Properties

Label 1260.2.f.a.629.5
Level $1260$
Weight $2$
Character 1260.629
Analytic conductor $10.061$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.10070523904.11
Defining polynomial: \(x^{8} - 10 x^{4} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 629.5
Root \(1.68014 + 0.420861i\) of defining polynomial
Character \(\chi\) \(=\) 1260.629
Dual form 1260.2.f.a.629.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.08495 - 1.95522i) q^{5} +(0.595188 + 2.57794i) q^{7} +O(q^{10})\) \(q+(1.08495 - 1.95522i) q^{5} +(0.595188 + 2.57794i) q^{7} +3.74166i q^{11} +3.36028 q^{13} -0.841723i q^{17} +5.59388i q^{19} -2.35425 q^{23} +(-2.64575 - 4.24264i) q^{25} -1.41421i q^{29} +8.66259i q^{31} +(5.68618 + 1.63322i) q^{35} +5.15587i q^{37} +5.74103 q^{41} -3.32941i q^{43} -6.43560i q^{47} +(-6.29150 + 3.06871i) q^{49} +9.64575 q^{53} +(7.31575 + 4.05952i) q^{55} +12.2508 q^{59} +(3.64575 - 6.57008i) q^{65} +1.82646i q^{67} +3.74166i q^{71} -0.979531 q^{73} +(-9.64575 + 2.22699i) q^{77} -6.58301 q^{79} -12.5730i q^{83} +(-1.64575 - 0.913230i) q^{85} -2.16991 q^{89} +(2.00000 + 8.66259i) q^{91} +(10.9373 + 6.06910i) q^{95} +12.0399 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + O(q^{10}) \) \( 8 q - 40 q^{23} - 16 q^{35} - 8 q^{49} + 56 q^{53} + 8 q^{65} - 56 q^{77} + 32 q^{79} + 8 q^{85} + 16 q^{91} + 24 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

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 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.08495 1.95522i 0.485206 0.874400i
\(6\) 0 0
\(7\) 0.595188 + 2.57794i 0.224960 + 0.974368i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.74166i 1.12815i 0.825723 + 0.564076i \(0.190768\pi\)
−0.825723 + 0.564076i \(0.809232\pi\)
\(12\) 0 0
\(13\) 3.36028 0.931975 0.465987 0.884791i \(-0.345699\pi\)
0.465987 + 0.884791i \(0.345699\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.841723i 0.204148i −0.994777 0.102074i \(-0.967452\pi\)
0.994777 0.102074i \(-0.0325478\pi\)
\(18\) 0 0
\(19\) 5.59388i 1.28332i 0.766987 + 0.641662i \(0.221755\pi\)
−0.766987 + 0.641662i \(0.778245\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.35425 −0.490895 −0.245447 0.969410i \(-0.578935\pi\)
−0.245447 + 0.969410i \(0.578935\pi\)
\(24\) 0 0
\(25\) −2.64575 4.24264i −0.529150 0.848528i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.41421i 0.262613i −0.991342 0.131306i \(-0.958083\pi\)
0.991342 0.131306i \(-0.0419172\pi\)
\(30\) 0 0
\(31\) 8.66259i 1.55585i 0.628359 + 0.777924i \(0.283727\pi\)
−0.628359 + 0.777924i \(0.716273\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 5.68618 + 1.63322i 0.961139 + 0.276064i
\(36\) 0 0
\(37\) 5.15587i 0.847620i 0.905751 + 0.423810i \(0.139308\pi\)
−0.905751 + 0.423810i \(0.860692\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.74103 0.896599 0.448300 0.893883i \(-0.352030\pi\)
0.448300 + 0.893883i \(0.352030\pi\)
\(42\) 0 0
\(43\) 3.32941i 0.507730i −0.967240 0.253865i \(-0.918298\pi\)
0.967240 0.253865i \(-0.0817020\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.43560i 0.938729i −0.883004 0.469365i \(-0.844483\pi\)
0.883004 0.469365i \(-0.155517\pi\)
\(48\) 0 0
\(49\) −6.29150 + 3.06871i −0.898786 + 0.438387i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.64575 1.32495 0.662473 0.749086i \(-0.269507\pi\)
0.662473 + 0.749086i \(0.269507\pi\)
\(54\) 0 0
\(55\) 7.31575 + 4.05952i 0.986456 + 0.547386i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.2508 1.59491 0.797456 0.603377i \(-0.206178\pi\)
0.797456 + 0.603377i \(0.206178\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.64575 6.57008i 0.452200 0.814919i
\(66\) 0 0
\(67\) 1.82646i 0.223138i 0.993757 + 0.111569i \(0.0355876\pi\)
−0.993757 + 0.111569i \(0.964412\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.74166i 0.444053i 0.975041 + 0.222027i \(0.0712672\pi\)
−0.975041 + 0.222027i \(0.928733\pi\)
\(72\) 0 0
\(73\) −0.979531 −0.114645 −0.0573227 0.998356i \(-0.518256\pi\)
−0.0573227 + 0.998356i \(0.518256\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.64575 + 2.22699i −1.09924 + 0.253789i
\(78\) 0 0
\(79\) −6.58301 −0.740646 −0.370323 0.928903i \(-0.620753\pi\)
−0.370323 + 0.928903i \(0.620753\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 12.5730i 1.38007i −0.723776 0.690035i \(-0.757595\pi\)
0.723776 0.690035i \(-0.242405\pi\)
\(84\) 0 0
\(85\) −1.64575 0.913230i −0.178507 0.0990537i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.16991 −0.230010 −0.115005 0.993365i \(-0.536688\pi\)
−0.115005 + 0.993365i \(0.536688\pi\)
\(90\) 0 0
\(91\) 2.00000 + 8.66259i 0.209657 + 0.908086i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 10.9373 + 6.06910i 1.12214 + 0.622677i
\(96\) 0 0
\(97\) 12.0399 1.22247 0.611234 0.791450i \(-0.290673\pi\)
0.611234 + 0.791450i \(0.290673\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.74103 −0.571254 −0.285627 0.958341i \(-0.592202\pi\)
−0.285627 + 0.958341i \(0.592202\pi\)
\(102\) 0 0
\(103\) 13.4411 1.32439 0.662197 0.749330i \(-0.269624\pi\)
0.662197 + 0.749330i \(0.269624\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.9373 −1.63739 −0.818693 0.574231i \(-0.805301\pi\)
−0.818693 + 0.574231i \(0.805301\pi\)
\(108\) 0 0
\(109\) 17.8745 1.71207 0.856034 0.516920i \(-0.172922\pi\)
0.856034 + 0.516920i \(0.172922\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.93725 0.464458 0.232229 0.972661i \(-0.425398\pi\)
0.232229 + 0.972661i \(0.425398\pi\)
\(114\) 0 0
\(115\) −2.55425 + 4.60307i −0.238185 + 0.429238i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.16991 0.500983i 0.198915 0.0459251i
\(120\) 0 0
\(121\) −3.00000 −0.272727
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.1658 + 0.569951i −0.998700 + 0.0509780i
\(126\) 0 0
\(127\) 10.3117i 0.915019i 0.889205 + 0.457510i \(0.151258\pi\)
−0.889205 + 0.457510i \(0.848742\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.91094 0.691182 0.345591 0.938385i \(-0.387678\pi\)
0.345591 + 0.938385i \(0.387678\pi\)
\(132\) 0 0
\(133\) −14.4207 + 3.32941i −1.25043 + 0.288696i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −12.2288 −1.04477 −0.522387 0.852709i \(-0.674958\pi\)
−0.522387 + 0.852709i \(0.674958\pi\)
\(138\) 0 0
\(139\) 3.61226i 0.306388i −0.988196 0.153194i \(-0.951044\pi\)
0.988196 0.153194i \(-0.0489559\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 12.5730i 1.05141i
\(144\) 0 0
\(145\) −2.76510 1.53436i −0.229629 0.127421i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 17.3828i 1.42406i 0.702151 + 0.712028i \(0.252223\pi\)
−0.702151 + 0.712028i \(0.747777\pi\)
\(150\) 0 0
\(151\) −5.29150 −0.430616 −0.215308 0.976546i \(-0.569076\pi\)
−0.215308 + 0.976546i \(0.569076\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 16.9373 + 9.39851i 1.36043 + 0.754907i
\(156\) 0 0
\(157\) −20.3725 −1.62591 −0.812953 0.582329i \(-0.802141\pi\)
−0.812953 + 0.582329i \(0.802141\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.40122 6.06910i −0.110432 0.478312i
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 20.6921i 1.60120i −0.599198 0.800601i \(-0.704514\pi\)
0.599198 0.800601i \(-0.295486\pi\)
\(168\) 0 0
\(169\) −1.70850 −0.131423
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 18.4651i 1.40387i 0.712239 + 0.701937i \(0.247681\pi\)
−0.712239 + 0.701937i \(0.752319\pi\)
\(174\) 0 0
\(175\) 9.36253 9.34574i 0.707741 0.706472i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.39655i 0.627587i −0.949491 0.313794i \(-0.898400\pi\)
0.949491 0.313794i \(-0.101600\pi\)
\(180\) 0 0
\(181\) 26.5313i 1.97206i −0.166575 0.986029i \(-0.553271\pi\)
0.166575 0.986029i \(-0.446729\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 10.0808 + 5.59388i 0.741159 + 0.411270i
\(186\) 0 0
\(187\) 3.14944 0.230310
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 16.8818i 1.22153i −0.791813 0.610763i \(-0.790863\pi\)
0.791813 0.610763i \(-0.209137\pi\)
\(192\) 0 0
\(193\) 15.4676i 1.11338i −0.830719 0.556692i \(-0.812071\pi\)
0.830719 0.556692i \(-0.187929\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −26.8118 −1.91026 −0.955129 0.296189i \(-0.904284\pi\)
−0.955129 + 0.296189i \(0.904284\pi\)
\(198\) 0 0
\(199\) 6.68097i 0.473601i 0.971558 + 0.236801i \(0.0760988\pi\)
−0.971558 + 0.236801i \(0.923901\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3.64575 0.841723i 0.255882 0.0590774i
\(204\) 0 0
\(205\) 6.22876 11.2250i 0.435035 0.783986i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −20.9304 −1.44779
\(210\) 0 0
\(211\) −5.29150 −0.364282 −0.182141 0.983272i \(-0.558303\pi\)
−0.182141 + 0.983272i \(0.558303\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.50972 3.61226i −0.443959 0.246354i
\(216\) 0 0
\(217\) −22.3316 + 5.15587i −1.51597 + 0.350003i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.82843i 0.190261i
\(222\) 0 0
\(223\) 14.2098 0.951560 0.475780 0.879564i \(-0.342166\pi\)
0.475780 + 0.879564i \(0.342166\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 17.0270i 1.13012i 0.825049 + 0.565061i \(0.191147\pi\)
−0.825049 + 0.565061i \(0.808853\pi\)
\(228\) 0 0
\(229\) 25.4442i 1.68140i −0.541499 0.840701i \(-0.682143\pi\)
0.541499 0.840701i \(-0.317857\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 21.6458 1.41806 0.709030 0.705178i \(-0.249133\pi\)
0.709030 + 0.705178i \(0.249133\pi\)
\(234\) 0 0
\(235\) −12.5830 6.98233i −0.820825 0.455477i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 15.0554i 0.973851i −0.873444 0.486925i \(-0.838118\pi\)
0.873444 0.486925i \(-0.161882\pi\)
\(240\) 0 0
\(241\) 8.11905i 0.522994i −0.965204 0.261497i \(-0.915784\pi\)
0.965204 0.261497i \(-0.0842161\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.825989 + 15.6307i −0.0527705 + 0.998607i
\(246\) 0 0
\(247\) 18.7970i 1.19603i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −16.5906 −1.04719 −0.523594 0.851968i \(-0.675409\pi\)
−0.523594 + 0.851968i \(0.675409\pi\)
\(252\) 0 0
\(253\) 8.80879i 0.553804i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.89206i 0.367537i −0.982970 0.183768i \(-0.941170\pi\)
0.982970 0.183768i \(-0.0588296\pi\)
\(258\) 0 0
\(259\) −13.2915 + 3.06871i −0.825894 + 0.190681i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.64575 −0.594783 −0.297391 0.954756i \(-0.596117\pi\)
−0.297391 + 0.954756i \(0.596117\pi\)
\(264\) 0 0
\(265\) 10.4652 18.8595i 0.642872 1.15853i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −25.9027 −1.57932 −0.789659 0.613546i \(-0.789742\pi\)
−0.789659 + 0.613546i \(0.789742\pi\)
\(270\) 0 0
\(271\) 14.8000i 0.899037i −0.893271 0.449519i \(-0.851596\pi\)
0.893271 0.449519i \(-0.148404\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 15.8745 9.89949i 0.957269 0.596962i
\(276\) 0 0
\(277\) 25.4558i 1.52949i 0.644331 + 0.764747i \(0.277136\pi\)
−0.644331 + 0.764747i \(0.722864\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.06713i 0.302280i −0.988512 0.151140i \(-0.951706\pi\)
0.988512 0.151140i \(-0.0482944\pi\)
\(282\) 0 0
\(283\) −27.6510 −1.64368 −0.821839 0.569719i \(-0.807052\pi\)
−0.821839 + 0.569719i \(0.807052\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.41699 + 14.8000i 0.201699 + 0.873617i
\(288\) 0 0
\(289\) 16.2915 0.958324
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 19.2540i 1.12483i −0.826855 0.562415i \(-0.809872\pi\)
0.826855 0.562415i \(-0.190128\pi\)
\(294\) 0 0
\(295\) 13.2915 23.9529i 0.773861 1.39459i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −7.91094 −0.457502
\(300\) 0 0
\(301\) 8.58301 1.98162i 0.494716 0.114219i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 18.5496 1.05868 0.529342 0.848409i \(-0.322439\pi\)
0.529342 + 0.848409i \(0.322439\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 20.9304 1.18685 0.593427 0.804888i \(-0.297775\pi\)
0.593427 + 0.804888i \(0.297775\pi\)
\(312\) 0 0
\(313\) −4.55066 −0.257218 −0.128609 0.991695i \(-0.541051\pi\)
−0.128609 + 0.991695i \(0.541051\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.8118 −0.831911 −0.415956 0.909385i \(-0.636553\pi\)
−0.415956 + 0.909385i \(0.636553\pi\)
\(318\) 0 0
\(319\) 5.29150 0.296267
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.70850 0.261988
\(324\) 0 0
\(325\) −8.89047 14.2565i −0.493155 0.790807i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 16.5906 3.83039i 0.914668 0.211176i
\(330\) 0 0
\(331\) 11.8745 0.652682 0.326341 0.945252i \(-0.394184\pi\)
0.326341 + 0.945252i \(0.394184\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.57113 + 1.98162i 0.195112 + 0.108268i
\(336\) 0 0
\(337\) 23.9529i 1.30480i 0.757876 + 0.652399i \(0.226237\pi\)
−0.757876 + 0.652399i \(0.773763\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −32.4125 −1.75523
\(342\) 0 0
\(343\) −11.6556 14.3926i −0.629342 0.777129i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −28.9373 −1.55343 −0.776717 0.629850i \(-0.783116\pi\)
−0.776717 + 0.629850i \(0.783116\pi\)
\(348\) 0 0
\(349\) 29.6000i 1.58445i −0.610227 0.792227i \(-0.708922\pi\)
0.610227 0.792227i \(-0.291078\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 18.4651i 0.982797i 0.870935 + 0.491399i \(0.163514\pi\)
−0.870935 + 0.491399i \(0.836486\pi\)
\(354\) 0 0
\(355\) 7.31575 + 4.05952i 0.388280 + 0.215457i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 29.1975i 1.54099i 0.637449 + 0.770493i \(0.279990\pi\)
−0.637449 + 0.770493i \(0.720010\pi\)
\(360\) 0 0
\(361\) −12.2915 −0.646921
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.06275 + 1.91520i −0.0556267 + 0.100246i
\(366\) 0 0
\(367\) −27.6510 −1.44337 −0.721684 0.692223i \(-0.756632\pi\)
−0.721684 + 0.692223i \(0.756632\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5.74103 + 24.8661i 0.298060 + 1.29098i
\(372\) 0 0
\(373\) 30.9352i 1.60177i −0.598821 0.800883i \(-0.704364\pi\)
0.598821 0.800883i \(-0.295636\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.75216i 0.244749i
\(378\) 0 0
\(379\) −2.70850 −0.139126 −0.0695631 0.997578i \(-0.522161\pi\)
−0.0695631 + 0.997578i \(0.522161\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 20.6921i 1.05732i −0.848835 0.528658i \(-0.822695\pi\)
0.848835 0.528658i \(-0.177305\pi\)
\(384\) 0 0
\(385\) −6.11094 + 21.2757i −0.311443 + 1.08431i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.06713i 0.256914i −0.991715 0.128457i \(-0.958998\pi\)
0.991715 0.128457i \(-0.0410024\pi\)
\(390\) 0 0
\(391\) 1.98162i 0.100215i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7.14226 + 12.8712i −0.359366 + 0.647621i
\(396\) 0 0
\(397\) −16.0327 −0.804660 −0.402330 0.915495i \(-0.631799\pi\)
−0.402330 + 0.915495i \(0.631799\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.5504i 0.626740i 0.949631 + 0.313370i \(0.101458\pi\)
−0.949631 + 0.313370i \(0.898542\pi\)
\(402\) 0 0
\(403\) 29.1088i 1.45001i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −19.2915 −0.956244
\(408\) 0 0
\(409\) 14.2565i 0.704937i 0.935824 + 0.352469i \(0.114658\pi\)
−0.935824 + 0.352469i \(0.885342\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.29150 + 31.5817i 0.358791 + 1.55403i
\(414\) 0 0
\(415\) −24.5830 13.6412i −1.20673 0.669618i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7.14226 0.348922 0.174461 0.984664i \(-0.444182\pi\)
0.174461 + 0.984664i \(0.444182\pi\)
\(420\) 0 0
\(421\) 23.8745 1.16357 0.581786 0.813342i \(-0.302354\pi\)
0.581786 + 0.813342i \(0.302354\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.57113 + 2.22699i −0.173225 + 0.108025i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8.39655i 0.404447i −0.979339 0.202224i \(-0.935183\pi\)
0.979339 0.202224i \(-0.0648168\pi\)
\(432\) 0 0
\(433\) 35.7727 1.71913 0.859564 0.511028i \(-0.170735\pi\)
0.859564 + 0.511028i \(0.170735\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 13.1694i 0.629977i
\(438\) 0 0
\(439\) 4.50679i 0.215098i 0.994200 + 0.107549i \(0.0343002\pi\)
−0.994200 + 0.107549i \(0.965700\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.64575 −0.458283 −0.229142 0.973393i \(-0.573592\pi\)
−0.229142 + 0.973393i \(0.573592\pi\)
\(444\) 0 0
\(445\) −2.35425 + 4.24264i −0.111602 + 0.201120i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 28.6965i 1.35427i −0.735858 0.677136i \(-0.763221\pi\)
0.735858 0.677136i \(-0.236779\pi\)
\(450\) 0 0
\(451\) 21.4810i 1.01150i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 19.1072 + 5.48808i 0.895758 + 0.257285i
\(456\) 0 0
\(457\) 9.98823i 0.467230i −0.972329 0.233615i \(-0.924945\pi\)
0.972329 0.233615i \(-0.0750555\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −31.0112 −1.44434 −0.722169 0.691717i \(-0.756855\pi\)
−0.722169 + 0.691717i \(0.756855\pi\)
\(462\) 0 0
\(463\) 16.9706i 0.788689i 0.918963 + 0.394344i \(0.129028\pi\)
−0.918963 + 0.394344i \(0.870972\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.7105i 0.865816i −0.901438 0.432908i \(-0.857487\pi\)
0.901438 0.432908i \(-0.142513\pi\)
\(468\) 0 0
\(469\) −4.70850 + 1.08709i −0.217418 + 0.0501970i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 12.4575 0.572797
\(474\) 0 0
\(475\) 23.7328 14.8000i 1.08894 0.679071i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 20.9304 0.956334 0.478167 0.878269i \(-0.341301\pi\)
0.478167 + 0.878269i \(0.341301\pi\)
\(480\) 0 0
\(481\) 17.3252i 0.789960i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 13.0627 23.5406i 0.593149 1.06893i
\(486\) 0 0
\(487\) 6.98233i 0.316400i 0.987407 + 0.158200i \(0.0505690\pi\)
−0.987407 + 0.158200i \(0.949431\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 26.1916i 1.18201i 0.806668 + 0.591005i \(0.201269\pi\)
−0.806668 + 0.591005i \(0.798731\pi\)
\(492\) 0 0
\(493\) −1.19038 −0.0536118
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −9.64575 + 2.22699i −0.432671 + 0.0998941i
\(498\) 0 0
\(499\) 18.7085 0.837507 0.418754 0.908100i \(-0.362467\pi\)
0.418754 + 0.908100i \(0.362467\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.82087i 0.348715i 0.984682 + 0.174358i \(0.0557849\pi\)
−0.984682 + 0.174358i \(0.944215\pi\)
\(504\) 0 0
\(505\) −6.22876 + 11.2250i −0.277176 + 0.499505i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 30.2425 1.34048 0.670239 0.742146i \(-0.266192\pi\)
0.670239 + 0.742146i \(0.266192\pi\)
\(510\) 0 0
\(511\) −0.583005 2.52517i −0.0257906 0.111707i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 14.5830 26.2803i 0.642604 1.15805i
\(516\) 0 0
\(517\) 24.0798 1.05903
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17.2231 0.754558 0.377279 0.926100i \(-0.376860\pi\)
0.377279 + 0.926100i \(0.376860\pi\)
\(522\) 0 0
\(523\) 13.4411 0.587740 0.293870 0.955845i \(-0.405057\pi\)
0.293870 + 0.955845i \(0.405057\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 7.29150 0.317623
\(528\) 0 0
\(529\) −17.4575 −0.759022
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 19.2915 0.835608
\(534\) 0 0
\(535\) −18.3761 + 33.1160i −0.794470 + 1.43173i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −11.4821 23.5406i −0.494568 1.01397i
\(540\) 0 0
\(541\) −19.8745 −0.854472 −0.427236 0.904140i \(-0.640513\pi\)
−0.427236 + 0.904140i \(0.640513\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 19.3930 34.9486i 0.830705 1.49703i
\(546\) 0 0
\(547\) 25.4558i 1.08841i −0.838951 0.544207i \(-0.816831\pi\)
0.838951 0.544207i \(-0.183169\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.91094 0.337017
\(552\) 0 0
\(553\) −3.91813 16.9706i −0.166616 0.721662i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19.5203 −0.827100 −0.413550 0.910481i \(-0.635711\pi\)
−0.413550 + 0.910481i \(0.635711\pi\)
\(558\) 0 0
\(559\) 11.1878i 0.473192i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.27980i 0.0960823i −0.998845 0.0480411i \(-0.984702\pi\)
0.998845 0.0480411i \(-0.0152979\pi\)
\(564\) 0 0
\(565\) 5.35669 9.65341i 0.225358 0.406122i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22.2152i 0.931308i 0.884967 + 0.465654i \(0.154181\pi\)
−0.884967 + 0.465654i \(0.845819\pi\)
\(570\) 0 0
\(571\) 22.5830 0.945069 0.472535 0.881312i \(-0.343339\pi\)
0.472535 + 0.881312i \(0.343339\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.22876 + 9.98823i 0.259757 + 0.416538i
\(576\) 0 0
\(577\) 27.0931 1.12790 0.563950 0.825809i \(-0.309281\pi\)
0.563950 + 0.825809i \(0.309281\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 32.4125 7.48331i 1.34470 0.310460i
\(582\) 0 0
\(583\) 36.0911i 1.49474i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 32.9669i 1.36069i −0.732892 0.680345i \(-0.761830\pi\)
0.732892 0.680345i \(-0.238170\pi\)
\(588\) 0 0
\(589\) −48.4575 −1.99666
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 27.3730i 1.12408i −0.827111 0.562038i \(-0.810017\pi\)
0.827111 0.562038i \(-0.189983\pi\)
\(594\) 0 0
\(595\) 1.37472 4.78618i 0.0563579 0.196214i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 26.1916i 1.07016i 0.844801 + 0.535080i \(0.179719\pi\)
−0.844801 + 0.535080i \(0.820281\pi\)
\(600\) 0 0
\(601\) 27.4259i 1.11872i 0.828923 + 0.559362i \(0.188954\pi\)
−0.828923 + 0.559362i \(0.811046\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.25486 + 5.86565i −0.132329 + 0.238473i
\(606\) 0 0
\(607\) 34.3715 1.39510 0.697548 0.716538i \(-0.254274\pi\)
0.697548 + 0.716538i \(0.254274\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 21.6255i 0.874872i
\(612\) 0 0
\(613\) 27.2823i 1.10192i −0.834531 0.550961i \(-0.814261\pi\)
0.834531 0.550961i \(-0.185739\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.52026 0.302754 0.151377 0.988476i \(-0.451629\pi\)
0.151377 + 0.988476i \(0.451629\pi\)
\(618\) 0 0
\(619\) 20.9374i 0.841547i 0.907166 + 0.420773i \(0.138241\pi\)
−0.907166 + 0.420773i \(0.861759\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.29150 5.59388i −0.0517430 0.224114i
\(624\) 0 0
\(625\) −11.0000 + 22.4499i −0.440000 + 0.897998i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4.33981 0.173040
\(630\) 0 0
\(631\) −21.1660 −0.842606 −0.421303 0.906920i \(-0.638427\pi\)
−0.421303 + 0.906920i \(0.638427\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 20.1617 + 11.1878i 0.800093 + 0.443973i
\(636\) 0 0
\(637\) −21.1412 + 10.3117i −0.837646 + 0.408566i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.23871i 0.0884236i 0.999022 + 0.0442118i \(0.0140776\pi\)
−0.999022 + 0.0442118i \(0.985922\pi\)
\(642\) 0 0
\(643\) 30.0317 1.18433 0.592167 0.805815i \(-0.298272\pi\)
0.592167 + 0.805815i \(0.298272\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 25.1461i 0.988593i 0.869293 + 0.494297i \(0.164574\pi\)
−0.869293 + 0.494297i \(0.835426\pi\)
\(648\) 0 0
\(649\) 45.8381i 1.79930i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 22.1033 0.864968 0.432484 0.901642i \(-0.357637\pi\)
0.432484 + 0.901642i \(0.357637\pi\)
\(654\) 0 0
\(655\) 8.58301 15.4676i 0.335366 0.604370i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.09070i 0.0424878i −0.999774 0.0212439i \(-0.993237\pi\)
0.999774 0.0212439i \(-0.00676264\pi\)
\(660\) 0 0
\(661\) 6.13742i 0.238718i −0.992851 0.119359i \(-0.961916\pi\)
0.992851 0.119359i \(-0.0380840\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −9.13603 + 31.8078i −0.354280 + 1.23345i
\(666\) 0 0
\(667\) 3.32941i 0.128915i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 8.16177i 0.314613i −0.987550 0.157307i \(-0.949719\pi\)
0.987550 0.157307i \(-0.0502811\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 33.8086i 1.29937i 0.760203 + 0.649686i \(0.225100\pi\)
−0.760203 + 0.649686i \(0.774900\pi\)
\(678\) 0 0
\(679\) 7.16601 + 31.0381i 0.275006 + 1.19113i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −19.5203 −0.746922 −0.373461 0.927646i \(-0.621829\pi\)
−0.373461 + 0.927646i \(0.621829\pi\)
\(684\) 0 0
\(685\) −13.2676 + 23.9099i −0.506930 + 0.913550i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 32.4125 1.23482
\(690\) 0 0
\(691\) 2.52517i 0.0960619i 0.998846 + 0.0480310i \(0.0152946\pi\)
−0.998846 + 0.0480310i \(0.984705\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.06275 3.91913i −0.267905 0.148661i
\(696\) 0 0
\(697\) 4.83236i 0.183039i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 13.7299i 0.518571i 0.965801 + 0.259285i \(0.0834870\pi\)
−0.965801 + 0.259285i \(0.916513\pi\)
\(702\) 0 0
\(703\) −28.8413 −1.08777
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.41699 14.8000i −0.128509 0.556612i
\(708\) 0 0
\(709\) 49.1660 1.84647 0.923234 0.384238i \(-0.125536\pi\)
0.923234 + 0.384238i \(0.125536\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 20.3939i 0.763757i
\(714\) 0 0
\(715\) 24.5830 + 13.6412i 0.919352 + 0.510150i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −38.2896 −1.42796 −0.713981 0.700165i \(-0.753110\pi\)
−0.713981 + 0.700165i \(0.753110\pi\)
\(720\) 0 0
\(721\) 8.00000 + 34.6504i 0.297936 + 1.29045i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.00000 + 3.74166i −0.222834 + 0.138962i
\(726\) 0 0
\(727\) −3.91813 −0.145315 −0.0726576 0.997357i \(-0.523148\pi\)
−0.0726576 + 0.997357i \(0.523148\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.80244 −0.103652
\(732\) 0 0
\(733\) −13.9990 −0.517064 −0.258532 0.966003i \(-0.583239\pi\)
−0.258532 + 0.966003i \(0.583239\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.83399 −0.251733
\(738\) 0 0
\(739\) −9.16601 −0.337177 −0.168589 0.985687i \(-0.553921\pi\)
−0.168589 + 0.985687i \(0.553921\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −28.9373 −1.06160 −0.530802 0.847496i \(-0.678109\pi\)
−0.530802 + 0.847496i \(0.678109\pi\)
\(744\) 0 0
\(745\) 33.9872 + 18.8595i 1.24519 + 0.690960i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −10.0808 43.6631i −0.368346 1.59542i
\(750\) 0 0
\(751\) −29.2915 −1.06886 −0.534431 0.845212i \(-0.679474\pi\)
−0.534431 + 0.845212i \(0.679474\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5.74103 + 10.3460i −0.208938 + 0.376531i
\(756\) 0 0
\(757\) 13.6412i 0.495796i 0.968786 + 0.247898i \(0.0797398\pi\)
−0.968786 + 0.247898i \(0.920260\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 51.1729 1.85502 0.927509 0.373802i \(-0.121946\pi\)
0.927509 + 0.373802i \(0.121946\pi\)
\(762\) 0 0
\(763\) 10.6387 + 46.0793i 0.385146 + 1.66818i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 41.1660 1.48642
\(768\) 0 0
\(769\) 27.4259i 0.989002i 0.869177 + 0.494501i \(0.164649\pi\)
−0.869177 + 0.494501i \(0.835351\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 11.1349i 0.400496i −0.979745 0.200248i \(-0.935825\pi\)
0.979745 0.200248i \(-0.0641748\pi\)
\(774\) 0 0
\(775\) 36.7523 22.9191i 1.32018 0.823277i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 32.1147i 1.15063i
\(780\) 0 0
\(781\) −14.0000 −0.500959
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −22.1033 + 39.8328i −0.788899 + 1.42169i
\(786\) 0 0
\(787\) −24.0798 −0.858353 −0.429177 0.903221i \(-0.641196\pi\)
−0.429177 + 0.903221i \(0.641196\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.93859 + 12.7279i 0.104484 + 0.452553i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 26.2860i 0.931096i −0.885023 0.465548i \(-0.845857\pi\)
0.885023 0.465548i \(-0.154143\pi\)
\(798\) 0 0
\(799\) −5.41699 −0.191639
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3.66507i 0.129338i
\(804\) 0 0
\(805\) −13.3867 3.84500i −0.471818 0.135519i
\(806\) 0 0
\(807\) 0 0