Properties

Label 1386.2.ba.a.989.2
Level $1386$
Weight $2$
Character 1386.989
Analytic conductor $11.067$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 989.2
Character \(\chi\) \(=\) 1386.989
Dual form 1386.2.ba.a.1187.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.42143 - 1.39801i) q^{5} +(2.62875 + 0.299420i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.42143 - 1.39801i) q^{5} +(2.62875 + 0.299420i) q^{7} +1.00000 q^{8} +(2.42143 - 1.39801i) q^{10} +(-1.93092 - 2.69658i) q^{11} -3.20191i q^{13} +(-1.57368 + 2.12686i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.05881 + 3.56596i) q^{17} +(-1.82770 - 1.05522i) q^{19} +2.79602i q^{20} +(3.30077 - 0.323937i) q^{22} +(-0.902766 - 0.521212i) q^{23} +(1.40887 + 2.44023i) q^{25} +(2.77293 + 1.60095i) q^{26} +(-1.05507 - 2.42628i) q^{28} -9.40956 q^{29} +(3.58777 + 6.21420i) q^{31} +(-0.500000 - 0.866025i) q^{32} -4.11761 q^{34} +(-5.94674 - 4.40005i) q^{35} +(-4.60502 + 7.97612i) q^{37} +(1.82770 - 1.05522i) q^{38} +(-2.42143 - 1.39801i) q^{40} +0.110771 q^{41} -4.20415i q^{43} +(-1.36985 + 3.02052i) q^{44} +(0.902766 - 0.521212i) q^{46} +(-7.27267 - 4.19888i) q^{47} +(6.82070 + 1.57420i) q^{49} -2.81773 q^{50} +(-2.77293 + 1.60095i) q^{52} +(10.3301 - 5.96410i) q^{53} +(0.905736 + 9.22901i) q^{55} +(2.62875 + 0.299420i) q^{56} +(4.70478 - 8.14891i) q^{58} +(-6.34962 + 3.66595i) q^{59} +(-9.21987 - 5.32310i) q^{61} -7.17555 q^{62} +1.00000 q^{64} +(-4.47630 + 7.75318i) q^{65} +(-3.97143 - 6.87872i) q^{67} +(2.05881 - 3.56596i) q^{68} +(6.78392 - 2.95000i) q^{70} +11.0925i q^{71} +(5.46860 - 3.15730i) q^{73} +(-4.60502 - 7.97612i) q^{74} +2.11045i q^{76} +(-4.26851 - 7.66680i) q^{77} +(-12.4344 - 7.17899i) q^{79} +(2.42143 - 1.39801i) q^{80} +(-0.0553856 + 0.0959306i) q^{82} -14.2335 q^{83} -11.5129i q^{85} +(3.64090 + 2.10208i) q^{86} +(-1.93092 - 2.69658i) q^{88} +(-10.3472 - 5.97394i) q^{89} +(0.958715 - 8.41703i) q^{91} +1.04242i q^{92} +(7.27267 - 4.19888i) q^{94} +(2.95043 + 5.11029i) q^{95} -17.6911 q^{97} +(-4.77365 + 5.11979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) \) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −2.42143 1.39801i −1.08289 0.625209i −0.151219 0.988500i \(-0.548320\pi\)
−0.931676 + 0.363291i \(0.881653\pi\)
\(6\) 0 0
\(7\) 2.62875 + 0.299420i 0.993576 + 0.113170i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 2.42143 1.39801i 0.765722 0.442090i
\(11\) −1.93092 2.69658i −0.582195 0.813049i
\(12\) 0 0
\(13\) 3.20191i 0.888050i −0.896015 0.444025i \(-0.853550\pi\)
0.896015 0.444025i \(-0.146450\pi\)
\(14\) −1.57368 + 2.12686i −0.420584 + 0.568427i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.05881 + 3.56596i 0.499334 + 0.864872i 1.00000 0.000768905i \(-0.000244750\pi\)
−0.500666 + 0.865641i \(0.666911\pi\)
\(18\) 0 0
\(19\) −1.82770 1.05522i −0.419304 0.242085i 0.275476 0.961308i \(-0.411165\pi\)
−0.694779 + 0.719223i \(0.744498\pi\)
\(20\) 2.79602i 0.625209i
\(21\) 0 0
\(22\) 3.30077 0.323937i 0.703726 0.0690637i
\(23\) −0.902766 0.521212i −0.188240 0.108680i 0.402919 0.915236i \(-0.367996\pi\)
−0.591158 + 0.806556i \(0.701329\pi\)
\(24\) 0 0
\(25\) 1.40887 + 2.44023i 0.281773 + 0.488046i
\(26\) 2.77293 + 1.60095i 0.543817 + 0.313973i
\(27\) 0 0
\(28\) −1.05507 2.42628i −0.199390 0.458523i
\(29\) −9.40956 −1.74731 −0.873655 0.486545i \(-0.838257\pi\)
−0.873655 + 0.486545i \(0.838257\pi\)
\(30\) 0 0
\(31\) 3.58777 + 6.21420i 0.644383 + 1.11610i 0.984444 + 0.175701i \(0.0562191\pi\)
−0.340061 + 0.940404i \(0.610448\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −4.11761 −0.706165
\(35\) −5.94674 4.40005i −1.00518 0.743744i
\(36\) 0 0
\(37\) −4.60502 + 7.97612i −0.757060 + 1.31127i 0.187284 + 0.982306i \(0.440032\pi\)
−0.944344 + 0.328961i \(0.893302\pi\)
\(38\) 1.82770 1.05522i 0.296492 0.171180i
\(39\) 0 0
\(40\) −2.42143 1.39801i −0.382861 0.221045i
\(41\) 0.110771 0.0172995 0.00864977 0.999963i \(-0.497247\pi\)
0.00864977 + 0.999963i \(0.497247\pi\)
\(42\) 0 0
\(43\) 4.20415i 0.641127i −0.947227 0.320564i \(-0.896128\pi\)
0.947227 0.320564i \(-0.103872\pi\)
\(44\) −1.36985 + 3.02052i −0.206512 + 0.455360i
\(45\) 0 0
\(46\) 0.902766 0.521212i 0.133106 0.0768485i
\(47\) −7.27267 4.19888i −1.06083 0.612469i −0.135167 0.990823i \(-0.543157\pi\)
−0.925661 + 0.378353i \(0.876490\pi\)
\(48\) 0 0
\(49\) 6.82070 + 1.57420i 0.974385 + 0.224886i
\(50\) −2.81773 −0.398488
\(51\) 0 0
\(52\) −2.77293 + 1.60095i −0.384537 + 0.222012i
\(53\) 10.3301 5.96410i 1.41895 0.819232i 0.422745 0.906249i \(-0.361067\pi\)
0.996207 + 0.0870162i \(0.0277332\pi\)
\(54\) 0 0
\(55\) 0.905736 + 9.22901i 0.122129 + 1.24444i
\(56\) 2.62875 + 0.299420i 0.351282 + 0.0400117i
\(57\) 0 0
\(58\) 4.70478 8.14891i 0.617768 1.07000i
\(59\) −6.34962 + 3.66595i −0.826650 + 0.477266i −0.852704 0.522394i \(-0.825039\pi\)
0.0260545 + 0.999661i \(0.491706\pi\)
\(60\) 0 0
\(61\) −9.21987 5.32310i −1.18048 0.681553i −0.224357 0.974507i \(-0.572028\pi\)
−0.956126 + 0.292954i \(0.905362\pi\)
\(62\) −7.17555 −0.911295
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −4.47630 + 7.75318i −0.555217 + 0.961664i
\(66\) 0 0
\(67\) −3.97143 6.87872i −0.485188 0.840370i 0.514667 0.857390i \(-0.327915\pi\)
−0.999855 + 0.0170201i \(0.994582\pi\)
\(68\) 2.05881 3.56596i 0.249667 0.432436i
\(69\) 0 0
\(70\) 6.78392 2.95000i 0.810834 0.352593i
\(71\) 11.0925i 1.31643i 0.752828 + 0.658217i \(0.228689\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(72\) 0 0
\(73\) 5.46860 3.15730i 0.640052 0.369534i −0.144583 0.989493i \(-0.546184\pi\)
0.784634 + 0.619959i \(0.212851\pi\)
\(74\) −4.60502 7.97612i −0.535322 0.927205i
\(75\) 0 0
\(76\) 2.11045i 0.242085i
\(77\) −4.26851 7.66680i −0.486442 0.873713i
\(78\) 0 0
\(79\) −12.4344 7.17899i −1.39898 0.807700i −0.404692 0.914453i \(-0.632621\pi\)
−0.994286 + 0.106753i \(0.965955\pi\)
\(80\) 2.42143 1.39801i 0.270724 0.156302i
\(81\) 0 0
\(82\) −0.0553856 + 0.0959306i −0.00611631 + 0.0105938i
\(83\) −14.2335 −1.56234 −0.781168 0.624321i \(-0.785376\pi\)
−0.781168 + 0.624321i \(0.785376\pi\)
\(84\) 0 0
\(85\) 11.5129i 1.24875i
\(86\) 3.64090 + 2.10208i 0.392609 + 0.226673i
\(87\) 0 0
\(88\) −1.93092 2.69658i −0.205837 0.287456i
\(89\) −10.3472 5.97394i −1.09680 0.633236i −0.161419 0.986886i \(-0.551607\pi\)
−0.935378 + 0.353650i \(0.884940\pi\)
\(90\) 0 0
\(91\) 0.958715 8.41703i 0.100501 0.882344i
\(92\) 1.04242i 0.108680i
\(93\) 0 0
\(94\) 7.27267 4.19888i 0.750119 0.433081i
\(95\) 2.95043 + 5.11029i 0.302708 + 0.524305i
\(96\) 0 0
\(97\) −17.6911 −1.79626 −0.898129 0.439733i \(-0.855073\pi\)
−0.898129 + 0.439733i \(0.855073\pi\)
\(98\) −4.77365 + 5.11979i −0.482211 + 0.517177i
\(99\) 0 0
\(100\) 1.40887 2.44023i 0.140887 0.244023i
\(101\) −0.117005 0.202659i −0.0116425 0.0201653i 0.860145 0.510049i \(-0.170373\pi\)
−0.871788 + 0.489883i \(0.837039\pi\)
\(102\) 0 0
\(103\) −6.27192 + 10.8633i −0.617991 + 1.07039i 0.371861 + 0.928288i \(0.378720\pi\)
−0.989852 + 0.142103i \(0.954614\pi\)
\(104\) 3.20191i 0.313973i
\(105\) 0 0
\(106\) 11.9282i 1.15857i
\(107\) 6.54545 11.3370i 0.632772 1.09599i −0.354210 0.935166i \(-0.615250\pi\)
0.986982 0.160828i \(-0.0514164\pi\)
\(108\) 0 0
\(109\) 5.63480 3.25325i 0.539716 0.311605i −0.205248 0.978710i \(-0.565800\pi\)
0.744964 + 0.667105i \(0.232467\pi\)
\(110\) −8.44543 3.83012i −0.805240 0.365187i
\(111\) 0 0
\(112\) −1.57368 + 2.12686i −0.148699 + 0.200969i
\(113\) 0.871772i 0.0820094i 0.999159 + 0.0410047i \(0.0130559\pi\)
−0.999159 + 0.0410047i \(0.986944\pi\)
\(114\) 0 0
\(115\) 1.45732 + 2.52415i 0.135896 + 0.235378i
\(116\) 4.70478 + 8.14891i 0.436828 + 0.756608i
\(117\) 0 0
\(118\) 7.33191i 0.674957i
\(119\) 4.34438 + 9.99047i 0.398248 + 0.915825i
\(120\) 0 0
\(121\) −3.54308 + 10.4138i −0.322098 + 0.946706i
\(122\) 9.21987 5.32310i 0.834728 0.481931i
\(123\) 0 0
\(124\) 3.58777 6.21420i 0.322192 0.558052i
\(125\) 6.10167i 0.545750i
\(126\) 0 0
\(127\) 9.15849i 0.812685i −0.913721 0.406342i \(-0.866804\pi\)
0.913721 0.406342i \(-0.133196\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −4.47630 7.75318i −0.392598 0.679999i
\(131\) −3.87340 + 6.70892i −0.338420 + 0.586161i −0.984136 0.177417i \(-0.943226\pi\)
0.645716 + 0.763578i \(0.276559\pi\)
\(132\) 0 0
\(133\) −4.48862 3.32118i −0.389213 0.287982i
\(134\) 7.94287 0.686159
\(135\) 0 0
\(136\) 2.05881 + 3.56596i 0.176541 + 0.305778i
\(137\) 6.78091 3.91496i 0.579333 0.334478i −0.181536 0.983384i \(-0.558107\pi\)
0.760868 + 0.648907i \(0.224773\pi\)
\(138\) 0 0
\(139\) 3.11030i 0.263812i −0.991262 0.131906i \(-0.957890\pi\)
0.991262 0.131906i \(-0.0421097\pi\)
\(140\) −0.837184 + 7.35005i −0.0707550 + 0.621193i
\(141\) 0 0
\(142\) −9.60636 5.54624i −0.806148 0.465430i
\(143\) −8.63420 + 6.18263i −0.722028 + 0.517018i
\(144\) 0 0
\(145\) 22.7845 + 13.1547i 1.89215 + 1.09243i
\(146\) 6.31460i 0.522600i
\(147\) 0 0
\(148\) 9.21003 0.757060
\(149\) 4.08541 7.07613i 0.334690 0.579699i −0.648736 0.761014i \(-0.724702\pi\)
0.983425 + 0.181314i \(0.0580352\pi\)
\(150\) 0 0
\(151\) 5.93139 3.42449i 0.482690 0.278681i −0.238847 0.971057i \(-0.576769\pi\)
0.721537 + 0.692376i \(0.243436\pi\)
\(152\) −1.82770 1.05522i −0.148246 0.0855900i
\(153\) 0 0
\(154\) 8.77390 + 0.136763i 0.707021 + 0.0110207i
\(155\) 20.0630i 1.61150i
\(156\) 0 0
\(157\) 4.04332 + 7.00324i 0.322692 + 0.558920i 0.981043 0.193792i \(-0.0620787\pi\)
−0.658350 + 0.752712i \(0.728745\pi\)
\(158\) 12.4344 7.17899i 0.989226 0.571130i
\(159\) 0 0
\(160\) 2.79602i 0.221045i
\(161\) −2.21709 1.64044i −0.174731 0.129285i
\(162\) 0 0
\(163\) −0.682357 + 1.18188i −0.0534463 + 0.0925717i −0.891511 0.453000i \(-0.850354\pi\)
0.838064 + 0.545571i \(0.183687\pi\)
\(164\) −0.0553856 0.0959306i −0.00432489 0.00749092i
\(165\) 0 0
\(166\) 7.11677 12.3266i 0.552369 0.956731i
\(167\) 7.34655 0.568493 0.284247 0.958751i \(-0.408257\pi\)
0.284247 + 0.958751i \(0.408257\pi\)
\(168\) 0 0
\(169\) 2.74778 0.211368
\(170\) 9.97049 + 5.75647i 0.764702 + 0.441501i
\(171\) 0 0
\(172\) −3.64090 + 2.10208i −0.277616 + 0.160282i
\(173\) −0.327674 + 0.567548i −0.0249126 + 0.0431498i −0.878213 0.478270i \(-0.841264\pi\)
0.853300 + 0.521420i \(0.174597\pi\)
\(174\) 0 0
\(175\) 2.97291 + 6.83660i 0.224731 + 0.516799i
\(176\) 3.30077 0.323937i 0.248805 0.0244177i
\(177\) 0 0
\(178\) 10.3472 5.97394i 0.775553 0.447765i
\(179\) −3.55106 + 2.05021i −0.265419 + 0.153240i −0.626804 0.779177i \(-0.715637\pi\)
0.361385 + 0.932417i \(0.382304\pi\)
\(180\) 0 0
\(181\) −11.0064 −0.818102 −0.409051 0.912511i \(-0.634140\pi\)
−0.409051 + 0.912511i \(0.634140\pi\)
\(182\) 6.81000 + 5.03879i 0.504791 + 0.373500i
\(183\) 0 0
\(184\) −0.902766 0.521212i −0.0665528 0.0384243i
\(185\) 22.3014 12.8757i 1.63963 0.946642i
\(186\) 0 0
\(187\) 5.64049 12.4373i 0.412474 0.909507i
\(188\) 8.39776i 0.612469i
\(189\) 0 0
\(190\) −5.90086 −0.428093
\(191\) 18.8331 + 10.8733i 1.36271 + 0.786763i 0.989984 0.141178i \(-0.0450890\pi\)
0.372728 + 0.927940i \(0.378422\pi\)
\(192\) 0 0
\(193\) −19.3131 + 11.1504i −1.39019 + 0.802625i −0.993336 0.115257i \(-0.963231\pi\)
−0.396852 + 0.917882i \(0.629898\pi\)
\(194\) 8.84554 15.3209i 0.635073 1.09998i
\(195\) 0 0
\(196\) −2.04705 6.69400i −0.146218 0.478143i
\(197\) 11.0036 0.783972 0.391986 0.919971i \(-0.371788\pi\)
0.391986 + 0.919971i \(0.371788\pi\)
\(198\) 0 0
\(199\) −8.22506 14.2462i −0.583059 1.00989i −0.995114 0.0987290i \(-0.968522\pi\)
0.412055 0.911159i \(-0.364811\pi\)
\(200\) 1.40887 + 2.44023i 0.0996219 + 0.172550i
\(201\) 0 0
\(202\) 0.234010 0.0164649
\(203\) −24.7354 2.81741i −1.73609 0.197743i
\(204\) 0 0
\(205\) −0.268224 0.154859i −0.0187336 0.0108158i
\(206\) −6.27192 10.8633i −0.436986 0.756881i
\(207\) 0 0
\(208\) 2.77293 + 1.60095i 0.192268 + 0.111006i
\(209\) 0.683653 + 6.96610i 0.0472893 + 0.481855i
\(210\) 0 0
\(211\) 0.618822i 0.0426015i 0.999773 + 0.0213007i \(0.00678075\pi\)
−0.999773 + 0.0213007i \(0.993219\pi\)
\(212\) −10.3301 5.96410i −0.709476 0.409616i
\(213\) 0 0
\(214\) 6.54545 + 11.3370i 0.447438 + 0.774985i
\(215\) −5.87745 + 10.1800i −0.400839 + 0.694273i
\(216\) 0 0
\(217\) 7.57072 + 17.4099i 0.513934 + 1.18186i
\(218\) 6.50650i 0.440676i
\(219\) 0 0
\(220\) 7.53969 5.39890i 0.508326 0.363994i
\(221\) 11.4179 6.59211i 0.768049 0.443433i
\(222\) 0 0
\(223\) 10.3553 0.693443 0.346722 0.937968i \(-0.387295\pi\)
0.346722 + 0.937968i \(0.387295\pi\)
\(224\) −1.05507 2.42628i −0.0704949 0.162112i
\(225\) 0 0
\(226\) −0.754977 0.435886i −0.0502203 0.0289947i
\(227\) 6.46564 + 11.1988i 0.429140 + 0.743292i 0.996797 0.0799731i \(-0.0254834\pi\)
−0.567657 + 0.823265i \(0.692150\pi\)
\(228\) 0 0
\(229\) −2.73849 + 4.74320i −0.180964 + 0.313439i −0.942209 0.335025i \(-0.891255\pi\)
0.761245 + 0.648465i \(0.224589\pi\)
\(230\) −2.91464 −0.192186
\(231\) 0 0
\(232\) −9.40956 −0.617768
\(233\) 13.7588 23.8310i 0.901372 1.56122i 0.0756568 0.997134i \(-0.475895\pi\)
0.825715 0.564088i \(-0.190772\pi\)
\(234\) 0 0
\(235\) 11.7402 + 20.3345i 0.765843 + 1.32648i
\(236\) 6.34962 + 3.66595i 0.413325 + 0.238633i
\(237\) 0 0
\(238\) −10.8242 1.23290i −0.701628 0.0799167i
\(239\) 13.3339 0.862499 0.431249 0.902233i \(-0.358073\pi\)
0.431249 + 0.902233i \(0.358073\pi\)
\(240\) 0 0
\(241\) −15.7035 + 9.06641i −1.01155 + 0.584019i −0.911645 0.410978i \(-0.865187\pi\)
−0.0999053 + 0.994997i \(0.531854\pi\)
\(242\) −7.24705 8.27528i −0.465858 0.531955i
\(243\) 0 0
\(244\) 10.6462i 0.681553i
\(245\) −14.3151 13.3472i −0.914555 0.852722i
\(246\) 0 0
\(247\) −3.37873 + 5.85213i −0.214984 + 0.372362i
\(248\) 3.58777 + 6.21420i 0.227824 + 0.394602i
\(249\) 0 0
\(250\) −5.28420 3.05083i −0.334202 0.192952i
\(251\) 18.5540i 1.17112i 0.810630 + 0.585559i \(0.199125\pi\)
−0.810630 + 0.585559i \(0.800875\pi\)
\(252\) 0 0
\(253\) 0.337680 + 3.44080i 0.0212298 + 0.216321i
\(254\) 7.93149 + 4.57925i 0.497666 + 0.287327i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −23.4582 13.5436i −1.46328 0.844826i −0.464120 0.885773i \(-0.653629\pi\)
−0.999161 + 0.0409470i \(0.986963\pi\)
\(258\) 0 0
\(259\) −14.4937 + 19.5884i −0.900593 + 1.21717i
\(260\) 8.95260 0.555217
\(261\) 0 0
\(262\) −3.87340 6.70892i −0.239299 0.414478i
\(263\) −5.53418 9.58548i −0.341252 0.591066i 0.643414 0.765519i \(-0.277518\pi\)
−0.984665 + 0.174453i \(0.944184\pi\)
\(264\) 0 0
\(265\) −33.3515 −2.04877
\(266\) 5.12053 2.22667i 0.313960 0.136526i
\(267\) 0 0
\(268\) −3.97143 + 6.87872i −0.242594 + 0.420185i
\(269\) −8.44523 + 4.87586i −0.514915 + 0.297286i −0.734852 0.678228i \(-0.762748\pi\)
0.219937 + 0.975514i \(0.429415\pi\)
\(270\) 0 0
\(271\) 2.91324 + 1.68196i 0.176967 + 0.102172i 0.585867 0.810407i \(-0.300754\pi\)
−0.408900 + 0.912579i \(0.634088\pi\)
\(272\) −4.11761 −0.249667
\(273\) 0 0
\(274\) 7.82992i 0.473023i
\(275\) 3.85986 8.51101i 0.232758 0.513233i
\(276\) 0 0
\(277\) −14.3722 + 8.29777i −0.863539 + 0.498564i −0.865196 0.501434i \(-0.832806\pi\)
0.00165684 + 0.999999i \(0.499473\pi\)
\(278\) 2.69360 + 1.55515i 0.161551 + 0.0932716i
\(279\) 0 0
\(280\) −5.94674 4.40005i −0.355386 0.262953i
\(281\) 5.58641 0.333257 0.166629 0.986020i \(-0.446712\pi\)
0.166629 + 0.986020i \(0.446712\pi\)
\(282\) 0 0
\(283\) −2.33852 + 1.35014i −0.139010 + 0.0802577i −0.567892 0.823103i \(-0.692241\pi\)
0.428882 + 0.903361i \(0.358908\pi\)
\(284\) 9.60636 5.54624i 0.570033 0.329109i
\(285\) 0 0
\(286\) −1.03722 10.5688i −0.0613320 0.624944i
\(287\) 0.291190 + 0.0331671i 0.0171884 + 0.00195779i
\(288\) 0 0
\(289\) 0.0226302 0.0391967i 0.00133119 0.00230569i
\(290\) −22.7845 + 13.1547i −1.33795 + 0.772468i
\(291\) 0 0
\(292\) −5.46860 3.15730i −0.320026 0.184767i
\(293\) 15.8185 0.924125 0.462062 0.886847i \(-0.347110\pi\)
0.462062 + 0.886847i \(0.347110\pi\)
\(294\) 0 0
\(295\) 20.5002 1.19357
\(296\) −4.60502 + 7.97612i −0.267661 + 0.463603i
\(297\) 0 0
\(298\) 4.08541 + 7.07613i 0.236661 + 0.409909i
\(299\) −1.66887 + 2.89057i −0.0965134 + 0.167166i
\(300\) 0 0
\(301\) 1.25881 11.0517i 0.0725564 0.637008i
\(302\) 6.84898i 0.394115i
\(303\) 0 0
\(304\) 1.82770 1.05522i 0.104826 0.0605213i
\(305\) 14.8835 + 25.7790i 0.852226 + 1.47610i
\(306\) 0 0
\(307\) 12.2813i 0.700932i 0.936575 + 0.350466i \(0.113977\pi\)
−0.936575 + 0.350466i \(0.886023\pi\)
\(308\) −4.50539 + 7.53004i −0.256718 + 0.429064i
\(309\) 0 0
\(310\) 17.3750 + 10.0315i 0.986836 + 0.569750i
\(311\) 17.6592 10.1956i 1.00136 0.578137i 0.0927112 0.995693i \(-0.470447\pi\)
0.908651 + 0.417556i \(0.137113\pi\)
\(312\) 0 0
\(313\) 1.62210 2.80957i 0.0916867 0.158806i −0.816534 0.577297i \(-0.804108\pi\)
0.908221 + 0.418491i \(0.137441\pi\)
\(314\) −8.08665 −0.456356
\(315\) 0 0
\(316\) 14.3580i 0.807700i
\(317\) −9.57584 5.52861i −0.537833 0.310518i 0.206368 0.978475i \(-0.433836\pi\)
−0.744200 + 0.667957i \(0.767169\pi\)
\(318\) 0 0
\(319\) 18.1691 + 25.3736i 1.01728 + 1.42065i
\(320\) −2.42143 1.39801i −0.135362 0.0781512i
\(321\) 0 0
\(322\) 2.52921 1.09983i 0.140947 0.0612913i
\(323\) 8.69001i 0.483525i
\(324\) 0 0
\(325\) 7.81339 4.51106i 0.433409 0.250229i
\(326\) −0.682357 1.18188i −0.0377922 0.0654581i
\(327\) 0 0
\(328\) 0.110771 0.00611631
\(329\) −17.8608 13.2154i −0.984700 0.728589i
\(330\) 0 0
\(331\) 7.27038 12.5927i 0.399616 0.692156i −0.594062 0.804419i \(-0.702477\pi\)
0.993678 + 0.112263i \(0.0358100\pi\)
\(332\) 7.11677 + 12.3266i 0.390584 + 0.676511i
\(333\) 0 0
\(334\) −3.67328 + 6.36230i −0.200993 + 0.348130i
\(335\) 22.2084i 1.21338i
\(336\) 0 0
\(337\) 20.0460i 1.09198i −0.837793 0.545988i \(-0.816154\pi\)
0.837793 0.545988i \(-0.183846\pi\)
\(338\) −1.37389 + 2.37965i −0.0747299 + 0.129436i
\(339\) 0 0
\(340\) −9.97049 + 5.75647i −0.540726 + 0.312188i
\(341\) 9.82939 21.6739i 0.532291 1.17371i
\(342\) 0 0
\(343\) 17.4586 + 6.18044i 0.942675 + 0.333713i
\(344\) 4.20415i 0.226673i
\(345\) 0 0
\(346\) −0.327674 0.567548i −0.0176158 0.0305115i
\(347\) 6.04444 + 10.4693i 0.324482 + 0.562020i 0.981407 0.191936i \(-0.0614766\pi\)
−0.656925 + 0.753956i \(0.728143\pi\)
\(348\) 0 0
\(349\) 4.92511i 0.263635i 0.991274 + 0.131818i \(0.0420813\pi\)
−0.991274 + 0.131818i \(0.957919\pi\)
\(350\) −7.40713 0.843685i −0.395928 0.0450969i
\(351\) 0 0
\(352\) −1.36985 + 3.02052i −0.0730130 + 0.160994i
\(353\) 8.28001 4.78047i 0.440700 0.254438i −0.263194 0.964743i \(-0.584776\pi\)
0.703895 + 0.710304i \(0.251443\pi\)
\(354\) 0 0
\(355\) 15.5074 26.8596i 0.823047 1.42556i
\(356\) 11.9479i 0.633236i
\(357\) 0 0
\(358\) 4.10041i 0.216714i
\(359\) −4.14103 + 7.17248i −0.218555 + 0.378549i −0.954366 0.298638i \(-0.903468\pi\)
0.735811 + 0.677187i \(0.236801\pi\)
\(360\) 0 0
\(361\) −7.27300 12.5972i −0.382790 0.663011i
\(362\) 5.50322 9.53186i 0.289243 0.500983i
\(363\) 0 0
\(364\) −7.76872 + 3.37824i −0.407191 + 0.177068i
\(365\) −17.6558 −0.924144
\(366\) 0 0
\(367\) 18.6919 + 32.3753i 0.975710 + 1.68998i 0.677572 + 0.735457i \(0.263032\pi\)
0.298138 + 0.954523i \(0.403634\pi\)
\(368\) 0.902766 0.521212i 0.0470599 0.0271701i
\(369\) 0 0
\(370\) 25.7514i 1.33875i
\(371\) 28.9411 12.5851i 1.50255 0.653386i
\(372\) 0 0
\(373\) −20.6889 11.9447i −1.07123 0.618475i −0.142713 0.989764i \(-0.545583\pi\)
−0.928517 + 0.371289i \(0.878916\pi\)
\(374\) 7.95079 + 11.1035i 0.411126 + 0.574147i
\(375\) 0 0
\(376\) −7.27267 4.19888i −0.375059 0.216541i
\(377\) 30.1285i 1.55170i
\(378\) 0 0
\(379\) 17.9926 0.924217 0.462109 0.886823i \(-0.347093\pi\)
0.462109 + 0.886823i \(0.347093\pi\)
\(380\) 2.95043 5.11029i 0.151354 0.262153i
\(381\) 0 0
\(382\) −18.8331 + 10.8733i −0.963583 + 0.556325i
\(383\) 14.6369 + 8.45064i 0.747913 + 0.431808i 0.824939 0.565221i \(-0.191209\pi\)
−0.0770265 + 0.997029i \(0.524543\pi\)
\(384\) 0 0
\(385\) −0.382394 + 24.5320i −0.0194886 + 1.25027i
\(386\) 22.3009i 1.13508i
\(387\) 0 0
\(388\) 8.84554 + 15.3209i 0.449064 + 0.777802i
\(389\) −9.20118 + 5.31230i −0.466518 + 0.269344i −0.714781 0.699348i \(-0.753474\pi\)
0.248263 + 0.968693i \(0.420140\pi\)
\(390\) 0 0
\(391\) 4.29230i 0.217071i
\(392\) 6.82070 + 1.57420i 0.344497 + 0.0795092i
\(393\) 0 0
\(394\) −5.50179 + 9.52937i −0.277176 + 0.480083i
\(395\) 20.0726 + 34.7668i 1.00996 + 1.74931i
\(396\) 0 0
\(397\) 11.4791 19.8824i 0.576120 0.997870i −0.419799 0.907617i \(-0.637899\pi\)
0.995919 0.0902525i \(-0.0287674\pi\)
\(398\) 16.4501 0.824570
\(399\) 0 0
\(400\) −2.81773 −0.140887
\(401\) −8.28001 4.78047i −0.413484 0.238725i 0.278802 0.960349i \(-0.410063\pi\)
−0.692286 + 0.721624i \(0.743396\pi\)
\(402\) 0 0
\(403\) 19.8973 11.4877i 0.991156 0.572244i
\(404\) −0.117005 + 0.202659i −0.00582123 + 0.0100827i
\(405\) 0 0
\(406\) 14.8077 20.0128i 0.734891 0.993218i
\(407\) 30.4002 2.98347i 1.50688 0.147885i
\(408\) 0 0
\(409\) 11.3509 6.55346i 0.561267 0.324048i −0.192387 0.981319i \(-0.561623\pi\)
0.753654 + 0.657271i \(0.228289\pi\)
\(410\) 0.268224 0.154859i 0.0132466 0.00764795i
\(411\) 0 0
\(412\) 12.5438 0.617991
\(413\) −17.7892 + 7.73569i −0.875351 + 0.380648i
\(414\) 0 0
\(415\) 34.4655 + 19.8987i 1.69184 + 0.976786i
\(416\) −2.77293 + 1.60095i −0.135954 + 0.0784932i
\(417\) 0 0
\(418\) −6.37465 2.89099i −0.311794 0.141403i
\(419\) 4.51379i 0.220513i 0.993903 + 0.110256i \(0.0351672\pi\)
−0.993903 + 0.110256i \(0.964833\pi\)
\(420\) 0 0
\(421\) −37.3188 −1.81881 −0.909403 0.415917i \(-0.863461\pi\)
−0.909403 + 0.415917i \(0.863461\pi\)
\(422\) −0.535916 0.309411i −0.0260880 0.0150619i
\(423\) 0 0
\(424\) 10.3301 5.96410i 0.501675 0.289642i
\(425\) −5.80117 + 10.0479i −0.281398 + 0.487395i
\(426\) 0 0
\(427\) −22.6429 16.7537i −1.09577 0.810770i
\(428\) −13.0909 −0.632772
\(429\) 0 0
\(430\) −5.87745 10.1800i −0.283436 0.490925i
\(431\) −13.8494 23.9878i −0.667100 1.15545i −0.978711 0.205242i \(-0.934202\pi\)
0.311611 0.950210i \(-0.399131\pi\)
\(432\) 0 0
\(433\) 8.18187 0.393196 0.196598 0.980484i \(-0.437011\pi\)
0.196598 + 0.980484i \(0.437011\pi\)
\(434\) −18.8627 2.14850i −0.905441 0.103131i
\(435\) 0 0
\(436\) −5.63480 3.25325i −0.269858 0.155802i
\(437\) 1.09999 + 1.90524i 0.0526197 + 0.0911400i
\(438\) 0 0
\(439\) −1.16163 0.670668i −0.0554416 0.0320092i 0.472023 0.881586i \(-0.343524\pi\)
−0.527465 + 0.849577i \(0.676857\pi\)
\(440\) 0.905736 + 9.22901i 0.0431793 + 0.439976i
\(441\) 0 0
\(442\) 13.1842i 0.627109i
\(443\) 23.5122 + 13.5748i 1.11710 + 0.644958i 0.940659 0.339354i \(-0.110208\pi\)
0.176441 + 0.984311i \(0.443542\pi\)
\(444\) 0 0
\(445\) 16.7033 + 28.9309i 0.791810 + 1.37146i
\(446\) −5.17766 + 8.96797i −0.245169 + 0.424646i
\(447\) 0 0
\(448\) 2.62875 + 0.299420i 0.124197 + 0.0141463i
\(449\) 37.3766i 1.76391i −0.471334 0.881955i \(-0.656227\pi\)
0.471334 0.881955i \(-0.343773\pi\)
\(450\) 0 0
\(451\) −0.213890 0.298703i −0.0100717 0.0140654i
\(452\) 0.754977 0.435886i 0.0355111 0.0205024i
\(453\) 0 0
\(454\) −12.9313 −0.606895
\(455\) −14.0886 + 19.0409i −0.660481 + 0.892652i
\(456\) 0 0
\(457\) −20.4149 11.7865i −0.954967 0.551350i −0.0603464 0.998177i \(-0.519221\pi\)
−0.894620 + 0.446827i \(0.852554\pi\)
\(458\) −2.73849 4.74320i −0.127961 0.221635i
\(459\) 0 0
\(460\) 1.45732 2.52415i 0.0679479 0.117689i
\(461\) 38.3140 1.78446 0.892231 0.451580i \(-0.149139\pi\)
0.892231 + 0.451580i \(0.149139\pi\)
\(462\) 0 0
\(463\) −9.80424 −0.455642 −0.227821 0.973703i \(-0.573160\pi\)
−0.227821 + 0.973703i \(0.573160\pi\)
\(464\) 4.70478 8.14891i 0.218414 0.378304i
\(465\) 0 0
\(466\) 13.7588 + 23.8310i 0.637366 + 1.10395i
\(467\) −10.8457 6.26175i −0.501878 0.289759i 0.227611 0.973752i \(-0.426909\pi\)
−0.729489 + 0.683993i \(0.760242\pi\)
\(468\) 0 0
\(469\) −8.38029 19.2716i −0.386966 0.889880i
\(470\) −23.4803 −1.08307
\(471\) 0 0
\(472\) −6.34962 + 3.66595i −0.292265 + 0.168739i
\(473\) −11.3368 + 8.11789i −0.521268 + 0.373261i
\(474\) 0 0
\(475\) 5.94668i 0.272852i
\(476\) 6.47982 8.75758i 0.297002 0.401403i
\(477\) 0 0
\(478\) −6.66695 + 11.5475i −0.304939 + 0.528170i
\(479\) −7.84197 13.5827i −0.358309 0.620609i 0.629370 0.777106i \(-0.283313\pi\)
−0.987678 + 0.156497i \(0.949980\pi\)
\(480\) 0 0
\(481\) 25.5388 + 14.7448i 1.16447 + 0.672307i
\(482\) 18.1328i 0.825928i
\(483\) 0 0
\(484\) 10.7901 2.13848i 0.490460 0.0972038i
\(485\) 42.8376 + 24.7323i 1.94516 + 1.12304i
\(486\) 0 0
\(487\) 19.0262 + 32.9544i 0.862161 + 1.49331i 0.869839 + 0.493336i \(0.164223\pi\)
−0.00767777 + 0.999971i \(0.502444\pi\)
\(488\) −9.21987 5.32310i −0.417364 0.240965i
\(489\) 0 0
\(490\) 18.7166 5.72359i 0.845528 0.258565i
\(491\) 3.63565 0.164075 0.0820373 0.996629i \(-0.473857\pi\)
0.0820373 + 0.996629i \(0.473857\pi\)
\(492\) 0 0
\(493\) −19.3725 33.5541i −0.872492 1.51120i
\(494\) −3.37873 5.85213i −0.152016 0.263300i
\(495\) 0 0
\(496\) −7.17555 −0.322192
\(497\) −3.32131 + 29.1594i −0.148981 + 1.30798i
\(498\) 0 0
\(499\) 9.18656 15.9116i 0.411247 0.712301i −0.583779 0.811912i \(-0.698427\pi\)
0.995026 + 0.0996117i \(0.0317601\pi\)
\(500\) 5.28420 3.05083i 0.236316 0.136437i
\(501\) 0 0
\(502\) −16.0682 9.27699i −0.717160 0.414053i
\(503\) −34.2342 −1.52643 −0.763213 0.646146i \(-0.776380\pi\)
−0.763213 + 0.646146i \(0.776380\pi\)
\(504\) 0 0
\(505\) 0.654298i 0.0291159i
\(506\) −3.14866 1.42796i −0.139975 0.0634806i
\(507\) 0 0
\(508\) −7.93149 + 4.57925i −0.351903 + 0.203171i
\(509\) 9.23009 + 5.32899i 0.409116 + 0.236203i 0.690410 0.723418i \(-0.257430\pi\)
−0.281294 + 0.959622i \(0.590763\pi\)
\(510\) 0 0
\(511\) 15.3210 6.66236i 0.677760 0.294725i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 23.4582 13.5436i 1.03470 0.597382i
\(515\) 30.3740 17.5364i 1.33844 0.772747i
\(516\) 0 0
\(517\) 2.72035 + 27.7190i 0.119641 + 1.21908i
\(518\) −9.71725 22.3461i −0.426951 0.981831i
\(519\) 0 0
\(520\) −4.47630 + 7.75318i −0.196299 + 0.339999i
\(521\) −18.3680 + 10.6048i −0.804716 + 0.464603i −0.845118 0.534581i \(-0.820470\pi\)
0.0404016 + 0.999184i \(0.487136\pi\)
\(522\) 0 0
\(523\) 18.1257 + 10.4649i 0.792583 + 0.457598i 0.840871 0.541236i \(-0.182043\pi\)
−0.0482882 + 0.998833i \(0.515377\pi\)
\(524\) 7.74679 0.338420
\(525\) 0 0
\(526\) 11.0684 0.482603
\(527\) −14.7731 + 25.5877i −0.643525 + 1.11462i
\(528\) 0 0
\(529\) −10.9567 18.9775i −0.476377 0.825110i
\(530\) 16.6758 28.8833i 0.724348 1.25461i
\(531\) 0 0
\(532\) −0.631910 + 5.54785i −0.0273968 + 0.240530i
\(533\) 0.354679i 0.0153629i
\(534\) 0 0
\(535\) −31.6986 + 18.3012i −1.37045 + 0.791230i
\(536\) −3.97143 6.87872i −0.171540 0.297116i
\(537\) 0 0
\(538\) 9.75172i 0.420426i
\(539\) −8.92527 21.4322i −0.384438 0.923151i
\(540\) 0 0
\(541\) −0.708020 0.408775i −0.0304402 0.0175746i 0.484703 0.874679i \(-0.338928\pi\)
−0.515143 + 0.857104i \(0.672261\pi\)
\(542\) −2.91324 + 1.68196i −0.125134 + 0.0722463i
\(543\) 0 0
\(544\) 2.05881 3.56596i 0.0882706 0.152889i
\(545\) −18.1923 −0.779273
\(546\) 0 0
\(547\) 16.2530i 0.694930i 0.937693 + 0.347465i \(0.112957\pi\)
−0.937693 + 0.347465i \(0.887043\pi\)
\(548\) −6.78091 3.91496i −0.289666 0.167239i
\(549\) 0 0
\(550\) 5.44082 + 7.59824i 0.231997 + 0.323990i
\(551\) 17.1979 + 9.92919i 0.732654 + 0.422998i
\(552\) 0 0
\(553\) −30.5374 22.5949i −1.29858 0.960833i
\(554\) 16.5955i 0.705077i
\(555\) 0 0
\(556\) −2.69360 + 1.55515i −0.114234 + 0.0659530i
\(557\) 3.81751 + 6.61212i 0.161753 + 0.280165i 0.935498 0.353333i \(-0.114952\pi\)
−0.773744 + 0.633498i \(0.781619\pi\)
\(558\) 0 0
\(559\) −13.4613 −0.569353
\(560\) 6.78392 2.95000i 0.286673 0.124660i
\(561\) 0 0
\(562\) −2.79320 + 4.83797i −0.117824 + 0.204078i
\(563\) −22.5824 39.1138i −0.951734 1.64845i −0.741672 0.670763i \(-0.765967\pi\)
−0.210061 0.977688i \(-0.567366\pi\)
\(564\) 0 0
\(565\) 1.21875 2.11093i 0.0512731 0.0888075i
\(566\) 2.70029i 0.113502i
\(567\) 0 0
\(568\) 11.0925i 0.465430i
\(569\) 16.3937 28.3948i 0.687261 1.19037i −0.285459 0.958391i \(-0.592146\pi\)
0.972720 0.231981i \(-0.0745207\pi\)
\(570\) 0 0
\(571\) −4.58774 + 2.64873i −0.191991 + 0.110846i −0.592914 0.805266i \(-0.702023\pi\)
0.400923 + 0.916112i \(0.368689\pi\)
\(572\) 9.67142 + 4.38612i 0.404382 + 0.183393i
\(573\) 0 0
\(574\) −0.174319 + 0.235594i −0.00727592 + 0.00983352i
\(575\) 2.93727i 0.122493i
\(576\) 0 0
\(577\) −6.83877 11.8451i −0.284702 0.493118i 0.687835 0.725867i \(-0.258561\pi\)
−0.972537 + 0.232749i \(0.925228\pi\)
\(578\) 0.0226302 + 0.0391967i 0.000941294 + 0.00163037i
\(579\) 0 0
\(580\) 26.3093i 1.09243i
\(581\) −37.4165 4.26181i −1.55230 0.176810i
\(582\) 0 0
\(583\) −36.0293 16.3398i −1.49218 0.676725i
\(584\) 5.46860 3.15730i 0.226292 0.130650i
\(585\) 0 0
\(586\) −7.90923 + 13.6992i −0.326727 + 0.565909i
\(587\) 24.5620i 1.01378i 0.862011 + 0.506890i \(0.169205\pi\)
−0.862011 + 0.506890i \(0.830795\pi\)
\(588\) 0 0
\(589\) 15.1436i 0.623982i
\(590\) −10.2501 + 17.7537i −0.421989 + 0.730907i
\(591\) 0 0
\(592\) −4.60502 7.97612i −0.189265 0.327817i
\(593\) 2.76466 4.78853i 0.113531 0.196641i −0.803661 0.595088i \(-0.797117\pi\)
0.917192 + 0.398447i \(0.130451\pi\)
\(594\) 0 0
\(595\) 3.44720 30.2647i 0.141321 1.24073i
\(596\) −8.17082 −0.334690
\(597\) 0 0
\(598\) −1.66887 2.89057i −0.0682453 0.118204i
\(599\) 20.9741 12.1094i 0.856977 0.494776i −0.00602174 0.999982i \(-0.501917\pi\)
0.862999 + 0.505206i \(0.168583\pi\)
\(600\) 0 0
\(601\) 16.7793i 0.684443i −0.939619 0.342222i \(-0.888821\pi\)
0.939619 0.342222i \(-0.111179\pi\)
\(602\) 8.94163 + 6.61600i 0.364434 + 0.269648i
\(603\) 0 0
\(604\) −5.93139 3.42449i −0.241345 0.139341i
\(605\) 23.1379 20.2629i 0.940688 0.823804i
\(606\) 0 0
\(607\) −30.9524 17.8704i −1.25632 0.725337i −0.283963 0.958835i \(-0.591649\pi\)
−0.972357 + 0.233498i \(0.924983\pi\)
\(608\) 2.11045i 0.0855900i
\(609\) 0 0
\(610\) −29.7670 −1.20523
\(611\) −13.4444 + 23.2864i −0.543903 + 0.942068i
\(612\) 0 0
\(613\) −7.82971 + 4.52049i −0.316239 + 0.182581i −0.649715 0.760178i \(-0.725112\pi\)
0.333476 + 0.942759i \(0.391778\pi\)
\(614\) −10.6359 6.14066i −0.429231 0.247817i
\(615\) 0 0
\(616\) −4.26851 7.66680i −0.171983 0.308904i
\(617\) 11.5919i 0.466672i 0.972396 + 0.233336i \(0.0749643\pi\)
−0.972396 + 0.233336i \(0.925036\pi\)
\(618\) 0 0
\(619\) 0.200558 + 0.347377i 0.00806111 + 0.0139622i 0.870028 0.493003i \(-0.164101\pi\)
−0.861967 + 0.506965i \(0.830767\pi\)
\(620\) −17.3750 + 10.0315i −0.697799 + 0.402874i
\(621\) 0 0
\(622\) 20.3911i 0.817609i
\(623\) −25.4114 18.8022i −1.01809 0.753292i
\(624\) 0 0
\(625\) 15.5745 26.9759i 0.622981 1.07903i
\(626\) 1.62210 + 2.80957i 0.0648323 + 0.112293i
\(627\) 0 0
\(628\) 4.04332 7.00324i 0.161346 0.279460i
\(629\) −37.9234 −1.51210
\(630\) 0 0
\(631\) 32.7927 1.30546 0.652728 0.757592i \(-0.273624\pi\)
0.652728 + 0.757592i \(0.273624\pi\)
\(632\) −12.4344 7.17899i −0.494613 0.285565i
\(633\) 0 0
\(634\) 9.57584 5.52861i 0.380305 0.219569i
\(635\) −12.8037 + 22.1766i −0.508098 + 0.880052i
\(636\) 0 0
\(637\) 5.04045 21.8392i 0.199710 0.865302i
\(638\) −31.0588 + 3.04811i −1.22963 + 0.120676i
\(639\) 0 0
\(640\) 2.42143 1.39801i 0.0957152 0.0552612i
\(641\) 27.3662 15.7999i 1.08090 0.624058i 0.149761 0.988722i \(-0.452150\pi\)
0.931139 + 0.364664i \(0.118816\pi\)
\(642\) 0 0
\(643\) −4.86178 −0.191730 −0.0958650 0.995394i \(-0.530562\pi\)
−0.0958650 + 0.995394i \(0.530562\pi\)
\(644\) −0.312123 + 2.74028i −0.0122994 + 0.107982i
\(645\) 0 0
\(646\) 7.52577 + 4.34501i 0.296098 + 0.170952i
\(647\) −18.9738 + 10.9545i −0.745937 + 0.430667i −0.824224 0.566264i \(-0.808388\pi\)
0.0782867 + 0.996931i \(0.475055\pi\)
\(648\) 0 0
\(649\) 22.1461 + 10.0436i 0.869312 + 0.394245i
\(650\) 9.02212i 0.353877i
\(651\) 0 0
\(652\) 1.36471 0.0534463
\(653\) −31.4813 18.1757i −1.23196 0.711271i −0.264520 0.964380i \(-0.585214\pi\)
−0.967438 + 0.253109i \(0.918547\pi\)
\(654\) 0 0
\(655\) 18.7583 10.8301i 0.732947 0.423167i
\(656\) −0.0553856 + 0.0959306i −0.00216244 + 0.00374546i
\(657\) 0 0
\(658\) 20.3753 8.86024i 0.794312 0.345408i
\(659\) −1.25809 −0.0490083 −0.0245041 0.999700i \(-0.507801\pi\)
−0.0245041 + 0.999700i \(0.507801\pi\)
\(660\) 0 0
\(661\) −19.0453 32.9875i −0.740778 1.28307i −0.952141 0.305658i \(-0.901124\pi\)
0.211363 0.977408i \(-0.432210\pi\)
\(662\) 7.27038 + 12.5927i 0.282571 + 0.489428i
\(663\) 0 0
\(664\) −14.2335 −0.552369
\(665\) 6.22583 + 14.3171i 0.241427 + 0.555194i
\(666\) 0 0
\(667\) 8.49463 + 4.90437i 0.328913 + 0.189898i
\(668\) −3.67328 6.36230i −0.142123 0.246165i
\(669\) 0 0
\(670\) −19.2331 11.1042i −0.743038 0.428993i
\(671\) 3.44870 + 35.1406i 0.133136 + 1.35659i
\(672\) 0 0
\(673\) 19.4116i 0.748263i −0.927376 0.374131i \(-0.877941\pi\)
0.927376 0.374131i \(-0.122059\pi\)
\(674\) 17.3604 + 10.0230i 0.668696 + 0.386072i
\(675\) 0 0
\(676\) −1.37389 2.37965i −0.0528420 0.0915250i
\(677\) −5.25697 + 9.10535i −0.202042 + 0.349947i −0.949186 0.314715i \(-0.898091\pi\)
0.747144 + 0.664662i \(0.231424\pi\)
\(678\) 0 0
\(679\) −46.5055 5.29706i −1.78472 0.203283i
\(680\) 11.5129i 0.441501i
\(681\) 0 0
\(682\) 13.8554 + 19.3494i 0.530551 + 0.740928i
\(683\) 37.1706 21.4605i 1.42230 0.821163i 0.425800 0.904817i \(-0.359993\pi\)
0.996495 + 0.0836546i \(0.0266593\pi\)
\(684\) 0 0
\(685\) −21.8926 −0.836474
\(686\) −14.0817 + 12.0294i −0.537642 + 0.459283i
\(687\) 0 0
\(688\) 3.64090 + 2.10208i 0.138808 + 0.0801409i
\(689\) −19.0965 33.0761i −0.727519 1.26010i
\(690\) 0 0
\(691\) 23.5279 40.7515i 0.895043 1.55026i 0.0612926 0.998120i \(-0.480478\pi\)
0.833751 0.552141i \(-0.186189\pi\)
\(692\) 0.655347 0.0249126
\(693\) 0 0
\(694\) −12.0889 −0.458887
\(695\) −4.34823 + 7.53135i −0.164938 + 0.285680i
\(696\) 0 0
\(697\) 0.228056 + 0.395005i 0.00863825 + 0.0149619i
\(698\) −4.26527 2.46255i −0.161443 0.0932091i
\(699\) 0 0
\(700\) 4.43422 5.99292i 0.167598 0.226511i
\(701\) 1.94709 0.0735406 0.0367703 0.999324i \(-0.488293\pi\)
0.0367703 + 0.999324i \(0.488293\pi\)
\(702\) 0 0
\(703\) 16.8332 9.71865i 0.634876 0.366546i
\(704\) −1.93092 2.69658i −0.0727744 0.101631i
\(705\) 0 0
\(706\) 9.56093i 0.359830i
\(707\) −0.246898 0.567774i −0.00928555 0.0213534i
\(708\) 0 0
\(709\) −11.4549 + 19.8405i −0.430199 + 0.745126i −0.996890 0.0788042i \(-0.974890\pi\)
0.566691 + 0.823930i \(0.308223\pi\)
\(710\) 15.5074 + 26.8596i 0.581982 + 1.00802i
\(711\) 0 0
\(712\) −10.3472 5.97394i −0.387776 0.223883i
\(713\) 7.47996i 0.280127i
\(714\) 0 0
\(715\) 29.5505 2.90008i 1.10512 0.108457i
\(716\) 3.55106 + 2.05021i 0.132709 + 0.0766199i
\(717\) 0 0
\(718\) −4.14103 7.17248i −0.154542 0.267674i
\(719\) 1.87531 + 1.08271i 0.0699372 + 0.0403782i 0.534561 0.845130i \(-0.320477\pi\)
−0.464624 + 0.885508i \(0.653810\pi\)
\(720\) 0 0
\(721\) −19.7400 + 26.6790i −0.735157 + 0.993577i
\(722\) 14.5460 0.541346
\(723\) 0 0
\(724\) 5.50322 + 9.53186i 0.204526 + 0.354249i
\(725\) −13.2568 22.9615i −0.492345 0.852767i
\(726\) 0 0
\(727\) 19.8670 0.736825 0.368412 0.929662i \(-0.379901\pi\)
0.368412 + 0.929662i \(0.379901\pi\)
\(728\) 0.958715 8.41703i 0.0355323 0.311956i
\(729\) 0 0
\(730\) 8.82788 15.2903i 0.326734 0.565921i
\(731\) 14.9918 8.65553i 0.554493 0.320137i
\(732\) 0 0
\(733\) 31.7695 + 18.3421i 1.17343 + 0.677483i 0.954487 0.298254i \(-0.0964042\pi\)
0.218948 + 0.975737i \(0.429738\pi\)
\(734\) −37.3838 −1.37986
\(735\) 0 0
\(736\) 1.04242i 0.0384243i
\(737\) −10.8805 + 23.9916i −0.400788 + 0.883741i
\(738\) 0 0
\(739\) 31.5162 18.1959i 1.15934 0.669346i 0.208195 0.978087i \(-0.433241\pi\)
0.951146 + 0.308742i \(0.0999079\pi\)
\(740\) −22.3014 12.8757i −0.819816 0.473321i
\(741\) 0 0
\(742\) −3.57154 + 31.3563i −0.131115 + 1.15113i
\(743\) −0.143528 −0.00526553 −0.00263276 0.999997i \(-0.500838\pi\)
−0.00263276 + 0.999997i \(0.500838\pi\)
\(744\) 0 0
\(745\) −19.7850 + 11.4229i −0.724867 + 0.418502i
\(746\) 20.6889 11.9447i 0.757474 0.437328i
\(747\) 0 0
\(748\) −13.5913 + 1.33385i −0.496947 + 0.0487704i
\(749\) 20.6009 27.8425i 0.752741 1.01734i
\(750\) 0 0
\(751\) 2.63144 4.55779i 0.0960226 0.166316i −0.814012 0.580848i \(-0.802721\pi\)
0.910035 + 0.414532i \(0.136055\pi\)
\(752\) 7.27267 4.19888i 0.265207 0.153117i
\(753\) 0 0
\(754\) −26.0921 15.0643i −0.950217 0.548608i
\(755\) −19.1499 −0.696936
\(756\) 0 0
\(757\) −13.6449 −0.495932 −0.247966 0.968769i \(-0.579762\pi\)
−0.247966 + 0.968769i \(0.579762\pi\)
\(758\) −8.99630 + 15.5820i −0.326760 + 0.565965i
\(759\) 0 0
\(760\) 2.95043 + 5.11029i 0.107023 + 0.185370i
\(761\) −14.3603 + 24.8727i −0.520559 + 0.901635i 0.479155 + 0.877730i \(0.340943\pi\)
−0.999714 + 0.0239048i \(0.992390\pi\)
\(762\) 0 0
\(763\) 15.7866 6.86483i 0.571513 0.248523i
\(764\) 21.7465i 0.786763i
\(765\) 0 0
\(766\) −14.6369 + 8.45064i −0.528854 + 0.305334i
\(767\) 11.7380 + 20.3309i 0.423836 + 0.734106i
\(768\) 0 0
\(769\) 40.9742i 1.47757i −0.673943 0.738783i \(-0.735401\pi\)
0.673943 0.738783i \(-0.264599\pi\)
\(770\) −21.0541 12.5972i −0.758739 0.453970i
\(771\) 0 0
\(772\) 19.3131 + 11.1504i 0.695094 + 0.401313i
\(773\) 9.44578 5.45352i 0.339741 0.196150i −0.320416 0.947277i \(-0.603823\pi\)
0.660158 + 0.751127i \(0.270490\pi\)
\(774\) 0 0
\(775\) −10.1094 + 17.5100i −0.363140 + 0.628977i
\(776\) −17.6911 −0.635073
\(777\) 0 0
\(778\) 10.6246i 0.380911i
\(779\) −0.202457 0.116888i −0.00725376 0.00418796i
\(780\) 0 0
\(781\) 29.9117 21.4187i 1.07033 0.766421i
\(782\) 3.71724 + 2.14615i 0.132928 + 0.0767462i
\(783\) 0 0
\(784\) −4.77365 + 5.11979i −0.170487 + 0.182850i
\(785\) 22.6104i 0.807001i
\(786\) 0 0
\(787\) 16.7122 9.64880i 0.595726 0.343943i −0.171632 0.985161i \(-0.554904\pi\)
0.767358 + 0.641219i \(0.221571\pi\)
\(788\) −5.50179 9.52937i −0.195993 0.339470i
\(789\) 0 0
\(790\) −40.1452 −1.42830