620i \(0.240469\pi\)
\(398\) 257.387i 0.646701i
\(399\) −216.000 −0.541353
\(400\) −96.0000 −0.240000
\(401\) −550.000 −1.37157 −0.685786 0.727804i \(-0.740541\pi\)
−0.685786 + 0.727804i \(0.740541\pi\)
\(402\) 125.865i 0.313097i
\(403\) 144.250i 0.357940i
\(404\) 16.9706i 0.0420063i
\(405\) −55.0000 −0.135802
\(406\) 407.294i 1.00319i
\(407\) 329.000 + 398.808i 0.808354 + 0.979873i
\(408\) 72.0000 0.176471
\(409\) 593.970i 1.45225i 0.687563 + 0.726124i \(0.258680\pi\)
−0.687563 + 0.726124i \(0.741320\pi\)
\(410\) 12.0000 0.0292683
\(411\) 167.000 0.406326
\(412\) 164.000 0.398058
\(413\) 466.690i 1.13000i
\(414\) 192.333i 0.464573i
\(415\) 33.9411i 0.0817858i
\(416\) −48.0000 −0.115385
\(417\) 93.3381i 0.223832i
\(418\) 252.000 + 305.470i 0.602871 + 0.730790i
\(419\) −370.000 −0.883055 −0.441527 0.897248i \(-0.645563\pi\)
−0.441527 + 0.897248i \(0.645563\pi\)
\(420\) 16.9706i 0.0404061i
\(421\) 338.000 0.802850 0.401425 0.915892i \(-0.368515\pi\)
0.401425 + 0.915892i \(0.368515\pi\)
\(422\) 168.000 0.398104
\(423\) 464.000 1.09693
\(424\) 5.65685i 0.0133416i
\(425\) 610.940i 1.43751i
\(426\) 9.89949i 0.0232383i
\(427\) −720.000 −1.68618
\(428\) 152.735i 0.356858i
\(429\) −72.0000 + 59.3970i −0.167832 + 0.138454i
\(430\) 24.0000 0.0558140
\(431\) 229.103i 0.531561i 0.964034 + 0.265780i \(0.0856296\pi\)
−0.964034 + 0.265780i \(0.914370\pi\)
\(432\) −68.0000 −0.157407
\(433\) −25.0000 −0.0577367 −0.0288684 0.999583i \(-0.509190\pi\)
−0.0288684 + 0.999583i \(0.509190\pi\)
\(434\) 204.000 0.470046
\(435\) 33.9411i 0.0780256i
\(436\) 305.470i 0.700620i
\(437\) 432.749i 0.990273i
\(438\) −180.000 −0.410959
\(439\) 373.352i 0.850461i 0.905085 + 0.425231i \(0.139807\pi\)
−0.905085 + 0.425231i \(0.860193\pi\)
\(440\) −24.0000 + 19.7990i −0.0545455 + 0.0449977i
\(441\) 184.000 0.417234
\(442\) 305.470i 0.691109i
\(443\) 257.000 0.580135 0.290068 0.957006i \(-0.406322\pi\)
0.290068 + 0.957006i \(0.406322\pi\)
\(444\) −94.0000 −0.211712
\(445\) 97.0000 0.217978
\(446\) 43.8406i 0.0982974i
\(447\) 161.220i 0.360672i
\(448\) 67.8823i 0.151523i
\(449\) 47.0000 0.104677 0.0523385 0.998629i \(-0.483333\pi\)
0.0523385 + 0.998629i \(0.483333\pi\)
\(450\) 271.529i 0.603398i
\(451\) −72.0000 + 59.3970i −0.159645 + 0.131701i
\(452\) 2.00000 0.00442478
\(453\) 288.500i 0.636864i
\(454\) −132.000 −0.290749
\(455\) −72.0000 −0.158242
\(456\) −72.0000 −0.157895
\(457\) 271.529i 0.594155i 0.954853 + 0.297078i \(0.0960120\pi\)
−0.954853 + 0.297078i \(0.903988\pi\)
\(458\) 103.238i 0.225410i
\(459\) 432.749i 0.942809i
\(460\) 34.0000 0.0739130
\(461\) 492.146i 1.06756i −0.845623 0.533781i \(-0.820771\pi\)
0.845623 0.533781i \(-0.179229\pi\)
\(462\) 84.0000 + 101.823i 0.181818 + 0.220397i
\(463\) −631.000 −1.36285 −0.681425 0.731887i \(-0.738640\pi\)
−0.681425 + 0.731887i \(0.738640\pi\)
\(464\) 135.765i 0.292596i
\(465\) −17.0000 −0.0365591
\(466\) 288.000 0.618026
\(467\) −367.000 −0.785867 −0.392934 0.919567i \(-0.628540\pi\)
−0.392934 + 0.919567i \(0.628540\pi\)
\(468\) 135.765i 0.290095i
\(469\) 755.190i 1.61021i
\(470\) 82.0244i 0.174520i
\(471\) −1.00000 −0.00212314
\(472\) 155.563i 0.329584i
\(473\) −144.000 + 118.794i −0.304440 + 0.251150i
\(474\) 48.0000 0.101266
\(475\) 610.940i 1.28619i
\(476\) −432.000 −0.907563
\(477\) −16.0000 −0.0335430
\(478\) −408.000 −0.853556
\(479\) 466.690i 0.974302i −0.873318 0.487151i \(-0.838036\pi\)
0.873318 0.487151i \(-0.161964\pi\)
\(480\) 5.65685i 0.0117851i
\(481\) 398.808i 0.829123i
\(482\) −168.000 −0.348548
\(483\) 144.250i 0.298654i
\(484\) 46.0000 237.588i 0.0950413 0.490884i
\(485\) 121.000 0.249485
\(486\) 294.156i 0.605260i
\(487\) −511.000 −1.04928 −0.524641 0.851324i \(-0.675800\pi\)
−0.524641 + 0.851324i \(0.675800\pi\)
\(488\) −240.000 −0.491803
\(489\) 110.000 0.224949
\(490\) 32.5269i 0.0663815i
\(491\) 33.9411i 0.0691265i 0.999403 + 0.0345633i \(0.0110040\pi\)
−0.999403 + 0.0345633i \(0.988996\pi\)
\(492\) 16.9706i 0.0344930i
\(493\) 864.000 1.75254
\(494\) 305.470i 0.618361i
\(495\) 56.0000 + 67.8823i 0.113131 + 0.137136i
\(496\) 68.0000 0.137097
\(497\) 59.3970i 0.119511i
\(498\) 48.0000 0.0963855
\(499\) 494.000 0.989980 0.494990 0.868899i \(-0.335172\pi\)
0.494990 + 0.868899i \(0.335172\pi\)
\(500\) −98.0000 −0.196000
\(501\) 110.309i 0.220177i
\(502\) 91.9239i 0.183115i
\(503\) 661.852i 1.31581i −0.753101 0.657905i \(-0.771443\pi\)
0.753101 0.657905i \(-0.228557\pi\)
\(504\) 192.000 0.380952
\(505\) 8.48528i 0.0168025i
\(506\) −204.000 + 168.291i −0.403162 + 0.332592i
\(507\) 97.0000 0.191321
\(508\) 50.9117i 0.100220i
\(509\) 503.000 0.988212 0.494106 0.869402i \(-0.335495\pi\)
0.494106 + 0.869402i \(0.335495\pi\)
\(510\) 36.0000 0.0705882
\(511\) 1080.00 2.11350
\(512\) 22.6274i 0.0441942i
\(513\) 432.749i 0.843566i
\(514\) 240.416i 0.467736i
\(515\) 82.0000 0.159223
\(516\) 33.9411i 0.0657774i
\(517\) −406.000 492.146i −0.785300 0.951927i
\(518\) 564.000 1.08880
\(519\) 16.9706i 0.0326986i
\(520\) −24.0000 −0.0461538
\(521\) −745.000 −1.42994 −0.714971 0.699154i \(-0.753560\pi\)
−0.714971 + 0.699154i \(0.753560\pi\)
\(522\) −384.000 −0.735632
\(523\) 330.926i 0.632746i 0.948635 + 0.316373i \(0.102465\pi\)
−0.948635 + 0.316373i \(0.897535\pi\)
\(524\) 186.676i 0.356252i
\(525\) 203.647i 0.387899i
\(526\) 444.000 0.844106
\(527\) 432.749i 0.821156i
\(528\) 28.0000 + 33.9411i 0.0530303 + 0.0642824i
\(529\) −240.000 −0.453686
\(530\) 2.82843i 0.00533665i
\(531\) 440.000 0.828625
\(532\) 432.000 0.812030
\(533\) −72.0000 −0.135084
\(534\) 137.179i 0.256889i
\(535\) 76.3675i 0.142743i
\(536\) 251.730i 0.469646i
\(537\) 209.000 0.389199
\(538\) 608.112i 1.13032i
\(539\) −161.000 195.161i −0.298701 0.362081i
\(540\) −34.0000 −0.0629630
\(541\) 687.308i 1.27044i −0.772331 0.635220i \(-0.780910\pi\)
0.772331 0.635220i \(-0.219090\pi\)
\(542\) −540.000 −0.996310
\(543\) 119.000 0.219153
\(544\) −144.000 −0.264706
\(545\) 152.735i 0.280248i
\(546\) 101.823i 0.186490i
\(547\) 831.558i 1.52021i 0.649797 + 0.760107i \(0.274854\pi\)
−0.649797 + 0.760107i \(0.725146\pi\)
\(548\) −334.000 −0.609489
\(549\) 678.823i 1.23647i
\(550\) 288.000 237.588i 0.523636 0.431978i
\(551\) −864.000 −1.56806
\(552\) 48.0833i 0.0871074i
\(553\) −288.000 −0.520796
\(554\) 120.000 0.216606
\(555\) −47.0000 −0.0846847
\(556\) 186.676i 0.335749i
\(557\) 636.396i 1.14254i 0.820761 + 0.571271i \(0.193550\pi\)
−0.820761 + 0.571271i \(0.806450\pi\)
\(558\) 192.333i 0.344683i
\(559\) −144.000 −0.257603
\(560\) 33.9411i 0.0606092i
\(561\) −216.000 + 178.191i −0.385027 + 0.317631i
\(562\) 192.000 0.341637
\(563\) 780.646i 1.38658i −0.720658 0.693291i \(-0.756160\pi\)
0.720658 0.693291i \(-0.243840\pi\)
\(564\) 116.000 0.205674
\(565\) 1.00000 0.00176991
\(566\) 96.0000 0.169611
\(567\) 466.690i 0.823087i
\(568\) 19.7990i 0.0348574i
\(569\) 576.999i 1.01406i 0.861929 + 0.507029i \(0.169256\pi\)
−0.861929 + 0.507029i \(0.830744\pi\)
\(570\) −36.0000 −0.0631579
\(571\) 627.911i 1.09967i −0.835274 0.549834i \(-0.814691\pi\)
0.835274 0.549834i \(-0.185309\pi\)
\(572\) 144.000 118.794i 0.251748 0.207682i
\(573\) −319.000 −0.556719
\(574\) 101.823i 0.177393i
\(575\) −408.000 −0.709565
\(576\) 64.0000 0.111111
\(577\) −385.000 −0.667244 −0.333622 0.942707i \(-0.608271\pi\)
−0.333622 + 0.942707i \(0.608271\pi\)
\(578\) 507.703i 0.878378i
\(579\) 16.9706i 0.0293101i
\(580\) 67.8823i 0.117038i
\(581\) −288.000 −0.495697
\(582\) 171.120i 0.294020i
\(583\) 14.0000 + 16.9706i 0.0240137 + 0.0291090i
\(584\) 360.000 0.616438
\(585\) 67.8823i 0.116038i
\(586\) −732.000 −1.24915
\(587\) 806.000 1.37308 0.686542 0.727090i \(-0.259128\pi\)
0.686542 + 0.727090i \(0.259128\pi\)
\(588\) 46.0000 0.0782313
\(589\) 432.749i 0.734719i
\(590\) 77.7817i 0.131833i
\(591\) 101.823i 0.172290i
\(592\) 188.000 0.317568
\(593\) 152.735i 0.257563i −0.991673 0.128782i \(-0.958893\pi\)
0.991673 0.128782i \(-0.0411066\pi\)
\(594\) 204.000 168.291i 0.343434 0.283319i
\(595\) −216.000 −0.363025
\(596\) 322.441i 0.541008i
\(597\) 182.000 0.304858
\(598\) −204.000 −0.341137
\(599\) 998.000 1.66611 0.833055 0.553190i \(-0.186590\pi\)
0.833055 + 0.553190i \(0.186590\pi\)
\(600\) 67.8823i 0.113137i
\(601\) 755.190i 1.25656i 0.777989 + 0.628278i \(0.216240\pi\)
−0.777989 + 0.628278i \(0.783760\pi\)
\(602\) 203.647i 0.338284i
\(603\) −712.000 −1.18076
\(604\) 576.999i 0.955297i
\(605\) 23.0000 118.794i 0.0380165 0.196354i
\(606\) 12.0000 0.0198020
\(607\) 373.352i 0.615078i −0.951535 0.307539i \(-0.900495\pi\)
0.951535 0.307539i \(-0.0995055\pi\)
\(608\) 144.000 0.236842
\(609\) −288.000 −0.472906
\(610\) −120.000 −0.196721
\(611\) 492.146i 0.805477i
\(612\) 407.294i 0.665512i
\(613\) 356.382i 0.581373i 0.956818 + 0.290687i \(0.0938837\pi\)
−0.956818 + 0.290687i \(0.906116\pi\)
\(614\) −36.0000 −0.0586319
\(615\) 8.48528i 0.0137972i
\(616\) −168.000 203.647i −0.272727 0.330595i
\(617\) 314.000 0.508914 0.254457 0.967084i \(-0.418103\pi\)
0.254457 + 0.967084i \(0.418103\pi\)
\(618\) 115.966i 0.187646i
\(619\) 1193.00 1.92730 0.963651 0.267164i \(-0.0860866\pi\)
0.963651 + 0.267164i \(0.0860866\pi\)
\(620\) 34.0000 0.0548387
\(621\) −289.000 −0.465378
\(622\) 217.789i 0.350143i
\(623\) 823.072i 1.32114i
\(624\) 33.9411i 0.0543928i
\(625\) 551.000 0.881600
\(626\) 134.350i 0.214617i
\(627\) 216.000 178.191i 0.344498 0.284196i
\(628\) 2.00000 0.00318471
\(629\) 1196.42i 1.90211i
\(630\) 96.0000 0.152381
\(631\) −439.000 −0.695721 −0.347861 0.937546i \(-0.613092\pi\)
−0.347861 + 0.937546i \(0.613092\pi\)
\(632\) −96.0000 −0.151899
\(633\) 118.794i 0.187668i
\(634\) 32.5269i 0.0513043i
\(635\) 25.4558i 0.0400879i
\(636\) −4.00000 −0.00628931
\(637\) 195.161i 0.306376i
\(638\) 336.000 + 407.294i 0.526646 + 0.638391i
\(639\) 56.0000 0.0876369
\(640\) 11.3137i 0.0176777i
\(641\) 671.000 1.04680 0.523401 0.852087i \(-0.324663\pi\)
0.523401 + 0.852087i \(0.324663\pi\)
\(642\) −108.000 −0.168224
\(643\) −487.000 −0.757387 −0.378694 0.925522i \(-0.623627\pi\)
−0.378694 + 0.925522i \(0.623627\pi\)
\(644\) 288.500i 0.447981i
\(645\) 16.9706i 0.0263109i
\(646\) 916.410i 1.41859i
\(647\) 569.000 0.879444 0.439722 0.898134i \(-0.355077\pi\)
0.439722 + 0.898134i \(0.355077\pi\)
\(648\) 155.563i 0.240067i
\(649\) −385.000 466.690i −0.593220 0.719092i
\(650\) 288.000 0.443077
\(651\) 144.250i 0.221582i
\(652\) −220.000 −0.337423
\(653\) −1081.00 −1.65544 −0.827718 0.561144i \(-0.810361\pi\)
−0.827718 + 0.561144i \(0.810361\pi\)
\(654\) −216.000 −0.330275
\(655\) 93.3381i 0.142501i
\(656\) 33.9411i 0.0517395i
\(657\) 1018.23i 1.54982i
\(658\) −696.000 −1.05775
\(659\) 780.646i 1.18459i 0.805721 + 0.592296i \(0.201778\pi\)
−0.805721 + 0.592296i \(0.798222\pi\)
\(660\) 14.0000 + 16.9706i 0.0212121 + 0.0257130i
\(661\) 1007.00 1.52345 0.761725 0.647901i \(-0.224353\pi\)
0.761725 + 0.647901i \(0.224353\pi\)
\(662\) 261.630i 0.395211i
\(663\) −216.000 −0.325792
\(664\) −96.0000 −0.144578
\(665\) 216.000 0.324812
\(666\) 531.744i 0.798415i
\(667\) 576.999i 0.865066i
\(668\) 220.617i 0.330265i
\(669\) −31.0000 −0.0463378
\(670\) 125.865i 0.187858i
\(671\) 720.000 593.970i 1.07303 0.885201i
\(672\) 48.0000 0.0714286
\(673\) 644.881i 0.958219i −0.877755 0.479109i \(-0.840960\pi\)
0.877755 0.479109i \(-0.159040\pi\)
\(674\) −12.0000 −0.0178042
\(675\) 408.000 0.604444
\(676\) −194.000 −0.286982
\(677\) 873.984i 1.29097i −0.763775 0.645483i \(-0.776656\pi\)
0.763775 0.645483i \(-0.223344\pi\)
\(678\) 1.41421i 0.00208586i
\(679\) 1026.72i 1.51210i
\(680\) −72.0000 −0.105882
\(681\) 93.3381i 0.137060i
\(682\) −204.000 + 168.291i −0.299120 + 0.246762i
\(683\) −610.000 −0.893119 −0.446559 0.894754i \(-0.647351\pi\)
−0.446559 + 0.894754i \(0.647351\pi\)
\(684\) 407.294i 0.595458i
\(685\) −167.000 −0.243796
\(686\) 312.000 0.454810
\(687\) −73.0000 −0.106259
\(688\) 67.8823i 0.0986661i
\(689\) 16.9706i 0.0246307i
\(690\) 24.0416i 0.0348429i
\(691\) −1255.00 −1.81621 −0.908104 0.418744i \(-0.862470\pi\)
−0.908104 + 0.418744i \(0.862470\pi\)
\(692\) 33.9411i 0.0490479i
\(693\) −576.000 + 475.176i −0.831169 + 0.685679i
\(694\) −300.000 −0.432277
\(695\) 93.3381i 0.134299i
\(696\) −96.0000 −0.137931
\(697\) −216.000 −0.309900
\(698\) 372.000 0.532951
\(699\) 203.647i 0.291340i
\(700\) 407.294i 0.581848i
\(701\) 76.3675i 0.108941i −0.998515 0.0544704i \(-0.982653\pi\)
0.998515 0.0544704i \(-0.0173471\pi\)
\(702\) 204.000 0.290598
\(703\) 1196.42i 1.70188i
\(704\) −56.0000 67.8823i −0.0795455 0.0964237i
\(705\) 58.0000 0.0822695
\(706\) 236.174i 0.334524i
\(707\) −72.0000 −0.101839
\(708\) 110.000 0.155367
\(709\) 455.000 0.641749 0.320874 0.947122i \(-0.396023\pi\)
0.320874 + 0.947122i \(0.396023\pi\)
\(710\) 9.89949i 0.0139430i
\(711\) 271.529i 0.381897i
\(712\) 274.357i 0.385333i
\(713\) 289.000 0.405330
\(714\) 305.470i 0.427829i
\(715\) 72.0000 59.3970i 0.100699 0.0830727i
\(716\) −418.000 −0.583799
\(717\) 288.500i 0.402370i
\(718\) 900.000 1.25348
\(719\) −223.000 −0.310153 −0.155076 0.987902i \(-0.549562\pi\)
−0.155076 + 0.987902i \(0.549562\pi\)
\(720\) 32.0000 0.0444444
\(721\) 695.793i 0.965039i
\(722\) 405.879i 0.562160i
\(723\) 118.794i 0.164307i
\(724\) −238.000 −0.328729
\(725\) 814.587i 1.12357i
\(726\) −168.000 32.5269i −0.231405 0.0448029i
\(727\) −535.000 −0.735901 −0.367950 0.929845i \(-0.619940\pi\)
−0.367950 + 0.929845i \(0.619940\pi\)
\(728\) 203.647i 0.279735i
\(729\) −287.000 −0.393690
\(730\) 180.000 0.246575
\(731\) −432.000 −0.590971
\(732\) 169.706i 0.231838i
\(733\) 627.911i 0.856631i −0.903629 0.428316i \(-0.859107\pi\)
0.903629 0.428316i \(-0.140893\pi\)
\(734\) 858.428i 1.16952i
\(735\) 23.0000 0.0312925
\(736\) 96.1665i 0.130661i
\(737\) 623.000 + 755.190i 0.845319 + 1.02468i
\(738\) 96.0000 0.130081
\(739\) 865.499i 1.17118i 0.810609 + 0.585588i \(0.199136\pi\)
−0.810609 + 0.585588i \(0.800864\pi\)
\(740\) 94.0000 0.127027
\(741\) 216.000 0.291498
\(742\) 24.0000 0.0323450
\(743\) 1154.00i 1.55316i 0.630018 + 0.776580i \(0.283047\pi\)
−0.630018 + 0.776580i \(0.716953\pi\)
\(744\) 48.0833i 0.0646280i
\(745\) 161.220i 0.216403i
\(746\) 492.000 0.659517
\(747\) 271.529i 0.363493i
\(748\) 432.000 356.382i 0.577540 0.476446i
\(749\) 648.000 0.865154
\(750\) 69.2965i 0.0923953i
\(751\) −55.0000 −0.0732357 −0.0366178 0.999329i \(-0.511658\pi\)
−0.0366178 + 0.999329i \(0.511658\pi\)
\(752\) −232.000 −0.308511
\(753\) 65.0000 0.0863214
\(754\) 407.294i 0.540177i
\(755\) 288.500i 0.382119i
\(756\) 288.500i 0.381613i
\(757\) 2.00000 0.00264201 0.00132100 0.999999i \(-0.499580\pi\)
0.00132100 + 0.999999i \(0.499580\pi\)
\(758\) 417.193i 0.550387i
\(759\) 119.000 + 144.250i 0.156785 + 0.190052i
\(760\) 72.0000 0.0947368
\(761\) 1264.31i 1.66138i −0.556738 0.830688i \(-0.687947\pi\)
0.556738 0.830688i \(-0.312053\pi\)
\(762\) 36.0000 0.0472441
\(763\) 1296.00 1.69856
\(764\) 638.000 0.835079
\(765\) 203.647i 0.266205i
\(766\) 533.159i 0.696029i
\(767\) 466.690i 0.608462i
\(768\) 16.0000 0.0208333
\(769\) 602.455i 0.783426i −0.920087 0.391713i \(-0.871883\pi\)
0.920087 0.391713i \(-0.128117\pi\)
\(770\) −84.0000 101.823i −0.109091 0.132238i
\(771\) 170.000 0.220493
\(772\) 33.9411i 0.0439652i
\(773\) −1222.00 −1.58085 −0.790427 0.612556i \(-0.790141\pi\)
−0.790427 + 0.612556i \(0.790141\pi\)
\(774\) 192.000 0.248062
\(775\) −408.000 −0.526452
\(776\) 342.240i 0.441031i
\(777\) 398.808i 0.513267i
\(778\) 171.120i 0.219948i
\(779\) 216.000 0.277279
\(780\) 16.9706i 0.0217571i
\(781\) −49.0000 59.3970i −0.0627401 0.0760525i
\(782\) −612.000 −0.782609
\(783\) 576.999i 0.736908i
\(784\) −92.0000 −0.117347
\(785\) 1.00000 0.00127389
\(786\) 132.000 0.167939
\(787\) 899.440i