Properties

Label 1764.3.z.l.901.2
Level $1764$
Weight $3$
Character 1764.901
Analytic conductor $48.066$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1764.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.0655186332\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.339738624.1
Defining polynomial: \(x^{8} - 4 x^{6} + 14 x^{4} - 8 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: no (minimal twist has level 588)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.2
Root \(1.60021 - 0.923880i\) of defining polynomial
Character \(\chi\) \(=\) 1764.901
Dual form 1764.3.z.l.325.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.804540 - 0.464502i) q^{5} +O(q^{10})\) \(q+(-0.804540 - 0.464502i) q^{5} +(4.84490 + 8.39161i) q^{11} -15.9753i q^{13} +(9.14154 - 5.27787i) q^{17} +(-6.25313 - 3.61025i) q^{19} +(-5.65003 + 9.78614i) q^{23} +(-12.0685 - 20.9032i) q^{25} -46.3148 q^{29} +(0.418333 - 0.241525i) q^{31} +(-1.24065 + 2.14887i) q^{37} +55.8520i q^{41} +60.6786 q^{43} +(31.6850 + 18.2933i) q^{47} +(-14.2615 - 24.7016i) q^{53} -9.00185i q^{55} +(81.4683 - 47.0358i) q^{59} +(-95.4301 - 55.0966i) q^{61} +(-7.42055 + 12.8528i) q^{65} +(-41.0155 - 71.0409i) q^{67} -127.349 q^{71} +(40.0577 - 23.1273i) q^{73} +(-9.35016 + 16.1949i) q^{79} -59.6357i q^{83} -9.80632 q^{85} +(-61.5988 - 35.5641i) q^{89} +(3.35393 + 5.80917i) q^{95} -102.239i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 48q^{17} - 96q^{19} - 8q^{23} - 36q^{25} - 80q^{29} + 48q^{31} - 64q^{37} - 112q^{43} + 264q^{47} - 72q^{53} - 168q^{59} - 144q^{61} + 120q^{65} + 32q^{67} - 224q^{71} + 336q^{73} + 216q^{79} - 96q^{85} - 96q^{89} - 136q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.804540 0.464502i −0.160908 0.0929003i 0.417384 0.908730i \(-0.362947\pi\)
−0.578292 + 0.815830i \(0.696280\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.84490 + 8.39161i 0.440445 + 0.762874i 0.997722 0.0674529i \(-0.0214872\pi\)
−0.557277 + 0.830327i \(0.688154\pi\)
\(12\) 0 0
\(13\) 15.9753i 1.22887i −0.788968 0.614434i \(-0.789384\pi\)
0.788968 0.614434i \(-0.210616\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 9.14154 5.27787i 0.537738 0.310463i −0.206424 0.978463i \(-0.566183\pi\)
0.744162 + 0.668000i \(0.232849\pi\)
\(18\) 0 0
\(19\) −6.25313 3.61025i −0.329112 0.190013i 0.326335 0.945254i \(-0.394186\pi\)
−0.655447 + 0.755241i \(0.727520\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.65003 + 9.78614i −0.245654 + 0.425484i −0.962315 0.271937i \(-0.912336\pi\)
0.716662 + 0.697421i \(0.245669\pi\)
\(24\) 0 0
\(25\) −12.0685 20.9032i −0.482739 0.836129i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −46.3148 −1.59706 −0.798532 0.601953i \(-0.794390\pi\)
−0.798532 + 0.601953i \(0.794390\pi\)
\(30\) 0 0
\(31\) 0.418333 0.241525i 0.0134946 0.00779111i −0.493238 0.869895i \(-0.664187\pi\)
0.506732 + 0.862104i \(0.330853\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1.24065 + 2.14887i −0.0335312 + 0.0580777i −0.882304 0.470680i \(-0.844009\pi\)
0.848773 + 0.528758i \(0.177342\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 55.8520i 1.36224i 0.732170 + 0.681122i \(0.238508\pi\)
−0.732170 + 0.681122i \(0.761492\pi\)
\(42\) 0 0
\(43\) 60.6786 1.41113 0.705566 0.708645i \(-0.250693\pi\)
0.705566 + 0.708645i \(0.250693\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 31.6850 + 18.2933i 0.674149 + 0.389220i 0.797647 0.603125i \(-0.206078\pi\)
−0.123498 + 0.992345i \(0.539411\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −14.2615 24.7016i −0.269084 0.466068i 0.699541 0.714592i \(-0.253388\pi\)
−0.968626 + 0.248524i \(0.920054\pi\)
\(54\) 0 0
\(55\) 9.00185i 0.163670i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 81.4683 47.0358i 1.38082 0.797216i 0.388563 0.921422i \(-0.372972\pi\)
0.992256 + 0.124206i \(0.0396383\pi\)
\(60\) 0 0
\(61\) −95.4301 55.0966i −1.56443 0.903223i −0.996800 0.0799382i \(-0.974528\pi\)
−0.567628 0.823285i \(-0.692139\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −7.42055 + 12.8528i −0.114162 + 0.197735i
\(66\) 0 0
\(67\) −41.0155 71.0409i −0.612171 1.06031i −0.990874 0.134793i \(-0.956963\pi\)
0.378702 0.925518i \(-0.376370\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −127.349 −1.79365 −0.896827 0.442382i \(-0.854133\pi\)
−0.896827 + 0.442382i \(0.854133\pi\)
\(72\) 0 0
\(73\) 40.0577 23.1273i 0.548735 0.316812i −0.199877 0.979821i \(-0.564054\pi\)
0.748612 + 0.663009i \(0.230721\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −9.35016 + 16.1949i −0.118356 + 0.204999i −0.919116 0.393986i \(-0.871096\pi\)
0.800760 + 0.598985i \(0.204429\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 59.6357i 0.718502i −0.933241 0.359251i \(-0.883032\pi\)
0.933241 0.359251i \(-0.116968\pi\)
\(84\) 0 0
\(85\) −9.80632 −0.115368
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −61.5988 35.5641i −0.692121 0.399596i 0.112285 0.993676i \(-0.464183\pi\)
−0.804406 + 0.594080i \(0.797516\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.35393 + 5.80917i 0.0353045 + 0.0611492i
\(96\) 0 0
\(97\) 102.239i 1.05401i −0.849861 0.527007i \(-0.823314\pi\)
0.849861 0.527007i \(-0.176686\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 94.3357 54.4647i 0.934017 0.539255i 0.0459371 0.998944i \(-0.485373\pi\)
0.888080 + 0.459690i \(0.152039\pi\)
\(102\) 0 0
\(103\) 0.647083 + 0.373594i 0.00628236 + 0.00362712i 0.503138 0.864206i \(-0.332179\pi\)
−0.496856 + 0.867833i \(0.665512\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.64630 13.2438i 0.0714608 0.123774i −0.828081 0.560609i \(-0.810567\pi\)
0.899542 + 0.436835i \(0.143901\pi\)
\(108\) 0 0
\(109\) 27.1116 + 46.9587i 0.248730 + 0.430814i 0.963174 0.268879i \(-0.0866533\pi\)
−0.714443 + 0.699693i \(0.753320\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −65.2511 −0.577444 −0.288722 0.957413i \(-0.593230\pi\)
−0.288722 + 0.957413i \(0.593230\pi\)
\(114\) 0 0
\(115\) 9.09136 5.24890i 0.0790553 0.0456426i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 13.5539 23.4761i 0.112016 0.194017i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 45.6484i 0.365187i
\(126\) 0 0
\(127\) −235.761 −1.85639 −0.928193 0.372098i \(-0.878639\pi\)
−0.928193 + 0.372098i \(0.878639\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −196.180 113.265i −1.49756 0.864616i −0.497563 0.867428i \(-0.665772\pi\)
−0.999996 + 0.00281117i \(0.999105\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −126.872 219.748i −0.926070 1.60400i −0.789832 0.613323i \(-0.789832\pi\)
−0.136238 0.990676i \(-0.543501\pi\)
\(138\) 0 0
\(139\) 148.040i 1.06503i 0.846419 + 0.532517i \(0.178754\pi\)
−0.846419 + 0.532517i \(0.821246\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 134.058 77.3986i 0.937471 0.541249i
\(144\) 0 0
\(145\) 37.2622 + 21.5133i 0.256980 + 0.148368i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −122.732 + 212.579i −0.823708 + 1.42670i 0.0791950 + 0.996859i \(0.474765\pi\)
−0.902903 + 0.429845i \(0.858568\pi\)
\(150\) 0 0
\(151\) −88.1270 152.640i −0.583623 1.01086i −0.995046 0.0994194i \(-0.968301\pi\)
0.411423 0.911445i \(-0.365032\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.448754 −0.00289519
\(156\) 0 0
\(157\) 179.836 103.828i 1.14545 0.661326i 0.197675 0.980268i \(-0.436661\pi\)
0.947774 + 0.318942i \(0.103327\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −47.5121 + 82.2933i −0.291485 + 0.504867i −0.974161 0.225854i \(-0.927483\pi\)
0.682676 + 0.730721i \(0.260816\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 158.478i 0.948972i −0.880263 0.474486i \(-0.842634\pi\)
0.880263 0.474486i \(-0.157366\pi\)
\(168\) 0 0
\(169\) −86.2098 −0.510117
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −187.054 107.995i −1.08123 0.624251i −0.150005 0.988685i \(-0.547929\pi\)
−0.931229 + 0.364434i \(0.881262\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −131.029 226.950i −0.732008 1.26787i −0.956024 0.293289i \(-0.905250\pi\)
0.224016 0.974585i \(-0.428083\pi\)
\(180\) 0 0
\(181\) 83.8554i 0.463290i 0.972800 + 0.231645i \(0.0744107\pi\)
−0.972800 + 0.231645i \(0.925589\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.99631 1.15257i 0.0107909 0.00623011i
\(186\) 0 0
\(187\) 88.5797 + 51.1415i 0.473688 + 0.273484i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 116.846 202.384i 0.611760 1.05960i −0.379183 0.925322i \(-0.623795\pi\)
0.990944 0.134278i \(-0.0428716\pi\)
\(192\) 0 0
\(193\) 111.819 + 193.677i 0.579375 + 1.00351i 0.995551 + 0.0942227i \(0.0300366\pi\)
−0.416176 + 0.909284i \(0.636630\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 133.006 0.675158 0.337579 0.941297i \(-0.390392\pi\)
0.337579 + 0.941297i \(0.390392\pi\)
\(198\) 0 0
\(199\) 52.5277 30.3269i 0.263959 0.152397i −0.362180 0.932108i \(-0.617968\pi\)
0.626139 + 0.779711i \(0.284634\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 25.9433 44.9352i 0.126553 0.219196i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 69.9651i 0.334761i
\(210\) 0 0
\(211\) −169.145 −0.801637 −0.400819 0.916157i \(-0.631274\pi\)
−0.400819 + 0.916157i \(0.631274\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −48.8184 28.1853i −0.227062 0.131095i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −84.3155 146.039i −0.381518 0.660809i
\(222\) 0 0
\(223\) 162.093i 0.726874i 0.931619 + 0.363437i \(0.118397\pi\)
−0.931619 + 0.363437i \(0.881603\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 306.755 177.105i 1.35134 0.780198i 0.362905 0.931826i \(-0.381785\pi\)
0.988438 + 0.151628i \(0.0484517\pi\)
\(228\) 0 0
\(229\) −113.844 65.7279i −0.497136 0.287021i 0.230394 0.973097i \(-0.425998\pi\)
−0.727530 + 0.686076i \(0.759332\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −71.4744 + 123.797i −0.306757 + 0.531319i −0.977651 0.210234i \(-0.932577\pi\)
0.670894 + 0.741553i \(0.265911\pi\)
\(234\) 0 0
\(235\) −16.9946 29.4354i −0.0723173 0.125257i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −47.5259 −0.198853 −0.0994266 0.995045i \(-0.531701\pi\)
−0.0994266 + 0.995045i \(0.531701\pi\)
\(240\) 0 0
\(241\) 205.380 118.576i 0.852198 0.492017i −0.00919389 0.999958i \(-0.502927\pi\)
0.861392 + 0.507941i \(0.169593\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −57.6747 + 99.8955i −0.233501 + 0.404435i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 309.248i 1.23206i −0.787722 0.616031i \(-0.788739\pi\)
0.787722 0.616031i \(-0.211261\pi\)
\(252\) 0 0
\(253\) −109.495 −0.432788
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −155.317 89.6724i −0.604347 0.348920i 0.166403 0.986058i \(-0.446785\pi\)
−0.770750 + 0.637138i \(0.780118\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 37.3848 + 64.7523i 0.142147 + 0.246206i 0.928305 0.371820i \(-0.121266\pi\)
−0.786158 + 0.618026i \(0.787933\pi\)
\(264\) 0 0
\(265\) 26.4979i 0.0999921i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −49.2164 + 28.4151i −0.182961 + 0.105632i −0.588683 0.808364i \(-0.700353\pi\)
0.405722 + 0.913996i \(0.367020\pi\)
\(270\) 0 0
\(271\) 11.6951 + 6.75218i 0.0431554 + 0.0249158i 0.521422 0.853299i \(-0.325402\pi\)
−0.478267 + 0.878214i \(0.658735\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 116.941 202.548i 0.425240 0.736538i
\(276\) 0 0
\(277\) 124.726 + 216.032i 0.450274 + 0.779897i 0.998403 0.0564965i \(-0.0179930\pi\)
−0.548129 + 0.836394i \(0.684660\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −200.268 −0.712696 −0.356348 0.934353i \(-0.615978\pi\)
−0.356348 + 0.934353i \(0.615978\pi\)
\(282\) 0 0
\(283\) −59.5549 + 34.3840i −0.210441 + 0.121498i −0.601516 0.798860i \(-0.705437\pi\)
0.391075 + 0.920359i \(0.372103\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −88.7881 + 153.786i −0.307225 + 0.532130i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 253.164i 0.864040i 0.901864 + 0.432020i \(0.142199\pi\)
−0.901864 + 0.432020i \(0.857801\pi\)
\(294\) 0 0
\(295\) −87.3927 −0.296247
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 156.336 + 90.2609i 0.522864 + 0.301876i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 51.1849 + 88.6549i 0.167819 + 0.290672i
\(306\) 0 0
\(307\) 529.913i 1.72610i −0.505116 0.863051i \(-0.668550\pi\)
0.505116 0.863051i \(-0.331450\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 26.4186 15.2528i 0.0849473 0.0490444i −0.456925 0.889505i \(-0.651049\pi\)
0.541872 + 0.840461i \(0.317716\pi\)
\(312\) 0 0
\(313\) 7.44956 + 4.30101i 0.0238005 + 0.0137412i 0.511853 0.859073i \(-0.328959\pi\)
−0.488053 + 0.872814i \(0.662293\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −240.076 + 415.824i −0.757337 + 1.31175i 0.186866 + 0.982385i \(0.440167\pi\)
−0.944204 + 0.329362i \(0.893167\pi\)
\(318\) 0 0
\(319\) −224.391 388.656i −0.703419 1.21836i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −76.2176 −0.235968
\(324\) 0 0
\(325\) −333.935 + 192.797i −1.02749 + 0.593223i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 44.5098 77.0932i 0.134471 0.232910i −0.790924 0.611914i \(-0.790400\pi\)
0.925395 + 0.379004i \(0.123733\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 76.2070i 0.227484i
\(336\) 0 0
\(337\) 495.701 1.47092 0.735461 0.677567i \(-0.236966\pi\)
0.735461 + 0.677567i \(0.236966\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4.05356 + 2.34032i 0.0118873 + 0.00686312i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −30.1767 52.2676i −0.0869645 0.150627i 0.819262 0.573419i \(-0.194383\pi\)
−0.906227 + 0.422792i \(0.861050\pi\)
\(348\) 0 0
\(349\) 72.2171i 0.206926i 0.994633 + 0.103463i \(0.0329923\pi\)
−0.994633 + 0.103463i \(0.967008\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −332.000 + 191.680i −0.940510 + 0.543004i −0.890120 0.455726i \(-0.849380\pi\)
−0.0503901 + 0.998730i \(0.516046\pi\)
\(354\) 0 0
\(355\) 102.458 + 59.1540i 0.288613 + 0.166631i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −40.0224 + 69.3209i −0.111483 + 0.193094i −0.916368 0.400336i \(-0.868893\pi\)
0.804885 + 0.593430i \(0.202227\pi\)
\(360\) 0 0
\(361\) −154.432 267.485i −0.427790 0.740954i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −42.9707 −0.117728
\(366\) 0 0
\(367\) −70.5218 + 40.7158i −0.192157 + 0.110942i −0.592992 0.805208i \(-0.702054\pi\)
0.400835 + 0.916150i \(0.368720\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 266.126 460.944i 0.713475 1.23577i −0.250070 0.968228i \(-0.580454\pi\)
0.963545 0.267547i \(-0.0862131\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 739.893i 1.96258i
\(378\) 0 0
\(379\) 440.518 1.16232 0.581159 0.813790i \(-0.302600\pi\)
0.581159 + 0.813790i \(0.302600\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 605.603 + 349.645i 1.58121 + 0.912911i 0.994683 + 0.102980i \(0.0328377\pi\)
0.586525 + 0.809931i \(0.300496\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 312.231 + 540.800i 0.802650 + 1.39023i 0.917866 + 0.396891i \(0.129911\pi\)
−0.115216 + 0.993340i \(0.536756\pi\)
\(390\) 0 0
\(391\) 119.281i 0.305065i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 15.0452 8.68632i 0.0380890 0.0219907i
\(396\) 0 0
\(397\) −547.801 316.273i −1.37985 0.796658i −0.387711 0.921781i \(-0.626734\pi\)
−0.992141 + 0.125123i \(0.960067\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 233.671 404.731i 0.582721 1.00930i −0.412434 0.910988i \(-0.635321\pi\)
0.995155 0.0983156i \(-0.0313455\pi\)
\(402\) 0 0
\(403\) −3.85842 6.68298i −0.00957425 0.0165831i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −24.0434 −0.0590746
\(408\) 0 0
\(409\) 280.848 162.148i 0.686671 0.396450i −0.115693 0.993285i \(-0.536909\pi\)
0.802364 + 0.596835i \(0.203575\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −27.7009 + 47.9793i −0.0667491 + 0.115613i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 28.8211i 0.0687854i −0.999408 0.0343927i \(-0.989050\pi\)
0.999408 0.0343927i \(-0.0109497\pi\)
\(420\) 0 0
\(421\) −0.326830 −0.000776319 −0.000388160 1.00000i \(-0.500124\pi\)
−0.000388160 1.00000i \(0.500124\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −220.649 127.392i −0.519174 0.299745i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 195.669 + 338.908i 0.453988 + 0.786329i 0.998629 0.0523393i \(-0.0166677\pi\)
−0.544642 + 0.838669i \(0.683334\pi\)
\(432\) 0 0
\(433\) 470.579i 1.08679i −0.839478 0.543394i \(-0.817139\pi\)
0.839478 0.543394i \(-0.182861\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 70.6607 40.7960i 0.161695 0.0933547i
\(438\) 0 0
\(439\) 116.395 + 67.2006i 0.265136 + 0.153077i 0.626675 0.779280i \(-0.284415\pi\)
−0.361539 + 0.932357i \(0.617749\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 164.528 284.971i 0.371395 0.643275i −0.618385 0.785875i \(-0.712213\pi\)
0.989780 + 0.142600i \(0.0455462\pi\)
\(444\) 0 0
\(445\) 33.0391 + 57.2254i 0.0742452 + 0.128596i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −130.592 −0.290851 −0.145426 0.989369i \(-0.546455\pi\)
−0.145426 + 0.989369i \(0.546455\pi\)
\(450\) 0 0
\(451\) −468.688 + 270.597i −1.03922 + 0.599994i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −158.141 + 273.908i −0.346041 + 0.599361i −0.985542 0.169429i \(-0.945808\pi\)
0.639501 + 0.768790i \(0.279141\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 31.4853i 0.0682979i −0.999417 0.0341490i \(-0.989128\pi\)
0.999417 0.0341490i \(-0.0108721\pi\)
\(462\) 0 0
\(463\) 667.424 1.44152 0.720761 0.693184i \(-0.243793\pi\)
0.720761 + 0.693184i \(0.243793\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 748.502 + 432.148i 1.60279 + 0.925370i 0.990927 + 0.134405i \(0.0429122\pi\)
0.611861 + 0.790965i \(0.290421\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 293.982 + 509.192i 0.621526 + 1.07651i
\(474\) 0 0
\(475\) 174.281i 0.366907i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −542.476 + 313.198i −1.13252 + 0.653859i −0.944567 0.328320i \(-0.893518\pi\)
−0.187950 + 0.982179i \(0.560184\pi\)
\(480\) 0 0
\(481\) 34.3289 + 19.8198i 0.0713698 + 0.0412054i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −47.4904 + 82.2557i −0.0979183 + 0.169599i
\(486\) 0 0
\(487\) 242.924 + 420.756i 0.498817 + 0.863976i 0.999999 0.00136550i \(-0.000434653\pi\)
−0.501182 + 0.865342i \(0.667101\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.00051 0.0122210 0.00611049 0.999981i \(-0.498055\pi\)
0.00611049 + 0.999981i \(0.498055\pi\)
\(492\) 0 0
\(493\) −423.389 + 244.444i −0.858801 + 0.495829i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 343.775 595.437i 0.688929 1.19326i −0.283256 0.959044i \(-0.591415\pi\)
0.972185 0.234215i \(-0.0752520\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 435.270i 0.865348i −0.901550 0.432674i \(-0.857570\pi\)
0.901550 0.432674i \(-0.142430\pi\)
\(504\) 0 0
\(505\) −101.196 −0.200388
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 418.381 + 241.553i 0.821967 + 0.474563i 0.851094 0.525013i \(-0.175939\pi\)
−0.0291272 + 0.999576i \(0.509273\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.347070 0.601142i −0.000673921 0.00116727i
\(516\) 0 0
\(517\) 354.517i 0.685720i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −272.425 + 157.285i −0.522888 + 0.301890i −0.738116 0.674674i \(-0.764284\pi\)
0.215227 + 0.976564i \(0.430951\pi\)
\(522\) 0 0
\(523\) 135.591 + 78.2835i 0.259256 + 0.149682i 0.623995 0.781428i \(-0.285508\pi\)
−0.364739 + 0.931110i \(0.618842\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.54947 4.41581i 0.00483771 0.00837915i
\(528\) 0 0
\(529\) 200.654 + 347.543i 0.379309 + 0.656982i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 892.251 1.67402
\(534\) 0 0
\(535\) −12.3035 + 7.10344i −0.0229972 + 0.0132775i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −386.033 + 668.628i −0.713554 + 1.23591i 0.249960 + 0.968256i \(0.419582\pi\)
−0.963515 + 0.267656i \(0.913751\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 50.3736i 0.0924285i
\(546\) 0 0
\(547\) 48.0113 0.0877721 0.0438860 0.999037i \(-0.486026\pi\)
0.0438860 + 0.999037i \(0.486026\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 289.613 + 167.208i 0.525613 + 0.303463i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 75.7027 + 131.121i 0.135911 + 0.235406i 0.925945 0.377658i \(-0.123270\pi\)
−0.790034 + 0.613063i \(0.789937\pi\)
\(558\) 0 0
\(559\) 969.359i 1.73409i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −732.918 + 423.150i −1.30181 + 0.751599i −0.980714 0.195448i \(-0.937384\pi\)
−0.321094 + 0.947047i \(0.604051\pi\)
\(564\) 0 0
\(565\) 52.4972 + 30.3093i 0.0929153 + 0.0536447i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.7887 + 18.6865i −0.0189608 + 0.0328410i −0.875350 0.483490i \(-0.839369\pi\)
0.856389 + 0.516331i \(0.172702\pi\)
\(570\) 0 0
\(571\) −141.623 245.298i −0.248026 0.429593i 0.714952 0.699173i \(-0.246448\pi\)
−0.962978 + 0.269580i \(0.913115\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 272.749 0.474346
\(576\) 0 0
\(577\) −406.431 + 234.653i −0.704387 + 0.406678i −0.808979 0.587837i \(-0.799979\pi\)
0.104593 + 0.994515i \(0.466646\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 138.191 239.353i 0.237034 0.410555i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 554.500i 0.944634i 0.881429 + 0.472317i \(0.156582\pi\)
−0.881429 + 0.472317i \(0.843418\pi\)
\(588\) 0 0
\(589\) −3.48785 −0.00592165
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −707.094 408.241i −1.19240 0.688433i −0.233550 0.972345i \(-0.575034\pi\)
−0.958850 + 0.283912i \(0.908368\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −434.341 752.301i −0.725111 1.25593i −0.958928 0.283648i \(-0.908455\pi\)
0.233818 0.972280i \(-0.424878\pi\)
\(600\) 0 0
\(601\) 705.861i 1.17448i 0.809413 + 0.587239i \(0.199785\pi\)
−0.809413 + 0.587239i \(0.800215\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −21.8093 + 12.5916i −0.0360485 + 0.0208126i
\(606\) 0 0
\(607\) 464.026 + 267.906i 0.764458 + 0.441360i 0.830894 0.556431i \(-0.187830\pi\)
−0.0664361 + 0.997791i \(0.521163\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 292.241 506.177i 0.478300 0.828440i
\(612\) 0 0
\(613\) 142.247 + 246.379i 0.232050 + 0.401923i 0.958411 0.285390i \(-0.0921232\pi\)
−0.726361 + 0.687313i \(0.758790\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 766.565 1.24241 0.621203 0.783650i \(-0.286644\pi\)
0.621203 + 0.783650i \(0.286644\pi\)
\(618\) 0 0
\(619\) 470.257 271.503i 0.759705 0.438616i −0.0694849 0.997583i \(-0.522136\pi\)
0.829190 + 0.558967i \(0.188802\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −280.508 + 485.854i −0.448813 + 0.777367i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 26.1920i 0.0416408i
\(630\) 0 0
\(631\) −967.080 −1.53261 −0.766307 0.642474i \(-0.777908\pi\)
−0.766307 + 0.642474i \(0.777908\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 189.679 + 109.511i 0.298708 + 0.172459i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 489.512 + 847.860i 0.763669 + 1.32271i 0.940947 + 0.338553i \(0.109937\pi\)
−0.177278 + 0.984161i \(0.556729\pi\)
\(642\) 0 0
\(643\) 991.244i 1.54159i 0.637081 + 0.770797i \(0.280142\pi\)
−0.637081 + 0.770797i \(0.719858\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1067.31 + 616.209i −1.64962 + 0.952409i −0.672400 + 0.740188i \(0.734736\pi\)
−0.977222 + 0.212222i \(0.931930\pi\)
\(648\) 0 0
\(649\) 789.412 + 455.767i 1.21635 + 0.702260i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −390.535 + 676.426i −0.598062 + 1.03587i 0.395045 + 0.918662i \(0.370729\pi\)
−0.993107 + 0.117212i \(0.962604\pi\)
\(654\) 0 0
\(655\) 105.223 + 182.252i 0.160646 + 0.278247i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 549.328 0.833578 0.416789 0.909003i \(-0.363155\pi\)
0.416789 + 0.909003i \(0.363155\pi\)
\(660\) 0 0
\(661\) −358.214 + 206.815i −0.541927 + 0.312882i −0.745860 0.666103i \(-0.767961\pi\)
0.203932 + 0.978985i \(0.434628\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 261.680 453.244i 0.392324 0.679526i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1067.75i 1.59128i
\(672\) 0 0
\(673\) 553.924 0.823067 0.411533 0.911395i \(-0.364993\pi\)
0.411533 + 0.911395i \(0.364993\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 95.5972 + 55.1930i 0.141207 + 0.0815259i 0.568939 0.822380i \(-0.307354\pi\)
−0.427732 + 0.903906i \(0.640687\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −97.8156 169.422i −0.143215 0.248055i 0.785491 0.618873i \(-0.212411\pi\)
−0.928705 + 0.370818i \(0.879077\pi\)
\(684\) 0 0
\(685\) 235.728i 0.344129i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −394.615 + 227.831i −0.572736 + 0.330669i
\(690\) 0 0
\(691\) 574.132 + 331.475i 0.830871 + 0.479703i 0.854151 0.520025i \(-0.174078\pi\)
−0.0232799 + 0.999729i \(0.507411\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 68.7647 119.104i 0.0989421 0.171373i
\(696\) 0 0
\(697\) 294.780 + 510.573i 0.422926 + 0.732530i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1236.29 1.76361 0.881807 0.471610i \(-0.156327\pi\)
0.881807 + 0.471610i \(0.156327\pi\)
\(702\) 0 0
\(703\) 15.5159 8.95812i 0.0220710 0.0127427i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 450.250 779.856i 0.635050 1.09994i −0.351455 0.936205i \(-0.614313\pi\)
0.986505 0.163734i \(-0.0523537\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 5.45848i 0.00765566i
\(714\) 0 0
\(715\) −143.807 −0.201129
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −103.145 59.5509i −0.143456 0.0828246i 0.426554 0.904462i \(-0.359727\pi\)
−0.570010 + 0.821638i \(0.693061\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 558.950 + 968.129i 0.770965 + 1.33535i
\(726\) 0 0
\(727\) 815.672i 1.12197i −0.827826 0.560985i \(-0.810423\pi\)
0.827826 0.560985i \(-0.189577\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 554.696 320.254i 0.758819 0.438104i
\(732\) 0 0
\(733\) 193.766 + 111.871i 0.264346 + 0.152620i 0.626316 0.779570i \(-0.284562\pi\)
−0.361969 + 0.932190i \(0.617896\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 397.432 688.372i 0.539256 0.934019i
\(738\) 0 0
\(739\) 636.897 + 1103.14i 0.861836 + 1.49274i 0.870155 + 0.492778i \(0.164019\pi\)
−0.00831892 + 0.999965i \(0.502648\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 204.339 0.275019 0.137510 0.990500i \(-0.456090\pi\)
0.137510 + 0.990500i \(0.456090\pi\)
\(744\) 0 0
\(745\) 197.486 114.019i 0.265082 0.153045i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 193.280 334.770i 0.257363 0.445766i −0.708172 0.706040i \(-0.750480\pi\)
0.965535 + 0.260275i \(0.0838131\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 163.741i 0.216875i
\(756\) 0 0
\(757\) −1254.03 −1.65658 −0.828290 0.560300i \(-0.810686\pi\)
−0.828290 + 0.560300i \(0.810686\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −702.009 405.305i −0.922483 0.532596i −0.0380564 0.999276i \(-0.512117\pi\)
−0.884426 + 0.466680i \(0.845450\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −751.410 1301.48i −0.979674 1.69684i
\(768\) 0 0
\(769\) 1338.07i 1.74002i 0.493036 + 0.870009i \(0.335887\pi\)
−0.493036 + 0.870009i \(0.664113\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 446.977 258.062i 0.578236 0.333845i −0.182196 0.983262i \(-0.558320\pi\)
0.760432 + 0.649417i \(0.224987\pi\)
\(774\) 0 0
\(775\) −10.0973 5.82967i −0.0130287 0.00752215i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 201.639 349.250i 0.258844 0.448331i
\(780\) 0 0
\(781\) −616.995 1068.67i −0.790006 1.36833i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −192.913 −0.245749
\(786\) 0 0
\(787\) 1302.69 752.107i 1.65526 0.955663i 0.680396 0.732844i \(-0.261808\pi\)
0.974860 0.222819i \(-0.0715257\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −880.184 + 1524.52i −1.10994 + 1.92248i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 147.647i 0.185254i −0.995701 0.0926268i \(-0.970474\pi\)
0.995701 0.0926268i \(-0.0295263\pi\)
\(798\) 0 0
\(799\) 386.200 0.483354
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 388.151 + 224.099i 0.483375 + 0.279077i
\(804\) 0 0