Properties

Label 882.3.s.c.863.2
Level $882$
Weight $3$
Character 882.863
Analytic conductor $24.033$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 863.2
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.863
Dual form 882.3.s.c.557.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-1.22474 - 0.707107i) q^{5} +2.82843i q^{8} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-1.22474 - 0.707107i) q^{5} +2.82843i q^{8} +(-1.00000 - 1.73205i) q^{10} +(-6.12372 + 3.53553i) q^{11} -15.0000 q^{13} +(-2.00000 + 3.46410i) q^{16} +(9.79796 - 5.65685i) q^{17} +(-6.50000 + 11.2583i) q^{19} -2.82843i q^{20} -10.0000 q^{22} +(-19.5959 - 11.3137i) q^{23} +(-11.5000 - 19.9186i) q^{25} +(-18.3712 - 10.6066i) q^{26} -22.6274i q^{29} +(1.50000 + 2.59808i) q^{31} +(-4.89898 + 2.82843i) q^{32} +16.0000 q^{34} +(-8.50000 + 14.7224i) q^{37} +(-15.9217 + 9.19239i) q^{38} +(2.00000 - 3.46410i) q^{40} +80.6102i q^{41} -85.0000 q^{43} +(-12.2474 - 7.07107i) q^{44} +(-16.0000 - 27.7128i) q^{46} +(-62.4620 - 36.0624i) q^{47} -32.5269i q^{50} +(-15.0000 - 25.9808i) q^{52} +(29.3939 - 16.9706i) q^{53} +10.0000 q^{55} +(16.0000 - 27.7128i) q^{58} +(78.3837 - 45.2548i) q^{59} +(-36.0000 + 62.3538i) q^{61} +4.24264i q^{62} -8.00000 q^{64} +(18.3712 + 10.6066i) q^{65} +(-21.5000 - 37.2391i) q^{67} +(19.5959 + 11.3137i) q^{68} +52.3259i q^{71} +(-47.5000 - 82.2724i) q^{73} +(-20.8207 + 12.0208i) q^{74} -26.0000 q^{76} +(-34.5000 + 59.7558i) q^{79} +(4.89898 - 2.82843i) q^{80} +(-57.0000 + 98.7269i) q^{82} -60.8112i q^{83} -16.0000 q^{85} +(-104.103 - 60.1041i) q^{86} +(-10.0000 - 17.3205i) q^{88} +(-117.576 - 67.8823i) q^{89} -45.2548i q^{92} +(-51.0000 - 88.3346i) q^{94} +(15.9217 - 9.19239i) q^{95} -16.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{4} + O(q^{10}) \) \( 4q + 4q^{4} - 4q^{10} - 60q^{13} - 8q^{16} - 26q^{19} - 40q^{22} - 46q^{25} + 6q^{31} + 64q^{34} - 34q^{37} + 8q^{40} - 340q^{43} - 64q^{46} - 60q^{52} + 40q^{55} + 64q^{58} - 144q^{61} - 32q^{64} - 86q^{67} - 190q^{73} - 104q^{76} - 138q^{79} - 228q^{82} - 64q^{85} - 40q^{88} - 204q^{94} - 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) −1.22474 0.707107i −0.244949 0.141421i 0.372500 0.928032i \(-0.378501\pi\)
−0.617449 + 0.786611i \(0.711834\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −1.00000 1.73205i −0.100000 0.173205i
\(11\) −6.12372 + 3.53553i −0.556702 + 0.321412i −0.751821 0.659367i \(-0.770824\pi\)
0.195119 + 0.980780i \(0.437491\pi\)
\(12\) 0 0
\(13\) −15.0000 −1.15385 −0.576923 0.816798i \(-0.695747\pi\)
−0.576923 + 0.816798i \(0.695747\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 9.79796 5.65685i 0.576351 0.332756i −0.183331 0.983051i \(-0.558688\pi\)
0.759682 + 0.650295i \(0.225355\pi\)
\(18\) 0 0
\(19\) −6.50000 + 11.2583i −0.342105 + 0.592544i −0.984823 0.173559i \(-0.944473\pi\)
0.642718 + 0.766103i \(0.277807\pi\)
\(20\) 2.82843i 0.141421i
\(21\) 0 0
\(22\) −10.0000 −0.454545
\(23\) −19.5959 11.3137i −0.851996 0.491900i 0.00932753 0.999956i \(-0.497031\pi\)
−0.861324 + 0.508056i \(0.830364\pi\)
\(24\) 0 0
\(25\) −11.5000 19.9186i −0.460000 0.796743i
\(26\) −18.3712 10.6066i −0.706584 0.407946i
\(27\) 0 0
\(28\) 0 0
\(29\) 22.6274i 0.780256i −0.920761 0.390128i \(-0.872431\pi\)
0.920761 0.390128i \(-0.127569\pi\)
\(30\) 0 0
\(31\) 1.50000 + 2.59808i 0.0483871 + 0.0838089i 0.889205 0.457510i \(-0.151259\pi\)
−0.840817 + 0.541319i \(0.817925\pi\)
\(32\) −4.89898 + 2.82843i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 16.0000 0.470588
\(35\) 0 0
\(36\) 0 0
\(37\) −8.50000 + 14.7224i −0.229730 + 0.397904i −0.957728 0.287675i \(-0.907118\pi\)
0.727998 + 0.685579i \(0.240451\pi\)
\(38\) −15.9217 + 9.19239i −0.418992 + 0.241905i
\(39\) 0 0
\(40\) 2.00000 3.46410i 0.0500000 0.0866025i
\(41\) 80.6102i 1.96610i 0.183333 + 0.983051i \(0.441311\pi\)
−0.183333 + 0.983051i \(0.558689\pi\)
\(42\) 0 0
\(43\) −85.0000 −1.97674 −0.988372 0.152055i \(-0.951411\pi\)
−0.988372 + 0.152055i \(0.951411\pi\)
\(44\) −12.2474 7.07107i −0.278351 0.160706i
\(45\) 0 0
\(46\) −16.0000 27.7128i −0.347826 0.602452i
\(47\) −62.4620 36.0624i −1.32898 0.767286i −0.343837 0.939029i \(-0.611727\pi\)
−0.985142 + 0.171743i \(0.945060\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 32.5269i 0.650538i
\(51\) 0 0
\(52\) −15.0000 25.9808i −0.288462 0.499630i
\(53\) 29.3939 16.9706i 0.554601 0.320199i −0.196374 0.980529i \(-0.562917\pi\)
0.750976 + 0.660330i \(0.229583\pi\)
\(54\) 0 0
\(55\) 10.0000 0.181818
\(56\) 0 0
\(57\) 0 0
\(58\) 16.0000 27.7128i 0.275862 0.477807i
\(59\) 78.3837 45.2548i 1.32854 0.767031i 0.343463 0.939166i \(-0.388400\pi\)
0.985073 + 0.172135i \(0.0550665\pi\)
\(60\) 0 0
\(61\) −36.0000 + 62.3538i −0.590164 + 1.02219i 0.404046 + 0.914739i \(0.367604\pi\)
−0.994210 + 0.107455i \(0.965730\pi\)
\(62\) 4.24264i 0.0684297i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 18.3712 + 10.6066i 0.282633 + 0.163178i
\(66\) 0 0
\(67\) −21.5000 37.2391i −0.320896 0.555807i 0.659778 0.751461i \(-0.270651\pi\)
−0.980673 + 0.195654i \(0.937317\pi\)
\(68\) 19.5959 + 11.3137i 0.288175 + 0.166378i
\(69\) 0 0
\(70\) 0 0
\(71\) 52.3259i 0.736985i 0.929631 + 0.368492i \(0.120126\pi\)
−0.929631 + 0.368492i \(0.879874\pi\)
\(72\) 0 0
\(73\) −47.5000 82.2724i −0.650685 1.12702i −0.982957 0.183836i \(-0.941149\pi\)
0.332272 0.943184i \(-0.392185\pi\)
\(74\) −20.8207 + 12.0208i −0.281360 + 0.162443i
\(75\) 0 0
\(76\) −26.0000 −0.342105
\(77\) 0 0
\(78\) 0 0
\(79\) −34.5000 + 59.7558i −0.436709 + 0.756402i −0.997433 0.0716005i \(-0.977189\pi\)
0.560725 + 0.828002i \(0.310523\pi\)
\(80\) 4.89898 2.82843i 0.0612372 0.0353553i
\(81\) 0 0
\(82\) −57.0000 + 98.7269i −0.695122 + 1.20399i
\(83\) 60.8112i 0.732665i −0.930484 0.366332i \(-0.880613\pi\)
0.930484 0.366332i \(-0.119387\pi\)
\(84\) 0 0
\(85\) −16.0000 −0.188235
\(86\) −104.103 60.1041i −1.21050 0.698885i
\(87\) 0 0
\(88\) −10.0000 17.3205i −0.113636 0.196824i
\(89\) −117.576 67.8823i −1.32107 0.762722i −0.337173 0.941443i \(-0.609471\pi\)
−0.983900 + 0.178721i \(0.942804\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 45.2548i 0.491900i
\(93\) 0 0
\(94\) −51.0000 88.3346i −0.542553 0.939730i
\(95\) 15.9217 9.19239i 0.167597 0.0967620i
\(96\) 0 0
\(97\) −16.0000 −0.164948 −0.0824742 0.996593i \(-0.526282\pi\)
−0.0824742 + 0.996593i \(0.526282\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 23.0000 39.8372i 0.230000 0.398372i
\(101\) 60.0125 34.6482i 0.594183 0.343052i −0.172567 0.984998i \(-0.555206\pi\)
0.766750 + 0.641946i \(0.221873\pi\)
\(102\) 0 0
\(103\) −30.5000 + 52.8275i −0.296117 + 0.512889i −0.975244 0.221131i \(-0.929025\pi\)
0.679127 + 0.734020i \(0.262358\pi\)
\(104\) 42.4264i 0.407946i
\(105\) 0 0
\(106\) 48.0000 0.452830
\(107\) 146.969 + 84.8528i 1.37355 + 0.793017i 0.991373 0.131074i \(-0.0418425\pi\)
0.382173 + 0.924091i \(0.375176\pi\)
\(108\) 0 0
\(109\) 32.5000 + 56.2917i 0.298165 + 0.516437i 0.975716 0.219039i \(-0.0702921\pi\)
−0.677551 + 0.735476i \(0.736959\pi\)
\(110\) 12.2474 + 7.07107i 0.111340 + 0.0642824i
\(111\) 0 0
\(112\) 0 0
\(113\) 137.179i 1.21397i −0.794713 0.606985i \(-0.792379\pi\)
0.794713 0.606985i \(-0.207621\pi\)
\(114\) 0 0
\(115\) 16.0000 + 27.7128i 0.139130 + 0.240981i
\(116\) 39.1918 22.6274i 0.337861 0.195064i
\(117\) 0 0
\(118\) 128.000 1.08475
\(119\) 0 0
\(120\) 0 0
\(121\) −35.5000 + 61.4878i −0.293388 + 0.508164i
\(122\) −88.1816 + 50.9117i −0.722800 + 0.417309i
\(123\) 0 0
\(124\) −3.00000 + 5.19615i −0.0241935 + 0.0419045i
\(125\) 67.8823i 0.543058i
\(126\) 0 0
\(127\) −171.000 −1.34646 −0.673228 0.739435i \(-0.735093\pi\)
−0.673228 + 0.739435i \(0.735093\pi\)
\(128\) −9.79796 5.65685i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 15.0000 + 25.9808i 0.115385 + 0.199852i
\(131\) 101.654 + 58.6899i 0.775983 + 0.448014i 0.835005 0.550242i \(-0.185465\pi\)
−0.0590215 + 0.998257i \(0.518798\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 60.8112i 0.453815i
\(135\) 0 0
\(136\) 16.0000 + 27.7128i 0.117647 + 0.203771i
\(137\) 186.161 107.480i 1.35884 0.784527i 0.369373 0.929281i \(-0.379572\pi\)
0.989468 + 0.144754i \(0.0462390\pi\)
\(138\) 0 0
\(139\) 83.0000 0.597122 0.298561 0.954391i \(-0.403493\pi\)
0.298561 + 0.954391i \(0.403493\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −37.0000 + 64.0859i −0.260563 + 0.451309i
\(143\) 91.8559 53.0330i 0.642349 0.370860i
\(144\) 0 0
\(145\) −16.0000 + 27.7128i −0.110345 + 0.191123i
\(146\) 134.350i 0.920207i
\(147\) 0 0
\(148\) −34.0000 −0.229730
\(149\) −88.1816 50.9117i −0.591823 0.341689i 0.173995 0.984747i \(-0.444332\pi\)
−0.765818 + 0.643057i \(0.777666\pi\)
\(150\) 0 0
\(151\) −20.0000 34.6410i −0.132450 0.229411i 0.792170 0.610300i \(-0.208951\pi\)
−0.924621 + 0.380889i \(0.875618\pi\)
\(152\) −31.8434 18.3848i −0.209496 0.120952i
\(153\) 0 0
\(154\) 0 0
\(155\) 4.24264i 0.0273719i
\(156\) 0 0
\(157\) 148.000 + 256.344i 0.942675 + 1.63276i 0.760340 + 0.649525i \(0.225032\pi\)
0.182335 + 0.983237i \(0.441635\pi\)
\(158\) −84.5074 + 48.7904i −0.534857 + 0.308800i
\(159\) 0 0
\(160\) 8.00000 0.0500000
\(161\) 0 0
\(162\) 0 0
\(163\) −64.0000 + 110.851i −0.392638 + 0.680069i −0.992797 0.119812i \(-0.961771\pi\)
0.600159 + 0.799881i \(0.295104\pi\)
\(164\) −139.621 + 80.6102i −0.851347 + 0.491525i
\(165\) 0 0
\(166\) 43.0000 74.4782i 0.259036 0.448664i
\(167\) 60.8112i 0.364139i 0.983286 + 0.182069i \(0.0582796\pi\)
−0.983286 + 0.182069i \(0.941720\pi\)
\(168\) 0 0
\(169\) 56.0000 0.331361
\(170\) −19.5959 11.3137i −0.115270 0.0665512i
\(171\) 0 0
\(172\) −85.0000 147.224i −0.494186 0.855955i
\(173\) 97.9796 + 56.5685i 0.566356 + 0.326986i 0.755693 0.654926i \(-0.227300\pi\)
−0.189337 + 0.981912i \(0.560634\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 28.2843i 0.160706i
\(177\) 0 0
\(178\) −96.0000 166.277i −0.539326 0.934140i
\(179\) −25.7196 + 14.8492i −0.143685 + 0.0829567i −0.570119 0.821562i \(-0.693103\pi\)
0.426434 + 0.904519i \(0.359770\pi\)
\(180\) 0 0
\(181\) −81.0000 −0.447514 −0.223757 0.974645i \(-0.571832\pi\)
−0.223757 + 0.974645i \(0.571832\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 32.0000 55.4256i 0.173913 0.301226i
\(185\) 20.8207 12.0208i 0.112544 0.0649774i
\(186\) 0 0
\(187\) −40.0000 + 69.2820i −0.213904 + 0.370492i
\(188\) 144.250i 0.767286i
\(189\) 0 0
\(190\) 26.0000 0.136842
\(191\) 55.1135 + 31.8198i 0.288552 + 0.166596i 0.637289 0.770625i \(-0.280056\pi\)
−0.348736 + 0.937221i \(0.613389\pi\)
\(192\) 0 0
\(193\) 111.500 + 193.124i 0.577720 + 1.00064i 0.995740 + 0.0922029i \(0.0293909\pi\)
−0.418020 + 0.908438i \(0.637276\pi\)
\(194\) −19.5959 11.3137i −0.101010 0.0583181i
\(195\) 0 0
\(196\) 0 0
\(197\) 158.392i 0.804020i 0.915635 + 0.402010i \(0.131688\pi\)
−0.915635 + 0.402010i \(0.868312\pi\)
\(198\) 0 0
\(199\) −68.0000 117.779i −0.341709 0.591857i 0.643042 0.765831i \(-0.277672\pi\)
−0.984750 + 0.173975i \(0.944339\pi\)
\(200\) 56.3383 32.5269i 0.281691 0.162635i
\(201\) 0 0
\(202\) 98.0000 0.485149
\(203\) 0 0
\(204\) 0 0
\(205\) 57.0000 98.7269i 0.278049 0.481595i
\(206\) −74.7094 + 43.1335i −0.362667 + 0.209386i
\(207\) 0 0
\(208\) 30.0000 51.9615i 0.144231 0.249815i
\(209\) 91.9239i 0.439827i
\(210\) 0 0
\(211\) 272.000 1.28910 0.644550 0.764562i \(-0.277045\pi\)
0.644550 + 0.764562i \(0.277045\pi\)
\(212\) 58.7878 + 33.9411i 0.277301 + 0.160100i
\(213\) 0 0
\(214\) 120.000 + 207.846i 0.560748 + 0.971243i
\(215\) 104.103 + 60.1041i 0.484201 + 0.279554i
\(216\) 0 0
\(217\) 0 0
\(218\) 91.9239i 0.421669i
\(219\) 0 0
\(220\) 10.0000 + 17.3205i 0.0454545 + 0.0787296i
\(221\) −146.969 + 84.8528i −0.665020 + 0.383949i
\(222\) 0 0
\(223\) −248.000 −1.11211 −0.556054 0.831146i \(-0.687685\pi\)
−0.556054 + 0.831146i \(0.687685\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 97.0000 168.009i 0.429204 0.743402i
\(227\) −143.295 + 82.7315i −0.631256 + 0.364456i −0.781238 0.624233i \(-0.785412\pi\)
0.149982 + 0.988689i \(0.452078\pi\)
\(228\) 0 0
\(229\) 216.500 374.989i 0.945415 1.63751i 0.190496 0.981688i \(-0.438990\pi\)
0.754918 0.655819i \(-0.227676\pi\)
\(230\) 45.2548i 0.196760i
\(231\) 0 0
\(232\) 64.0000 0.275862
\(233\) 197.184 + 113.844i 0.846283 + 0.488602i 0.859395 0.511312i \(-0.170840\pi\)
−0.0131120 + 0.999914i \(0.504174\pi\)
\(234\) 0 0
\(235\) 51.0000 + 88.3346i 0.217021 + 0.375892i
\(236\) 156.767 + 90.5097i 0.664268 + 0.383516i
\(237\) 0 0
\(238\) 0 0
\(239\) 343.654i 1.43788i 0.695071 + 0.718941i \(0.255373\pi\)
−0.695071 + 0.718941i \(0.744627\pi\)
\(240\) 0 0
\(241\) 79.0000 + 136.832i 0.327801 + 0.567768i 0.982075 0.188490i \(-0.0603592\pi\)
−0.654274 + 0.756257i \(0.727026\pi\)
\(242\) −86.9569 + 50.2046i −0.359326 + 0.207457i
\(243\) 0 0
\(244\) −144.000 −0.590164
\(245\) 0 0
\(246\) 0 0
\(247\) 97.5000 168.875i 0.394737 0.683704i
\(248\) −7.34847 + 4.24264i −0.0296309 + 0.0171074i
\(249\) 0 0
\(250\) −48.0000 + 83.1384i −0.192000 + 0.332554i
\(251\) 237.588i 0.946565i 0.880911 + 0.473283i \(0.156931\pi\)
−0.880911 + 0.473283i \(0.843069\pi\)
\(252\) 0 0
\(253\) 160.000 0.632411
\(254\) −209.431 120.915i −0.824533 0.476044i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −275.568 159.099i −1.07225 0.619062i −0.143453 0.989657i \(-0.545821\pi\)
−0.928795 + 0.370595i \(0.879154\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 42.4264i 0.163178i
\(261\) 0 0
\(262\) 83.0000 + 143.760i 0.316794 + 0.548703i
\(263\) −146.969 + 84.8528i −0.558819 + 0.322634i −0.752671 0.658396i \(-0.771235\pi\)
0.193852 + 0.981031i \(0.437902\pi\)
\(264\) 0 0
\(265\) −48.0000 −0.181132
\(266\) 0 0
\(267\) 0 0
\(268\) 43.0000 74.4782i 0.160448 0.277904i
\(269\) 420.087 242.538i 1.56166 0.901627i 0.564574 0.825382i \(-0.309040\pi\)
0.997089 0.0762447i \(-0.0242930\pi\)
\(270\) 0 0
\(271\) 108.000 187.061i 0.398524 0.690264i −0.595020 0.803711i \(-0.702856\pi\)
0.993544 + 0.113447i \(0.0361892\pi\)
\(272\) 45.2548i 0.166378i
\(273\) 0 0
\(274\) 304.000 1.10949
\(275\) 140.846 + 81.3173i 0.512166 + 0.295699i
\(276\) 0 0
\(277\) −152.500 264.138i −0.550542 0.953566i −0.998236 0.0593790i \(-0.981088\pi\)
0.447694 0.894187i \(-0.352245\pi\)
\(278\) 101.654 + 58.6899i 0.365661 + 0.211115i
\(279\) 0 0
\(280\) 0 0
\(281\) 22.6274i 0.0805246i 0.999189 + 0.0402623i \(0.0128194\pi\)
−0.999189 + 0.0402623i \(0.987181\pi\)
\(282\) 0 0
\(283\) 78.5000 + 135.966i 0.277385 + 0.480445i 0.970734 0.240157i \(-0.0771989\pi\)
−0.693349 + 0.720602i \(0.743866\pi\)
\(284\) −90.6311 + 52.3259i −0.319124 + 0.184246i
\(285\) 0 0
\(286\) 150.000 0.524476
\(287\) 0 0
\(288\) 0 0
\(289\) −80.5000 + 139.430i −0.278547 + 0.482457i
\(290\) −39.1918 + 22.6274i −0.135144 + 0.0780256i
\(291\) 0 0
\(292\) 95.0000 164.545i 0.325342 0.563510i
\(293\) 101.823i 0.347520i −0.984788 0.173760i \(-0.944408\pi\)
0.984788 0.173760i \(-0.0555917\pi\)
\(294\) 0 0
\(295\) −128.000 −0.433898
\(296\) −41.6413 24.0416i −0.140680 0.0812217i
\(297\) 0 0
\(298\) −72.0000 124.708i −0.241611 0.418482i
\(299\) 293.939 + 169.706i 0.983073 + 0.567577i
\(300\) 0 0
\(301\) 0 0
\(302\) 56.5685i 0.187313i
\(303\) 0 0
\(304\) −26.0000 45.0333i −0.0855263 0.148136i
\(305\) 88.1816 50.9117i 0.289120 0.166924i
\(306\) 0 0
\(307\) 11.0000 0.0358306 0.0179153 0.999840i \(-0.494297\pi\)
0.0179153 + 0.999840i \(0.494297\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 3.00000 5.19615i 0.00967742 0.0167618i
\(311\) −454.380 + 262.337i −1.46103 + 0.843526i −0.999059 0.0433690i \(-0.986191\pi\)
−0.461971 + 0.886895i \(0.652858\pi\)
\(312\) 0 0
\(313\) 276.500 478.912i 0.883387 1.53007i 0.0358348 0.999358i \(-0.488591\pi\)
0.847552 0.530713i \(-0.178076\pi\)
\(314\) 418.607i 1.33314i
\(315\) 0 0
\(316\) −138.000 −0.436709
\(317\) −117.576 67.8823i −0.370901 0.214140i 0.302951 0.953006i \(-0.402028\pi\)
−0.673852 + 0.738866i \(0.735361\pi\)
\(318\) 0 0
\(319\) 80.0000 + 138.564i 0.250784 + 0.434370i
\(320\) 9.79796 + 5.65685i 0.0306186 + 0.0176777i
\(321\) 0 0
\(322\) 0 0
\(323\) 147.078i 0.455350i
\(324\) 0 0
\(325\) 172.500 + 298.779i 0.530769 + 0.919319i
\(326\) −156.767 + 90.5097i −0.480881 + 0.277637i
\(327\) 0 0
\(328\) −228.000 −0.695122
\(329\) 0 0
\(330\) 0 0
\(331\) 30.5000 52.8275i 0.0921450 0.159600i −0.816268 0.577673i \(-0.803961\pi\)
0.908413 + 0.418073i \(0.137294\pi\)
\(332\) 105.328 60.8112i 0.317253 0.183166i
\(333\) 0 0
\(334\) −43.0000 + 74.4782i −0.128743 + 0.222989i
\(335\) 60.8112i 0.181526i
\(336\) 0 0
\(337\) 135.000 0.400593 0.200297 0.979735i \(-0.435809\pi\)
0.200297 + 0.979735i \(0.435809\pi\)
\(338\) 68.5857 + 39.5980i 0.202916 + 0.117154i
\(339\) 0 0
\(340\) −16.0000 27.7128i −0.0470588 0.0815083i
\(341\) −18.3712 10.6066i −0.0538744 0.0311044i
\(342\) 0 0
\(343\) 0 0
\(344\) 240.416i 0.698885i
\(345\) 0 0
\(346\) 80.0000 + 138.564i 0.231214 + 0.400474i
\(347\) 88.1816 50.9117i 0.254126 0.146720i −0.367526 0.930013i \(-0.619795\pi\)
0.621652 + 0.783294i \(0.286462\pi\)
\(348\) 0 0
\(349\) 152.000 0.435530 0.217765 0.976001i \(-0.430123\pi\)
0.217765 + 0.976001i \(0.430123\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 20.0000 34.6410i 0.0568182 0.0984120i
\(353\) −334.355 + 193.040i −0.947182 + 0.546856i −0.892205 0.451632i \(-0.850842\pi\)
−0.0549778 + 0.998488i \(0.517509\pi\)
\(354\) 0 0
\(355\) 37.0000 64.0859i 0.104225 0.180524i
\(356\) 271.529i 0.762722i
\(357\) 0 0
\(358\) −42.0000 −0.117318
\(359\) −39.1918 22.6274i −0.109169 0.0630290i 0.444421 0.895818i \(-0.353409\pi\)
−0.553591 + 0.832789i \(0.686743\pi\)
\(360\) 0 0
\(361\) 96.0000 + 166.277i 0.265928 + 0.460601i
\(362\) −99.2043 57.2756i −0.274045 0.158220i
\(363\) 0 0
\(364\) 0 0
\(365\) 134.350i 0.368083i
\(366\) 0 0
\(367\) 50.5000 + 87.4686i 0.137602 + 0.238334i 0.926588 0.376077i \(-0.122727\pi\)
−0.788986 + 0.614411i \(0.789394\pi\)
\(368\) 78.3837 45.2548i 0.212999 0.122975i
\(369\) 0 0
\(370\) 34.0000 0.0918919
\(371\) 0 0
\(372\) 0 0
\(373\) 155.500 269.334i 0.416890 0.722075i −0.578735 0.815516i \(-0.696453\pi\)
0.995625 + 0.0934411i \(0.0297867\pi\)
\(374\) −97.9796 + 56.5685i −0.261978 + 0.151253i
\(375\) 0 0
\(376\) 102.000 176.669i 0.271277 0.469865i
\(377\) 339.411i 0.900295i
\(378\) 0 0
\(379\) 91.0000 0.240106 0.120053 0.992768i \(-0.461694\pi\)
0.120053 + 0.992768i \(0.461694\pi\)
\(380\) 31.8434 + 18.3848i 0.0837983 + 0.0483810i
\(381\) 0 0
\(382\) 45.0000 + 77.9423i 0.117801 + 0.204037i
\(383\) 284.141 + 164.049i 0.741882 + 0.428326i 0.822753 0.568399i \(-0.192437\pi\)
−0.0808712 + 0.996725i \(0.525770\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 315.370i 0.817020i
\(387\) 0 0
\(388\) −16.0000 27.7128i −0.0412371 0.0714248i
\(389\) −596.451 + 344.361i −1.53329 + 0.885247i −0.534085 + 0.845431i \(0.679344\pi\)
−0.999207 + 0.0398163i \(0.987323\pi\)
\(390\) 0 0
\(391\) −256.000 −0.654731
\(392\) 0 0
\(393\) 0 0
\(394\) −112.000 + 193.990i −0.284264 + 0.492360i
\(395\) 84.5074 48.7904i 0.213943 0.123520i
\(396\) 0 0
\(397\) −139.500 + 241.621i −0.351385 + 0.608617i −0.986492 0.163807i \(-0.947623\pi\)
0.635107 + 0.772424i \(0.280956\pi\)
\(398\) 192.333i 0.483249i
\(399\) 0 0
\(400\) 92.0000 0.230000
\(401\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) −22.5000 38.9711i −0.0558313 0.0967026i
\(404\) 120.025 + 69.2965i 0.297092 + 0.171526i
\(405\) 0 0
\(406\) 0 0
\(407\) 120.208i 0.295352i
\(408\) 0 0
\(409\) −111.500 193.124i −0.272616 0.472185i 0.696915 0.717154i \(-0.254556\pi\)
−0.969531 + 0.244969i \(0.921222\pi\)
\(410\) 139.621 80.6102i 0.340539 0.196610i
\(411\) 0 0
\(412\) −122.000 −0.296117
\(413\) 0 0
\(414\) 0 0
\(415\) −43.0000 + 74.4782i −0.103614 + 0.179466i
\(416\) 73.4847 42.4264i 0.176646 0.101987i
\(417\) 0 0
\(418\) 65.0000 112.583i 0.155502 0.269338i
\(419\) 581.242i 1.38721i −0.720355 0.693606i \(-0.756021\pi\)
0.720355 0.693606i \(-0.243979\pi\)
\(420\) 0 0
\(421\) 153.000 0.363420 0.181710 0.983352i \(-0.441837\pi\)
0.181710 + 0.983352i \(0.441837\pi\)
\(422\) 333.131 + 192.333i 0.789409 + 0.455766i
\(423\) 0 0
\(424\) 48.0000 + 83.1384i 0.113208 + 0.196081i
\(425\) −225.353 130.108i −0.530242 0.306136i
\(426\) 0 0
\(427\) 0 0
\(428\) 339.411i 0.793017i
\(429\) 0 0
\(430\) 85.0000 + 147.224i 0.197674 + 0.342382i
\(431\) −121.250 + 70.0036i −0.281322 + 0.162421i −0.634022 0.773315i \(-0.718597\pi\)
0.352700 + 0.935737i \(0.385264\pi\)
\(432\) 0 0
\(433\) −137.000 −0.316397 −0.158199 0.987407i \(-0.550569\pi\)
−0.158199 + 0.987407i \(0.550569\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −65.0000 + 112.583i −0.149083 + 0.258219i
\(437\) 254.747 147.078i 0.582945 0.336563i
\(438\) 0 0
\(439\) −300.000 + 519.615i −0.683371 + 1.18363i 0.290574 + 0.956852i \(0.406154\pi\)
−0.973946 + 0.226781i \(0.927180\pi\)
\(440\) 28.2843i 0.0642824i
\(441\) 0 0
\(442\) −240.000 −0.542986
\(443\) −548.686 316.784i −1.23857 0.715088i −0.269767 0.962926i \(-0.586947\pi\)
−0.968801 + 0.247838i \(0.920280\pi\)
\(444\) 0 0
\(445\) 96.0000 + 166.277i 0.215730 + 0.373656i
\(446\) −303.737 175.362i −0.681024 0.393189i
\(447\) 0 0
\(448\) 0 0
\(449\) 383.252i 0.853568i −0.904354 0.426784i \(-0.859647\pi\)
0.904354 0.426784i \(-0.140353\pi\)
\(450\) 0 0
\(451\) −285.000 493.634i −0.631929 1.09453i
\(452\) 237.601 137.179i 0.525665 0.303493i
\(453\) 0 0
\(454\) −234.000 −0.515419
\(455\) 0 0
\(456\) 0 0
\(457\) 119.500 206.980i 0.261488 0.452910i −0.705150 0.709059i \(-0.749120\pi\)
0.966638 + 0.256148i \(0.0824535\pi\)
\(458\) 530.315 306.177i 1.15789 0.668509i
\(459\) 0 0
\(460\) −32.0000 + 55.4256i −0.0695652 + 0.120490i
\(461\) 452.548i 0.981667i −0.871253 0.490833i \(-0.836692\pi\)
0.871253 0.490833i \(-0.163308\pi\)
\(462\) 0 0
\(463\) 211.000 0.455724 0.227862 0.973693i \(-0.426827\pi\)
0.227862 + 0.973693i \(0.426827\pi\)
\(464\) 78.3837 + 45.2548i 0.168930 + 0.0975320i
\(465\) 0 0
\(466\) 161.000 + 278.860i 0.345494 + 0.598412i
\(467\) 270.669 + 156.271i 0.579590 + 0.334627i 0.760971 0.648786i \(-0.224723\pi\)
−0.181380 + 0.983413i \(0.558056\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 144.250i 0.306914i
\(471\) 0 0
\(472\) 128.000 + 221.703i 0.271186 + 0.469709i
\(473\) 520.517 300.520i 1.10046 0.635350i
\(474\) 0 0
\(475\) 299.000 0.629474
\(476\) 0 0
\(477\) 0 0
\(478\) −243.000 + 420.888i −0.508368 + 0.880520i
\(479\) −607.473 + 350.725i −1.26821 + 0.732202i −0.974649 0.223737i \(-0.928174\pi\)
−0.293562 + 0.955940i \(0.594841\pi\)
\(480\) 0 0
\(481\) 127.500 220.836i 0.265073 0.459119i
\(482\) 223.446i 0.463580i
\(483\) 0 0
\(484\) −142.000 −0.293388
\(485\) 19.5959 + 11.3137i 0.0404040 + 0.0233272i
\(486\) 0 0
\(487\) −209.500 362.865i −0.430185 0.745102i 0.566704 0.823921i \(-0.308218\pi\)
−0.996889 + 0.0788195i \(0.974885\pi\)
\(488\) −176.363 101.823i −0.361400 0.208654i
\(489\) 0 0
\(490\) 0 0
\(491\) 169.706i 0.345633i −0.984954 0.172816i \(-0.944713\pi\)
0.984954 0.172816i \(-0.0552867\pi\)
\(492\) 0 0
\(493\) −128.000 221.703i −0.259635 0.449701i
\(494\) 238.825 137.886i 0.483452 0.279121i
\(495\) 0 0
\(496\) −12.0000 −0.0241935
\(497\) 0 0
\(498\) 0 0
\(499\) −93.5000 + 161.947i −0.187375 + 0.324543i −0.944374 0.328873i \(-0.893331\pi\)
0.756999 + 0.653416i \(0.226665\pi\)
\(500\) −117.576 + 67.8823i −0.235151 + 0.135765i
\(501\) 0 0
\(502\) −168.000 + 290.985i −0.334661 + 0.579650i
\(503\) 173.948i 0.345822i 0.984937 + 0.172911i \(0.0553172\pi\)
−0.984937 + 0.172911i \(0.944683\pi\)
\(504\) 0 0
\(505\) −98.0000 −0.194059
\(506\) 195.959 + 113.137i 0.387271 + 0.223591i
\(507\) 0 0
\(508\) −171.000 296.181i −0.336614 0.583033i
\(509\) −224.128 129.401i −0.440331 0.254225i 0.263407 0.964685i \(-0.415154\pi\)
−0.703738 + 0.710460i \(0.748487\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −225.000 389.711i −0.437743 0.758193i
\(515\) 74.7094 43.1335i 0.145067 0.0837544i
\(516\) 0 0
\(517\) 510.000 0.986460
\(518\) 0 0
\(519\) 0 0
\(520\) −30.0000 + 51.9615i −0.0576923 + 0.0999260i
\(521\) 352.727 203.647i 0.677018 0.390877i −0.121712 0.992565i \(-0.538839\pi\)
0.798731 + 0.601689i \(0.205505\pi\)
\(522\) 0 0
\(523\) −405.500 + 702.347i −0.775335 + 1.34292i 0.159272 + 0.987235i \(0.449085\pi\)
−0.934606 + 0.355684i \(0.884248\pi\)
\(524\) 234.759i 0.448014i
\(525\) 0 0
\(526\) −240.000 −0.456274
\(527\) 29.3939 + 16.9706i 0.0557759 + 0.0322022i
\(528\) 0 0
\(529\) −8.50000 14.7224i −0.0160681 0.0278307i
\(530\) −58.7878 33.9411i −0.110920 0.0640399i
\(531\) 0 0
\(532\) 0 0
\(533\) 1209.15i 2.26858i
\(534\) 0 0
\(535\) −120.000 207.846i −0.224299 0.388497i
\(536\) 105.328 60.8112i 0.196508 0.113454i
\(537\) 0 0
\(538\) 686.000 1.27509
\(539\) 0 0
\(540\) 0 0
\(541\) 172.500 298.779i 0.318854 0.552271i −0.661395 0.750038i \(-0.730035\pi\)
0.980249 + 0.197766i \(0.0633687\pi\)
\(542\) 264.545 152.735i 0.488090 0.281799i
\(543\) 0 0
\(544\) −32.0000 + 55.4256i −0.0588235 + 0.101885i
\(545\) 91.9239i 0.168668i
\(546\) 0 0
\(547\) −864.000 −1.57952 −0.789762 0.613413i \(-0.789796\pi\)
−0.789762 + 0.613413i \(0.789796\pi\)
\(548\) 372.322 + 214.960i 0.679421 + 0.392264i
\(549\) 0 0
\(550\) 115.000 + 199.186i 0.209091 + 0.362156i
\(551\) 254.747 + 147.078i 0.462336 + 0.266930i
\(552\) 0 0
\(553\) 0 0
\(554\) 431.335i 0.778583i
\(555\) 0 0
\(556\) 83.0000 + 143.760i 0.149281 + 0.258562i
\(557\) 821.804 474.469i 1.47541 0.851829i 0.475795 0.879556i \(-0.342160\pi\)
0.999616 + 0.0277272i \(0.00882699\pi\)
\(558\) 0 0
\(559\) 1275.00 2.28086
\(560\) 0 0
\(561\) 0 0
\(562\) −16.0000 + 27.7128i −0.0284698 + 0.0493111i
\(563\) −640.542 + 369.817i −1.13773 + 0.656868i −0.945867 0.324554i \(-0.894786\pi\)
−0.191862 + 0.981422i \(0.561453\pi\)
\(564\) 0 0
\(565\) −97.0000 + 168.009i −0.171681 + 0.297361i
\(566\) 222.032i 0.392282i
\(567\) 0 0
\(568\) −148.000 −0.260563
\(569\) −665.036 383.959i −1.16878 0.674796i −0.215388 0.976528i \(-0.569102\pi\)
−0.953393 + 0.301732i \(0.902435\pi\)
\(570\) 0 0
\(571\) −238.500 413.094i −0.417688 0.723457i 0.578018 0.816024i \(-0.303826\pi\)
−0.995706 + 0.0925665i \(0.970493\pi\)
\(572\) 183.712 + 106.066i 0.321174 + 0.185430i
\(573\) 0 0
\(574\) 0 0
\(575\) 520.431i 0.905097i
\(576\) 0 0
\(577\) −131.500 227.765i −0.227903 0.394739i 0.729283 0.684212i \(-0.239854\pi\)
−0.957186 + 0.289472i \(0.906520\pi\)
\(578\) −197.184 + 113.844i −0.341149 + 0.196962i
\(579\) 0 0
\(580\) −64.0000 −0.110345
\(581\) 0 0
\(582\) 0 0
\(583\) −120.000 + 207.846i −0.205832 + 0.356511i
\(584\) 232.702 134.350i 0.398462 0.230052i
\(585\) 0 0
\(586\) 72.0000 124.708i 0.122867 0.212812i
\(587\) 531.744i 0.905868i −0.891544 0.452934i \(-0.850377\pi\)
0.891544 0.452934i \(-0.149623\pi\)
\(588\) 0 0
\(589\) −39.0000 −0.0662139
\(590\) −156.767 90.5097i −0.265707 0.153406i
\(591\) 0 0
\(592\) −34.0000 58.8897i −0.0574324 0.0994759i
\(593\) −694.430 400.930i −1.17105 0.676104i −0.217120 0.976145i \(-0.569666\pi\)
−0.953926 + 0.300041i \(0.903000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 203.647i 0.341689i
\(597\) 0 0
\(598\) 240.000 + 415.692i 0.401338 + 0.695137i
\(599\) −676.059 + 390.323i −1.12865 + 0.651624i −0.943594 0.331104i \(-0.892579\pi\)
−0.185052 + 0.982729i \(0.559245\pi\)
\(600\) 0 0
\(601\) −383.000 −0.637271 −0.318636 0.947877i \(-0.603225\pi\)
−0.318636 + 0.947877i \(0.603225\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 40.0000 69.2820i 0.0662252 0.114705i
\(605\) 86.9569 50.2046i 0.143730 0.0829828i
\(606\) 0 0
\(607\) −382.500 + 662.509i −0.630148 + 1.09145i 0.357373 + 0.933962i \(0.383673\pi\)
−0.987521 + 0.157487i \(0.949661\pi\)
\(608\) 73.5391i 0.120952i
\(609\) 0 0
\(610\) 144.000 0.236066
\(611\) 936.930 + 540.937i 1.53344 + 0.885330i
\(612\) 0 0
\(613\) −204.000 353.338i −0.332790 0.576408i 0.650268 0.759705i \(-0.274657\pi\)
−0.983058 + 0.183296i \(0.941323\pi\)
\(614\) 13.4722 + 7.77817i 0.0219417 + 0.0126680i
\(615\) 0 0
\(616\) 0 0
\(617\) 914.996i 1.48298i −0.670966 0.741488i \(-0.734120\pi\)
0.670966 0.741488i \(-0.265880\pi\)
\(618\) 0 0
\(619\) −473.500 820.126i −0.764943 1.32492i −0.940276 0.340412i \(-0.889434\pi\)
0.175333 0.984509i \(-0.443900\pi\)
\(620\) 7.34847 4.24264i 0.0118524 0.00684297i
\(621\) 0 0
\(622\) −742.000 −1.19293
\(623\) 0 0
\(624\) 0 0
\(625\) −239.500 + 414.826i −0.383200 + 0.663722i
\(626\) 677.284 391.030i 1.08192 0.624649i
\(627\) 0 0
\(628\) −296.000 + 512.687i −0.471338 + 0.816381i
\(629\) 192.333i 0.305776i
\(630\) 0 0
\(631\) −760.000 −1.20444 −0.602219 0.798331i \(-0.705716\pi\)
−0.602219 + 0.798331i \(0.705716\pi\)
\(632\) −169.015 97.5807i −0.267428 0.154400i
\(633\) 0 0
\(634\) −96.0000 166.277i −0.151420 0.262266i
\(635\) 209.431 + 120.915i 0.329813 + 0.190418i
\(636\) 0 0
\(637\) 0 0
\(638\) 226.274i 0.354662i
\(639\) 0 0
\(640\) 8.00000 + 13.8564i 0.0125000 + 0.0216506i
\(641\) 401.716 231.931i 0.626703 0.361827i −0.152771 0.988262i \(-0.548820\pi\)
0.779474 + 0.626435i \(0.215486\pi\)
\(642\) 0 0
\(643\) 19.0000 0.0295490 0.0147745 0.999891i \(-0.495297\pi\)
0.0147745 + 0.999891i \(0.495297\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −104.000 + 180.133i −0.160991 + 0.278844i
\(647\) 1003.07 579.120i 1.55033 0.895086i 0.552220 0.833698i \(-0.313781\pi\)
0.998114 0.0613872i \(-0.0195524\pi\)
\(648\) 0 0
\(649\) −320.000 + 554.256i −0.493066 + 0.854016i
\(650\) 487.904i 0.750621i
\(651\) 0 0
\(652\) −256.000 −0.392638
\(653\) −892.839 515.481i −1.36729 0.789404i −0.376707 0.926332i \(-0.622944\pi\)
−0.990581 + 0.136928i \(0.956277\pi\)
\(654\) 0 0
\(655\) −83.0000 143.760i −0.126718 0.219481i
\(656\) −279.242 161.220i −0.425674 0.245763i
\(657\) 0 0
\(658\) 0 0
\(659\) 972.979i 1.47645i 0.674556 + 0.738224i \(0.264335\pi\)
−0.674556 + 0.738224i \(0.735665\pi\)
\(660\) 0 0
\(661\) −200.500 347.276i −0.303328 0.525380i 0.673559 0.739133i \(-0.264765\pi\)
−0.976888 + 0.213753i \(0.931431\pi\)
\(662\) 74.7094 43.1335i 0.112854 0.0651564i
\(663\) 0 0
\(664\) 172.000 0.259036
\(665\) 0 0
\(666\) 0 0
\(667\) −256.000 + 443.405i −0.383808 + 0.664775i
\(668\) −105.328 + 60.8112i −0.157677 + 0.0910347i
\(669\) 0 0
\(670\) −43.0000 + 74.4782i −0.0641791 + 0.111161i
\(671\) 509.117i 0.758743i
\(672\) 0 0
\(673\) 665.000 0.988113 0.494056 0.869430i \(-0.335514\pi\)
0.494056 + 0.869430i \(0.335514\pi\)
\(674\) 165.341 + 95.4594i 0.245312 + 0.141631i
\(675\) 0 0
\(676\) 56.0000 + 96.9948i 0.0828402 + 0.143483i
\(677\) −793.635 458.205i −1.17228 0.676817i −0.218065 0.975934i \(-0.569975\pi\)
−0.954216 + 0.299117i \(0.903308\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 45.2548i 0.0665512i
\(681\) 0 0
\(682\) −15.0000 25.9808i −0.0219941 0.0380950i
\(683\) 117.576 67.8823i 0.172146 0.0993884i −0.411452 0.911432i \(-0.634978\pi\)
0.583597 + 0.812043i \(0.301645\pi\)
\(684\) 0 0
\(685\) −304.000 −0.443796
\(686\) 0 0
\(687\) 0 0
\(688\) 170.000 294.449i 0.247093 0.427978i
\(689\) −440.908 + 254.558i −0.639925 + 0.369461i
\(690\) 0 0
\(691\) 110.500 191.392i 0.159913 0.276978i −0.774924 0.632054i \(-0.782212\pi\)
0.934837 + 0.355077i \(0.115545\pi\)
\(692\) 226.274i 0.326986i
\(693\) 0 0
\(694\) 144.000 0.207493
\(695\) −101.654 58.6899i −0.146264 0.0844458i
\(696\) 0 0
\(697\) 456.000 + 789.815i 0.654232 + 1.13316i
\(698\) 186.161 + 107.480i 0.266707 + 0.153983i
\(699\) 0 0
\(700\) 0 0
\(701\) 192.333i 0.274370i −0.990545 0.137185i \(-0.956195\pi\)
0.990545 0.137185i \(-0.0438054\pi\)
\(702\) 0 0
\(703\) −110.500 191.392i −0.157183 0.272250i
\(704\) 48.9898 28.2843i 0.0695878 0.0401765i
\(705\) 0 0
\(706\) −546.000 −0.773371
\(707\) 0 0
\(708\) 0 0
\(709\) 164.000 284.056i 0.231312 0.400644i −0.726883 0.686762i \(-0.759032\pi\)
0.958194 + 0.286118i \(0.0923649\pi\)
\(710\) 90.6311 52.3259i 0.127649 0.0736985i
\(711\) 0 0
\(712\) 192.000 332.554i 0.269663 0.467070i
\(713\) 67.8823i 0.0952065i
\(714\) 0 0
\(715\) −150.000 −0.209790
\(716\) −51.4393 29.6985i −0.0718426 0.0414783i
\(717\) 0 0
\(718\) −32.0000 55.4256i −0.0445682 0.0771945i
\(719\) −878.142 506.996i −1.22134 0.705140i −0.256135 0.966641i \(-0.582449\pi\)
−0.965203 + 0.261501i \(0.915782\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 271.529i 0.376079i
\(723\) 0 0
\(724\) −81.0000 140.296i −0.111878 0.193779i
\(725\) −450.706 + 260.215i −0.621664 + 0.358918i
\(726\) 0 0
\(727\) −1069.00 −1.47043 −0.735213 0.677836i \(-0.762918\pi\)
−0.735213 + 0.677836i \(0.762918\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −95.0000 + 164.545i −0.130137 + 0.225404i
\(731\) −832.827 + 480.833i −1.13930 + 0.657774i
\(732\) 0 0
\(733\) 247.500 428.683i 0.337653 0.584833i −0.646337 0.763052i \(-0.723700\pi\)
0.983991 + 0.178219i \(0.0570335\pi\)
\(734\) 142.836i 0.194599i
\(735\) 0 0
\(736\) 128.000 0.173913
\(737\) 263.320 + 152.028i 0.357286 + 0.206279i
\(738\) 0 0
\(739\) −226.500 392.310i −0.306495 0.530865i 0.671098 0.741369i \(-0.265823\pi\)
−0.977593 + 0.210503i \(0.932490\pi\)
\(740\) 41.6413 + 24.0416i 0.0562721 + 0.0324887i
\(741\) 0 0
\(742\) 0 0
\(743\) 538.815i 0.725189i −0.931947 0.362594i \(-0.881891\pi\)
0.931947 0.362594i \(-0.118109\pi\)
\(744\) 0 0
\(745\) 72.0000 + 124.708i 0.0966443 + 0.167393i
\(746\) 380.896 219.910i 0.510584 0.294786i
\(747\) 0 0
\(748\) −160.000 −0.213904
\(749\) 0 0
\(750\) 0 0
\(751\) 169.500 293.583i 0.225699 0.390922i −0.730830 0.682560i \(-0.760867\pi\)
0.956529 + 0.291637i \(0.0942001\pi\)
\(752\) 249.848 144.250i 0.332245 0.191822i
\(753\) 0 0
\(754\) −240.000 + 415.692i −0.318302 + 0.551316i
\(755\) 56.5685i 0.0749252i
\(756\) 0 0
\(757\) 198.000 0.261559 0.130779 0.991411i \(-0.458252\pi\)
0.130779 + 0.991411i \(0.458252\pi\)
\(758\) 111.452 + 64.3467i 0.147034 + 0.0848901i
\(759\) 0 0
\(760\) 26.0000 + 45.0333i 0.0342105 + 0.0592544i
\(761\) 313.535 + 181.019i 0.412004 + 0.237870i 0.691650 0.722233i \(-0.256884\pi\)
−0.279647 + 0.960103i \(0.590217\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 127.279i 0.166596i
\(765\) 0 0
\(766\) 232.000 + 401.836i 0.302872 + 0.524590i
\(767\) −1175.76 + 678.823i −1.53293 + 0.885036i
\(768\) 0 0
\(769\) 929.000 1.20806 0.604031 0.796961i \(-0.293560\pi\)
0.604031 + 0.796961i \(0.293560\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −223.000 + 386.247i −0.288860 + 0.500320i
\(773\) 148.194 85.5599i 0.191713 0.110686i −0.401071 0.916047i \(-0.631362\pi\)
0.592784 + 0.805361i \(0.298029\pi\)
\(774\) 0 0
\(775\) 34.5000 59.7558i 0.0445161 0.0771042i
\(776\) 45.2548i 0.0583181i
\(777\) 0 0
\(778\) −974.000 −1.25193
\(779\) −907.536 523.966i −1.16500 0.672614i
\(780\) 0 0
\(781\) −185.000 320.429i −0.236876 0.410281i
\(782\) −313.535 181.019i −0.400939 0.231483i
\(783\) 0 0
\(784\) 0 0
\(785\) 418.607i 0.533258i
\(786\) 0 0
\(787\) 45.0000 + 77.9423i 0.0571792 + 0.0990372i 0.893198 0.449663i \(-0.148456\pi\)
−0.836019 + 0.548701i \(0.815123\pi\)
\(788\) −274.343 + 158.392i −0.348151 + 0.201005i
\(789\) 0 0
\(790\) 138.000 0.174684
\(791\) 0