Properties

Label 6048.2.j.a.5615.4
Level 6048
Weight 2
Character 6048.5615
Analytic conductor 48.294
Analytic rank 0
Dimension 8
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.j (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.56070144.2
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 1512)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5615.4
Root \(0.500000 + 0.564882i\)
Character \(\chi\) = 6048.5615
Dual form 6048.2.j.a.5615.3

$q$-expansion

\(f(q)\) \(=\) \(q-3.12976 q^{5} +1.00000i q^{7} +O(q^{10})\) \(q-3.12976 q^{5} +1.00000i q^{7} -0.397714i q^{11} +6.55068i q^{13} -2.00000i q^{17} +0.527479 q^{19} -8.21634 q^{23} +4.79543 q^{25} -4.73205 q^{29} +7.55068i q^{31} -3.12976i q^{35} -3.35452i q^{37} +7.48429i q^{41} -1.62247 q^{43} +10.4557 q^{47} -1.00000 q^{49} +0.795428 q^{53} +1.24475i q^{55} -2.47252i q^{59} -11.4641i q^{61} -20.5021i q^{65} +6.55068 q^{67} +2.21634 q^{71} -5.75525 q^{73} +0.397714 q^{77} +10.2911i q^{79} +8.36930i q^{83} +6.25953i q^{85} -5.31114i q^{89} -6.55068 q^{91} -1.65089 q^{95} -19.1014 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{5} + O(q^{10}) \) \( 8q - 8q^{5} - 16q^{19} - 16q^{23} + 32q^{25} - 24q^{29} - 8q^{43} + 8q^{47} - 8q^{49} - 8q^{67} - 32q^{71} + 8q^{73} + 8q^{91} - 112q^{95} - 32q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).

\(n\) \(2593\) \(3781\) \(3809\) \(4159\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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
\(5\) −3.12976 −1.39967 −0.699837 0.714303i \(-0.746744\pi\)
−0.699837 + 0.714303i \(0.746744\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 0.397714i − 0.119915i −0.998201 0.0599577i \(-0.980903\pi\)
0.998201 0.0599577i \(-0.0190966\pi\)
\(12\) 0 0
\(13\) 6.55068i 1.81683i 0.418069 + 0.908415i \(0.362707\pi\)
−0.418069 + 0.908415i \(0.637293\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 2.00000i − 0.485071i −0.970143 0.242536i \(-0.922021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) 0 0
\(19\) 0.527479 0.121012 0.0605060 0.998168i \(-0.480729\pi\)
0.0605060 + 0.998168i \(0.480729\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −8.21634 −1.71323 −0.856613 0.515960i \(-0.827435\pi\)
−0.856613 + 0.515960i \(0.827435\pi\)
\(24\) 0 0
\(25\) 4.79543 0.959086
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.73205 −0.878720 −0.439360 0.898311i \(-0.644795\pi\)
−0.439360 + 0.898311i \(0.644795\pi\)
\(30\) 0 0
\(31\) 7.55068i 1.35614i 0.734997 + 0.678071i \(0.237184\pi\)
−0.734997 + 0.678071i \(0.762816\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 3.12976i − 0.529027i
\(36\) 0 0
\(37\) − 3.35452i − 0.551480i −0.961232 0.275740i \(-0.911077\pi\)
0.961232 0.275740i \(-0.0889229\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7.48429i 1.16885i 0.811448 + 0.584425i \(0.198680\pi\)
−0.811448 + 0.584425i \(0.801320\pi\)
\(42\) 0 0
\(43\) −1.62247 −0.247425 −0.123712 0.992318i \(-0.539480\pi\)
−0.123712 + 0.992318i \(0.539480\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.4557 1.52512 0.762559 0.646919i \(-0.223943\pi\)
0.762559 + 0.646919i \(0.223943\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.795428 0.109260 0.0546302 0.998507i \(-0.482602\pi\)
0.0546302 + 0.998507i \(0.482602\pi\)
\(54\) 0 0
\(55\) 1.24475i 0.167842i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 2.47252i − 0.321895i −0.986963 0.160947i \(-0.948545\pi\)
0.986963 0.160947i \(-0.0514550\pi\)
\(60\) 0 0
\(61\) − 11.4641i − 1.46783i −0.679243 0.733914i \(-0.737692\pi\)
0.679243 0.733914i \(-0.262308\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 20.5021i − 2.54297i
\(66\) 0 0
\(67\) 6.55068 0.800293 0.400146 0.916451i \(-0.368959\pi\)
0.400146 + 0.916451i \(0.368959\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.21634 0.263031 0.131516 0.991314i \(-0.458016\pi\)
0.131516 + 0.991314i \(0.458016\pi\)
\(72\) 0 0
\(73\) −5.75525 −0.673601 −0.336800 0.941576i \(-0.609345\pi\)
−0.336800 + 0.941576i \(0.609345\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.397714 0.0453237
\(78\) 0 0
\(79\) 10.2911i 1.15784i 0.815383 + 0.578922i \(0.196527\pi\)
−0.815383 + 0.578922i \(0.803473\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.36930i 0.918650i 0.888268 + 0.459325i \(0.151909\pi\)
−0.888268 + 0.459325i \(0.848091\pi\)
\(84\) 0 0
\(85\) 6.25953i 0.678941i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 5.31114i − 0.562980i −0.959564 0.281490i \(-0.909171\pi\)
0.959564 0.281490i \(-0.0908286\pi\)
\(90\) 0 0
\(91\) −6.55068 −0.686697
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.65089 −0.169377
\(96\) 0 0
\(97\) −19.1014 −1.93945 −0.969724 0.244202i \(-0.921474\pi\)
−0.969724 + 0.244202i \(0.921474\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 0 0
\(103\) 17.0148i 1.67652i 0.545274 + 0.838258i \(0.316426\pi\)
−0.545274 + 0.838258i \(0.683574\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 1.91362i − 0.184997i −0.995713 0.0924983i \(-0.970515\pi\)
0.995713 0.0924983i \(-0.0294853\pi\)
\(108\) 0 0
\(109\) 7.07816i 0.677964i 0.940793 + 0.338982i \(0.110083\pi\)
−0.940793 + 0.338982i \(0.889917\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 9.98316i − 0.939137i −0.882896 0.469568i \(-0.844410\pi\)
0.882896 0.469568i \(-0.155590\pi\)
\(114\) 0 0
\(115\) 25.7152 2.39796
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.00000 0.183340
\(120\) 0 0
\(121\) 10.8418 0.985620
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0.640262 0.0572668
\(126\) 0 0
\(127\) − 7.75525i − 0.688167i −0.938939 0.344084i \(-0.888190\pi\)
0.938939 0.344084i \(-0.111810\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 14.9052i − 1.30227i −0.758960 0.651137i \(-0.774292\pi\)
0.758960 0.651137i \(-0.225708\pi\)
\(132\) 0 0
\(133\) 0.527479i 0.0457382i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 22.4557i − 1.91852i −0.282527 0.959259i \(-0.591173\pi\)
0.282527 0.959259i \(-0.408827\pi\)
\(138\) 0 0
\(139\) −3.05496 −0.259118 −0.129559 0.991572i \(-0.541356\pi\)
−0.129559 + 0.991572i \(0.541356\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.60530 0.217866
\(144\) 0 0
\(145\) 14.8102 1.22992
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.01458 0.574657 0.287329 0.957832i \(-0.407233\pi\)
0.287329 + 0.957832i \(0.407233\pi\)
\(150\) 0 0
\(151\) 9.81001i 0.798327i 0.916880 + 0.399164i \(0.130699\pi\)
−0.916880 + 0.399164i \(0.869301\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 23.6318i − 1.89816i
\(156\) 0 0
\(157\) − 10.8966i − 0.869642i −0.900517 0.434821i \(-0.856812\pi\)
0.900517 0.434821i \(-0.143188\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 8.21634i − 0.647538i
\(162\) 0 0
\(163\) 10.0148 0.784418 0.392209 0.919876i \(-0.371711\pi\)
0.392209 + 0.919876i \(0.371711\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14.5655 1.12711 0.563554 0.826079i \(-0.309434\pi\)
0.563554 + 0.826079i \(0.309434\pi\)
\(168\) 0 0
\(169\) −29.9114 −2.30087
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −14.3175 −1.08854 −0.544270 0.838910i \(-0.683193\pi\)
−0.544270 + 0.838910i \(0.683193\pi\)
\(174\) 0 0
\(175\) 4.79543i 0.362500i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 19.8104i 1.48070i 0.672222 + 0.740349i \(0.265340\pi\)
−0.672222 + 0.740349i \(0.734660\pi\)
\(180\) 0 0
\(181\) − 20.1732i − 1.49946i −0.661745 0.749729i \(-0.730184\pi\)
0.661745 0.749729i \(-0.269816\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 10.4989i 0.771892i
\(186\) 0 0
\(187\) −0.795428 −0.0581675
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.43549 −0.465656 −0.232828 0.972518i \(-0.574798\pi\)
−0.232828 + 0.972518i \(0.574798\pi\)
\(192\) 0 0
\(193\) −9.98316 −0.718604 −0.359302 0.933221i \(-0.616985\pi\)
−0.359302 + 0.933221i \(0.616985\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −23.6373 −1.68408 −0.842042 0.539412i \(-0.818647\pi\)
−0.842042 + 0.539412i \(0.818647\pi\)
\(198\) 0 0
\(199\) − 21.6202i − 1.53262i −0.642473 0.766308i \(-0.722092\pi\)
0.642473 0.766308i \(-0.277908\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 4.73205i − 0.332125i
\(204\) 0 0
\(205\) − 23.4241i − 1.63601i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 0.209786i − 0.0145112i
\(210\) 0 0
\(211\) −2.51906 −0.173419 −0.0867096 0.996234i \(-0.527635\pi\)
−0.0867096 + 0.996234i \(0.527635\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.07796 0.346314
\(216\) 0 0
\(217\) −7.55068 −0.512573
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 13.1014 0.881292
\(222\) 0 0
\(223\) − 0.882003i − 0.0590633i −0.999564 0.0295316i \(-0.990598\pi\)
0.999564 0.0295316i \(-0.00940158\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 8.47868i − 0.562750i −0.959598 0.281375i \(-0.909210\pi\)
0.959598 0.281375i \(-0.0907905\pi\)
\(228\) 0 0
\(229\) − 13.4641i − 0.889733i −0.895597 0.444866i \(-0.853251\pi\)
0.895597 0.444866i \(-0.146749\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 17.4641i − 1.14411i −0.820215 0.572056i \(-0.806146\pi\)
0.820215 0.572056i \(-0.193854\pi\)
\(234\) 0 0
\(235\) −32.7238 −2.13467
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −27.6836 −1.79071 −0.895353 0.445357i \(-0.853077\pi\)
−0.895353 + 0.445357i \(0.853077\pi\)
\(240\) 0 0
\(241\) 21.9116 1.41145 0.705724 0.708487i \(-0.250622\pi\)
0.705724 + 0.708487i \(0.250622\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.12976 0.199953
\(246\) 0 0
\(247\) 3.45534i 0.219858i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 15.9136i − 1.00446i −0.864734 0.502229i \(-0.832513\pi\)
0.864734 0.502229i \(-0.167487\pi\)
\(252\) 0 0
\(253\) 3.26775i 0.205442i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.70344i 0.231014i 0.993307 + 0.115507i \(0.0368493\pi\)
−0.993307 + 0.115507i \(0.963151\pi\)
\(258\) 0 0
\(259\) 3.35452 0.208440
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −22.1995 −1.36888 −0.684440 0.729069i \(-0.739953\pi\)
−0.684440 + 0.729069i \(0.739953\pi\)
\(264\) 0 0
\(265\) −2.48950 −0.152929
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −16.2480 −0.990655 −0.495328 0.868706i \(-0.664952\pi\)
−0.495328 + 0.868706i \(0.664952\pi\)
\(270\) 0 0
\(271\) − 18.3755i − 1.11623i −0.829764 0.558115i \(-0.811525\pi\)
0.829764 0.558115i \(-0.188475\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 1.90721i − 0.115009i
\(276\) 0 0
\(277\) − 31.7764i − 1.90926i −0.297798 0.954629i \(-0.596252\pi\)
0.297798 0.954629i \(-0.403748\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 4.86483i − 0.290211i −0.989416 0.145106i \(-0.953648\pi\)
0.989416 0.145106i \(-0.0463522\pi\)
\(282\) 0 0
\(283\) 24.7386 1.47056 0.735279 0.677765i \(-0.237051\pi\)
0.735279 + 0.677765i \(0.237051\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7.48429 −0.441784
\(288\) 0 0
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 15.9428 0.931388 0.465694 0.884946i \(-0.345805\pi\)
0.465694 + 0.884946i \(0.345805\pi\)
\(294\) 0 0
\(295\) 7.73841i 0.450548i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 53.8226i − 3.11264i
\(300\) 0 0
\(301\) − 1.62247i − 0.0935178i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 35.8799i 2.05448i
\(306\) 0 0
\(307\) 5.64567 0.322215 0.161108 0.986937i \(-0.448493\pi\)
0.161108 + 0.986937i \(0.448493\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −19.0084 −1.07787 −0.538934 0.842348i \(-0.681173\pi\)
−0.538934 + 0.842348i \(0.681173\pi\)
\(312\) 0 0
\(313\) 2.24475 0.126881 0.0634404 0.997986i \(-0.479793\pi\)
0.0634404 + 0.997986i \(0.479793\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 24.4852 1.37523 0.687614 0.726076i \(-0.258658\pi\)
0.687614 + 0.726076i \(0.258658\pi\)
\(318\) 0 0
\(319\) 1.88200i 0.105372i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 1.05496i − 0.0586994i
\(324\) 0 0
\(325\) 31.4133i 1.74250i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 10.4557i 0.576440i
\(330\) 0 0
\(331\) −4.34591 −0.238873 −0.119436 0.992842i \(-0.538109\pi\)
−0.119436 + 0.992842i \(0.538109\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −20.5021 −1.12015
\(336\) 0 0
\(337\) −27.5655 −1.50159 −0.750793 0.660538i \(-0.770328\pi\)
−0.750793 + 0.660538i \(0.770328\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.00301 0.162622
\(342\) 0 0
\(343\) − 1.00000i − 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 20.8364i − 1.11856i −0.828980 0.559279i \(-0.811078\pi\)
0.828980 0.559279i \(-0.188922\pi\)
\(348\) 0 0
\(349\) 4.88181i 0.261317i 0.991427 + 0.130659i \(0.0417092\pi\)
−0.991427 + 0.130659i \(0.958291\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 7.44391i − 0.396200i −0.980182 0.198100i \(-0.936523\pi\)
0.980182 0.198100i \(-0.0634770\pi\)
\(354\) 0 0
\(355\) −6.93662 −0.368158
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −22.3923 −1.18182 −0.590910 0.806737i \(-0.701231\pi\)
−0.590910 + 0.806737i \(0.701231\pi\)
\(360\) 0 0
\(361\) −18.7218 −0.985356
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 18.0126 0.942821
\(366\) 0 0
\(367\) − 35.2575i − 1.84042i −0.391419 0.920212i \(-0.628016\pi\)
0.391419 0.920212i \(-0.371984\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.795428i 0.0412966i
\(372\) 0 0
\(373\) 11.2681i 0.583442i 0.956503 + 0.291721i \(0.0942279\pi\)
−0.956503 + 0.291721i \(0.905772\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 30.9981i − 1.59649i
\(378\) 0 0
\(379\) 5.47888 0.281431 0.140716 0.990050i \(-0.455060\pi\)
0.140716 + 0.990050i \(0.455060\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 31.6668 1.61810 0.809049 0.587741i \(-0.199983\pi\)
0.809049 + 0.587741i \(0.199983\pi\)
\(384\) 0 0
\(385\) −1.24475 −0.0634384
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −25.1014 −1.27269 −0.636345 0.771405i \(-0.719554\pi\)
−0.636345 + 0.771405i \(0.719554\pi\)
\(390\) 0 0
\(391\) 16.4327i 0.831036i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 32.2089i − 1.62060i
\(396\) 0 0
\(397\) 4.04640i 0.203083i 0.994831 + 0.101541i \(0.0323774\pi\)
−0.994831 + 0.101541i \(0.967623\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 5.87339i − 0.293303i −0.989188 0.146652i \(-0.953150\pi\)
0.989188 0.146652i \(-0.0468496\pi\)
\(402\) 0 0
\(403\) −49.4620 −2.46388
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.33414 −0.0661309
\(408\) 0 0
\(409\) 25.1101 1.24162 0.620808 0.783963i \(-0.286805\pi\)
0.620808 + 0.783963i \(0.286805\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.47252 0.121665
\(414\) 0 0
\(415\) − 26.1939i − 1.28581i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12.3059i 0.601184i 0.953753 + 0.300592i \(0.0971842\pi\)
−0.953753 + 0.300592i \(0.902816\pi\)
\(420\) 0 0
\(421\) 22.4095i 1.09217i 0.837729 + 0.546086i \(0.183883\pi\)
−0.837729 + 0.546086i \(0.816117\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 9.59086i − 0.465225i
\(426\) 0 0
\(427\) 11.4641 0.554787
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 21.4041 1.03100 0.515499 0.856890i \(-0.327607\pi\)
0.515499 + 0.856890i \(0.327607\pi\)
\(432\) 0 0
\(433\) 19.3925 0.931944 0.465972 0.884799i \(-0.345705\pi\)
0.465972 + 0.884799i \(0.345705\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.33395 −0.207321
\(438\) 0 0
\(439\) 18.3755i 0.877013i 0.898728 + 0.438507i \(0.144492\pi\)
−0.898728 + 0.438507i \(0.855508\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 8.58770i − 0.408014i −0.978969 0.204007i \(-0.934603\pi\)
0.978969 0.204007i \(-0.0653965\pi\)
\(444\) 0 0
\(445\) 16.6226i 0.787988i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 7.78687i − 0.367485i −0.982974 0.183742i \(-0.941179\pi\)
0.982974 0.183742i \(-0.0588212\pi\)
\(450\) 0 0
\(451\) 2.97661 0.140163
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 20.5021 0.961152
\(456\) 0 0
\(457\) 10.3205 0.482773 0.241387 0.970429i \(-0.422398\pi\)
0.241387 + 0.970429i \(0.422398\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 22.2016 1.03403 0.517015 0.855976i \(-0.327043\pi\)
0.517015 + 0.855976i \(0.327043\pi\)
\(462\) 0 0
\(463\) − 27.9028i − 1.29675i −0.761320 0.648377i \(-0.775448\pi\)
0.761320 0.648377i \(-0.224552\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 21.9602i 1.01619i 0.861300 + 0.508097i \(0.169651\pi\)
−0.861300 + 0.508097i \(0.830349\pi\)
\(468\) 0 0
\(469\) 6.55068i 0.302482i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.645280i 0.0296700i
\(474\) 0 0
\(475\) 2.52949 0.116061
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.13278 −0.280214 −0.140107 0.990136i \(-0.544745\pi\)
−0.140107 + 0.990136i \(0.544745\pi\)
\(480\) 0 0
\(481\) 21.9744 1.00195
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 59.7827 2.71459
\(486\) 0 0
\(487\) 19.7848i 0.896535i 0.893899 + 0.448268i \(0.147959\pi\)
−0.893899 + 0.448268i \(0.852041\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 28.3809i 1.28081i 0.768037 + 0.640405i \(0.221234\pi\)
−0.768037 + 0.640405i \(0.778766\pi\)
\(492\) 0 0
\(493\) 9.46410i 0.426242i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.21634i 0.0994164i
\(498\) 0 0
\(499\) −10.7407 −0.480818 −0.240409 0.970672i \(-0.577282\pi\)
−0.240409 + 0.970672i \(0.577282\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 14.7321 0.656870 0.328435 0.944527i \(-0.393479\pi\)
0.328435 + 0.944527i \(0.393479\pi\)
\(504\) 0 0
\(505\) 6.25953 0.278545
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −23.2913 −1.03237 −0.516185 0.856477i \(-0.672648\pi\)
−0.516185 + 0.856477i \(0.672648\pi\)
\(510\) 0 0
\(511\) − 5.75525i − 0.254597i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 53.2523i − 2.34657i
\(516\) 0 0
\(517\) − 4.15837i − 0.182885i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.91027i 0.0836905i 0.999124 + 0.0418453i \(0.0133237\pi\)
−0.999124 + 0.0418453i \(0.986676\pi\)
\(522\) 0 0
\(523\) −25.5885 −1.11891 −0.559453 0.828862i \(-0.688989\pi\)
−0.559453 + 0.828862i \(0.688989\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 15.1014 0.657825
\(528\) 0 0
\(529\) 44.5082 1.93514
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −49.0272 −2.12360
\(534\) 0 0
\(535\) 5.98918i 0.258935i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.397714i 0.0171308i
\(540\) 0 0
\(541\) 7.91959i 0.340490i 0.985402 + 0.170245i \(0.0544559\pi\)
−0.985402 + 0.170245i \(0.945544\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) − 22.1530i − 0.948929i
\(546\) 0 0
\(547\) 7.65409 0.327265 0.163633 0.986521i \(-0.447679\pi\)
0.163633 + 0.986521i \(0.447679\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.49606 −0.106336
\(552\) 0 0
\(553\) −10.2911 −0.437624
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −27.6373 −1.17103 −0.585514 0.810662i \(-0.699107\pi\)
−0.585514 + 0.810662i \(0.699107\pi\)
\(558\) 0 0
\(559\) − 10.6283i − 0.449529i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 33.9198i 1.42955i 0.699355 + 0.714774i \(0.253471\pi\)
−0.699355 + 0.714774i \(0.746529\pi\)
\(564\) 0 0
\(565\) 31.2449i 1.31448i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 18.7382i − 0.785547i −0.919635 0.392773i \(-0.871516\pi\)
0.919635 0.392773i \(-0.128484\pi\)
\(570\) 0 0
\(571\) −15.2449 −0.637981 −0.318991 0.947758i \(-0.603344\pi\)
−0.318991 + 0.947758i \(0.603344\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −39.4009 −1.64313
\(576\) 0 0
\(577\) 1.49366 0.0621818 0.0310909 0.999517i \(-0.490102\pi\)
0.0310909 + 0.999517i \(0.490102\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −8.36930 −0.347217
\(582\) 0 0
\(583\) − 0.316353i − 0.0131020i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 16.2195i − 0.669452i −0.942315 0.334726i \(-0.891356\pi\)
0.942315 0.334726i \(-0.108644\pi\)
\(588\) 0 0
\(589\) 3.98282i 0.164109i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 21.3871i 0.878263i 0.898423 + 0.439131i \(0.144714\pi\)
−0.898423 + 0.439131i \(0.855286\pi\)
\(594\) 0 0
\(595\) −6.25953 −0.256616
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −11.7672 −0.480795 −0.240398 0.970674i \(-0.577278\pi\)
−0.240398 + 0.970674i \(0.577278\pi\)
\(600\) 0 0
\(601\) −15.7552 −0.642670 −0.321335 0.946966i \(-0.604132\pi\)
−0.321335 + 0.946966i \(0.604132\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −33.9324 −1.37955
\(606\) 0 0
\(607\) − 1.95400i − 0.0793102i −0.999213 0.0396551i \(-0.987374\pi\)
0.999213 0.0396551i \(-0.0126259\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 68.4918i 2.77088i
\(612\) 0 0
\(613\) − 3.47046i − 0.140171i −0.997541 0.0700853i \(-0.977673\pi\)
0.997541 0.0700853i \(-0.0223271\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24.9456i 1.00427i 0.864789 + 0.502136i \(0.167452\pi\)
−0.864789 + 0.502136i \(0.832548\pi\)
\(618\) 0 0
\(619\) 37.3233 1.50015 0.750075 0.661353i \(-0.230017\pi\)
0.750075 + 0.661353i \(0.230017\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.31114 0.212786
\(624\) 0 0
\(625\) −25.9810 −1.03924
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6.70905 −0.267507
\(630\) 0 0
\(631\) 9.51886i 0.378940i 0.981887 + 0.189470i \(0.0606770\pi\)
−0.981887 + 0.189470i \(0.939323\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 24.2721i 0.963209i
\(636\) 0 0
\(637\) − 6.55068i − 0.259547i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 41.9263i − 1.65599i −0.560735 0.827995i \(-0.689481\pi\)
0.560735 0.827995i \(-0.310519\pi\)
\(642\) 0 0
\(643\) −2.79303 −0.110146 −0.0550732 0.998482i \(-0.517539\pi\)
−0.0550732 + 0.998482i \(0.517539\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 30.2089 1.18763 0.593817 0.804600i \(-0.297620\pi\)
0.593817 + 0.804600i \(0.297620\pi\)
\(648\) 0 0
\(649\) −0.983356 −0.0386001
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −36.8020 −1.44017 −0.720086 0.693884i \(-0.755898\pi\)
−0.720086 + 0.693884i \(0.755898\pi\)
\(654\) 0 0
\(655\) 46.6498i 1.82276i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 27.5858i 1.07459i 0.843394 + 0.537296i \(0.180554\pi\)
−0.843394 + 0.537296i \(0.819446\pi\)
\(660\) 0 0
\(661\) − 43.9007i − 1.70754i −0.520650 0.853770i \(-0.674310\pi\)
0.520650 0.853770i \(-0.325690\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 1.65089i − 0.0640186i
\(666\) 0 0
\(667\) 38.8801 1.50544
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.55943 −0.176015
\(672\) 0 0
\(673\) −1.78085 −0.0686465 −0.0343233 0.999411i \(-0.510928\pi\)
−0.0343233 + 0.999411i \(0.510928\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 45.7356 1.75776 0.878881 0.477041i \(-0.158291\pi\)
0.878881 + 0.477041i \(0.158291\pi\)
\(678\) 0 0
\(679\) − 19.1014i − 0.733043i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 23.5159i − 0.899811i −0.893076 0.449906i \(-0.851458\pi\)
0.893076 0.449906i \(-0.148542\pi\)
\(684\) 0 0
\(685\) 70.2810i 2.68530i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5.21059i 0.198508i
\(690\) 0 0
\(691\) 31.3501 1.19261 0.596306 0.802757i \(-0.296634\pi\)
0.596306 + 0.802757i \(0.296634\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.56130 0.362681
\(696\) 0 0
\(697\) 14.9686 0.566975
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.40072 −0.0529046 −0.0264523 0.999650i \(-0.508421\pi\)
−0.0264523 + 0.999650i \(0.508421\pi\)
\(702\) 0 0
\(703\) − 1.76944i − 0.0667357i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 2.00000i − 0.0752177i
\(708\) 0 0
\(709\) 39.4709i 1.48236i 0.671307 + 0.741179i \(0.265733\pi\)
−0.671307 + 0.741179i \(0.734267\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 62.0389i − 2.32338i
\(714\) 0 0
\(715\) −8.15396 −0.304941
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 12.0694 0.450113 0.225056 0.974346i \(-0.427743\pi\)
0.225056 + 0.974346i \(0.427743\pi\)
\(720\) 0 0
\(721\) −17.0148 −0.633663
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −22.6922 −0.842768
\(726\) 0 0
\(727\) 2.39230i 0.0887257i 0.999015 + 0.0443628i \(0.0141258\pi\)
−0.999015 + 0.0443628i \(0.985874\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3.24495i 0.120019i
\(732\) 0 0
\(733\) − 14.5802i − 0.538533i −0.963066 0.269267i \(-0.913219\pi\)
0.963066 0.269267i \(-0.0867813\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 2.60530i − 0.0959673i
\(738\) 0 0
\(739\) −30.3459 −1.11629 −0.558146 0.829743i \(-0.688487\pi\)
−0.558146 + 0.829743i \(0.688487\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −16.6659 −0.611411 −0.305706 0.952126i \(-0.598892\pi\)
−0.305706 + 0.952126i \(0.598892\pi\)
\(744\) 0 0
\(745\) −21.9540 −0.804332
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.91362 0.0699222
\(750\) 0 0
\(751\) 2.10155i 0.0766866i 0.999265 + 0.0383433i \(0.0122080\pi\)
−0.999265 + 0.0383433i \(0.987792\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 30.7030i − 1.11740i
\(756\) 0 0
\(757\) 39.2408i 1.42623i 0.701046 + 0.713116i \(0.252717\pi\)
−0.701046 + 0.713116i \(0.747283\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 22.7618i 0.825113i 0.910932 + 0.412556i \(0.135364\pi\)
−0.910932 + 0.412556i \(0.864636\pi\)
\(762\) 0 0
\(763\) −7.07816 −0.256246
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 16.1967 0.584828
\(768\) 0 0
\(769\) −52.9030 −1.90773 −0.953865 0.300234i \(-0.902935\pi\)
−0.953865 + 0.300234i \(0.902935\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −6.27110 −0.225556 −0.112778 0.993620i \(-0.535975\pi\)
−0.112778 + 0.993620i \(0.535975\pi\)
\(774\) 0 0
\(775\) 36.2087i 1.30066i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.94780i 0.141445i
\(780\) 0 0
\(781\) − 0.881470i − 0.0315415i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 34.1038i 1.21722i
\(786\) 0 0
\(787\) 20.5651 0.733065 0.366533 0.930405i \(-0.380545\pi\)
0.366533 + 0.930405i \(0.380545\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 9.98316 0.354960
\(792\) 0 0
\(793\) 75.0976 2.66679
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.6802 0.590845 0.295422 0.955367i \(-0.404540\pi\)
0.295422 + 0.955367i \(0.404540\pi\)
\(798\) 0 0
\(799\) − 20.9114i − 0.739791i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.28894i 0.0807751i
\(804\) 0 0
\(805\) 25.7152i 0.906342i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 54.5485i 1.91782i 0.283707 + 0.958911i \(0.408436\pi\)
−0.283707 + 0.958911i \(0.591564\pi\)
\(810\) 0 0
\(811\) 9.77845 0.343368 0.171684 0.985152i \(-0.445079\pi\)
0.171684 + 0.985152i \(0.445079\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −31.3439 −1.09793
\(816\) 0 0
\(817\) −0.855821 −0.0299414
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −28.5488 −0.996359 −0.498179 0.867074i \(-0.665998\pi\)
−0.498179 + 0.867074i \(0.665998\pi\)
\(822\) 0 0
\(823\) − 33.5912i − 1.17092i −0.810702 0.585459i \(-0.800914\pi\)
0.810702 0.585459i \(-0.199086\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 25.9650i 0.902893i 0.892298 + 0.451446i \(0.149092\pi\)
−0.892298 + 0.451446i \(0.850908\pi\)
\(828\) 0 0
\(829\) 23.7613i 0.825263i 0.910898 + 0.412631i \(0.135390\pi\)
−0.910898 + 0.412631i \(0.864610\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.00000i 0.0692959i
\(834\) 0 0
\(835\) −45.5864 −1.57758
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.77243 0.0957148 0.0478574 0.998854i \(-0.484761\pi\)
0.0478574 + 0.998854i \(0.484761\pi\)
\(840\) 0 0
\(841\) −6.60770 −0.227852
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 93.6155 3.22047
\(846\) 0 0
\(847\) 10.8418i 0.372529i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 27.5619i 0.944810i
\(852\) 0 0
\(853\) − 0.236670i − 0.00810344i −0.999992 0.00405172i \(-0.998710\pi\)
0.999992 0.00405172i \(-0.00128971\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 21.2139i − 0.724654i −0.932051 0.362327i \(-0.881982\pi\)
0.932051 0.362327i \(-0.118018\pi\)
\(858\) 0 0
\(859\) −12.6199 −0.430585 −0.215292 0.976550i \(-0.569070\pi\)
−0.215292 + 0.976550i \(0.569070\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 25.8396 0.879589 0.439795 0.898098i \(-0.355051\pi\)
0.439795 + 0.898098i \(0.355051\pi\)
\(864\) 0 0
\(865\) 44.8104 1.52360
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.09293 0.138843
\(870\) 0 0
\(871\) 42.9114i 1.45400i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0.640262i 0.0216448i
\(876\) 0 0
\(877\) − 55.0972i − 1.86050i −0.366925 0.930251i \(-0.619589\pi\)
0.366925 0.930251i \(-0.380411\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 33.7034i 1.13550i 0.823202 + 0.567749i \(0.192186\pi\)
−0.823202 + 0.567749i \(0.807814\pi\)
\(882\) 0 0
\(883\) −19.8396 −0.667655 −0.333827 0.942634i \(-0.608340\pi\)
−0.333827 + 0.942634i \(0.608340\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 17.5967 0.590840 0.295420 0.955367i \(-0.404540\pi\)
0.295420 + 0.955367i \(0.404540\pi\)
\(888\) 0 0
\(889\) 7.75525 0.260103
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 5.51515 0.184558
\(894\) 0 0
\(895\) − 62.0019i − 2.07249i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 35.7302i − 1.19167i
\(900\) 0 0
\(901\) − 1.59086i − 0.0529991i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 63.1372i 2.09875i
\(906\) 0 0
\(907\) 10.8190 0.359238 0.179619 0.983736i \(-0.442514\pi\)
0.179619 + 0.983736i \(0.442514\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −33.4364 −1.10780 −0.553899 0.832584i \(-0.686861\pi\)
−0.553899 + 0.832584i \(0.686861\pi\)
\(912\) 0 0
\(913\) 3.32859 0.110160
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 14.9052 0.492213
\(918\) 0 0
\(919\) − 3.70049i − 0.122068i −0.998136 0.0610339i \(-0.980560\pi\)
0.998136 0.0610339i \(-0.0194398\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 14.5185i 0.477883i
\(924\) 0 0
\(925\) − 16.0864i − 0.528917i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 17.0318i − 0.558796i −0.960175 0.279398i \(-0.909865\pi\)
0.960175 0.279398i \(-0.0901348\pi\)
\(930\) 0 0
\(931\) −0.527479 −0.0172874
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.48950 0.0814155
\(936\) 0 0
\(937\) −11.6077 −0.379207 −0.189603 0.981861i \(-0.560720\pi\)
−0.189603 + 0.981861i \(0.560720\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −50.5834 −1.64897 −0.824486 0.565882i \(-0.808536\pi\)
−0.824486 + 0.565882i \(0.808536\pi\)
\(942\) 0 0
\(943\) − 61.4935i − 2.00250i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 42.8764i − 1.39330i −0.717413 0.696648i \(-0.754674\pi\)
0.717413 0.696648i \(-0.245326\pi\)
\(948\) 0 0
\(949\) − 37.7008i − 1.22382i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 11.4074i − 0.369523i −0.982783 0.184761i \(-0.940849\pi\)
0.982783 0.184761i \(-0.0591512\pi\)
\(954\) 0 0
\(955\) 20.1416 0.651766
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 22.4557 0.725132
\(960\) 0 0
\(961\) −26.0127 −0.839120
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 31.2449 1.00581
\(966\) 0 0
\(967\) 24.7090i 0.794589i 0.917691 + 0.397295i \(0.130051\pi\)
−0.917691 + 0.397295i \(0.869949\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 28.3585i 0.910067i 0.890474 + 0.455034i \(0.150373\pi\)
−0.890474 + 0.455034i \(0.849627\pi\)
\(972\) 0 0
\(973\) − 3.05496i − 0.0979375i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 23.4704i − 0.750885i −0.926846 0.375442i \(-0.877491\pi\)
0.926846 0.375442i \(-0.122509\pi\)
\(978\) 0 0
\(979\) −2.11231 −0.0675099
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 26.2425 0.837007 0.418504 0.908215i \(-0.362555\pi\)
0.418504 + 0.908215i \(0.362555\pi\)
\(984\) 0 0
\(985\) 73.9790 2.35717
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 13.3308 0.423895
\(990\) 0 0
\(991\) − 44.2579i − 1.40590i −0.711241 0.702949i \(-0.751866\pi\)
0.711241 0.702949i \(-0.248134\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 67.6662i 2.14516i
\(996\) 0 0
\(997\) − 28.1271i − 0.890796i −0.895333 0.445398i \(-0.853062\pi\)
0.895333 0.445398i \(-0.146938\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6048.2.j.a.5615.4 8
3.2 odd 2 6048.2.j.b.5615.6 8
4.3 odd 2 1512.2.j.a.323.1 8
8.3 odd 2 6048.2.j.b.5615.5 8
8.5 even 2 1512.2.j.b.323.6 yes 8
12.11 even 2 1512.2.j.b.323.8 yes 8
24.5 odd 2 1512.2.j.a.323.3 yes 8
24.11 even 2 inner 6048.2.j.a.5615.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.j.a.323.1 8 4.3 odd 2
1512.2.j.a.323.3 yes 8 24.5 odd 2
1512.2.j.b.323.6 yes 8 8.5 even 2
1512.2.j.b.323.8 yes 8 12.11 even 2
6048.2.j.a.5615.3 8 24.11 even 2 inner
6048.2.j.a.5615.4 8 1.1 even 1 trivial
6048.2.j.b.5615.5 8 8.3 odd 2
6048.2.j.b.5615.6 8 3.2 odd 2