Properties

Label 7448.2.a.bq.1.2
Level $7448$
Weight $2$
Character 7448.1
Self dual yes
Analytic conductor $59.473$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4725794254\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 15 x^{6} - x^{5} + 66 x^{4} + 4 x^{3} - 76 x^{2} + 8 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 1064)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.46993\) of defining polynomial
Character \(\chi\) \(=\) 7448.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46993 q^{3} -4.03871 q^{5} +3.10055 q^{9} +O(q^{10})\) \(q-2.46993 q^{3} -4.03871 q^{5} +3.10055 q^{9} +1.60209 q^{11} +3.15476 q^{13} +9.97534 q^{15} +0.652775 q^{17} +1.00000 q^{19} +2.91726 q^{23} +11.3112 q^{25} -0.248363 q^{27} +2.12163 q^{29} -7.02322 q^{31} -3.95705 q^{33} -5.30985 q^{37} -7.79204 q^{39} -2.00000 q^{41} +7.97365 q^{43} -12.5223 q^{45} -0.605361 q^{47} -1.61231 q^{51} +12.4824 q^{53} -6.47038 q^{55} -2.46993 q^{57} +14.4517 q^{59} +9.34534 q^{61} -12.7412 q^{65} -2.78539 q^{67} -7.20542 q^{69} -9.50073 q^{71} -16.6278 q^{73} -27.9379 q^{75} +4.85650 q^{79} -8.68822 q^{81} -8.73966 q^{83} -2.63637 q^{85} -5.24028 q^{87} -2.27610 q^{89} +17.3469 q^{93} -4.03871 q^{95} +1.24899 q^{97} +4.96736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{5} + 6 q^{9} + O(q^{10}) \) \( 8 q - q^{5} + 6 q^{9} + 9 q^{11} + 8 q^{15} + 4 q^{17} + 8 q^{19} + 25 q^{23} + 15 q^{25} + 3 q^{27} + 6 q^{29} + 8 q^{33} + 13 q^{37} - 11 q^{39} - 16 q^{41} + 17 q^{43} + 17 q^{45} - 24 q^{47} + 5 q^{51} + 2 q^{53} + 5 q^{55} + 2 q^{59} - 13 q^{61} - 26 q^{65} + 2 q^{67} - 11 q^{69} + 10 q^{71} + 5 q^{73} - 20 q^{75} + 16 q^{79} - 12 q^{81} - 43 q^{83} + 24 q^{85} + 20 q^{87} + 8 q^{89} + 2 q^{93} - q^{95} - 12 q^{97} + 37 q^{99} + O(q^{100}) \)

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
\(3\) −2.46993 −1.42601 −0.713007 0.701157i \(-0.752667\pi\)
−0.713007 + 0.701157i \(0.752667\pi\)
\(4\) 0 0
\(5\) −4.03871 −1.80617 −0.903084 0.429464i \(-0.858703\pi\)
−0.903084 + 0.429464i \(0.858703\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 3.10055 1.03352
\(10\) 0 0
\(11\) 1.60209 0.483048 0.241524 0.970395i \(-0.422353\pi\)
0.241524 + 0.970395i \(0.422353\pi\)
\(12\) 0 0
\(13\) 3.15476 0.874974 0.437487 0.899225i \(-0.355869\pi\)
0.437487 + 0.899225i \(0.355869\pi\)
\(14\) 0 0
\(15\) 9.97534 2.57562
\(16\) 0 0
\(17\) 0.652775 0.158321 0.0791605 0.996862i \(-0.474776\pi\)
0.0791605 + 0.996862i \(0.474776\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.91726 0.608290 0.304145 0.952626i \(-0.401629\pi\)
0.304145 + 0.952626i \(0.401629\pi\)
\(24\) 0 0
\(25\) 11.3112 2.26224
\(26\) 0 0
\(27\) −0.248363 −0.0477975
\(28\) 0 0
\(29\) 2.12163 0.393977 0.196988 0.980406i \(-0.436884\pi\)
0.196988 + 0.980406i \(0.436884\pi\)
\(30\) 0 0
\(31\) −7.02322 −1.26141 −0.630704 0.776024i \(-0.717234\pi\)
−0.630704 + 0.776024i \(0.717234\pi\)
\(32\) 0 0
\(33\) −3.95705 −0.688833
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.30985 −0.872934 −0.436467 0.899720i \(-0.643770\pi\)
−0.436467 + 0.899720i \(0.643770\pi\)
\(38\) 0 0
\(39\) −7.79204 −1.24773
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 7.97365 1.21597 0.607985 0.793948i \(-0.291978\pi\)
0.607985 + 0.793948i \(0.291978\pi\)
\(44\) 0 0
\(45\) −12.5223 −1.86671
\(46\) 0 0
\(47\) −0.605361 −0.0883009 −0.0441505 0.999025i \(-0.514058\pi\)
−0.0441505 + 0.999025i \(0.514058\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −1.61231 −0.225768
\(52\) 0 0
\(53\) 12.4824 1.71459 0.857296 0.514823i \(-0.172142\pi\)
0.857296 + 0.514823i \(0.172142\pi\)
\(54\) 0 0
\(55\) −6.47038 −0.872465
\(56\) 0 0
\(57\) −2.46993 −0.327150
\(58\) 0 0
\(59\) 14.4517 1.88146 0.940728 0.339163i \(-0.110144\pi\)
0.940728 + 0.339163i \(0.110144\pi\)
\(60\) 0 0
\(61\) 9.34534 1.19655 0.598274 0.801292i \(-0.295854\pi\)
0.598274 + 0.801292i \(0.295854\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.7412 −1.58035
\(66\) 0 0
\(67\) −2.78539 −0.340289 −0.170145 0.985419i \(-0.554423\pi\)
−0.170145 + 0.985419i \(0.554423\pi\)
\(68\) 0 0
\(69\) −7.20542 −0.867430
\(70\) 0 0
\(71\) −9.50073 −1.12753 −0.563764 0.825936i \(-0.690647\pi\)
−0.563764 + 0.825936i \(0.690647\pi\)
\(72\) 0 0
\(73\) −16.6278 −1.94613 −0.973067 0.230523i \(-0.925956\pi\)
−0.973067 + 0.230523i \(0.925956\pi\)
\(74\) 0 0
\(75\) −27.9379 −3.22599
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 4.85650 0.546399 0.273199 0.961957i \(-0.411918\pi\)
0.273199 + 0.961957i \(0.411918\pi\)
\(80\) 0 0
\(81\) −8.68822 −0.965358
\(82\) 0 0
\(83\) −8.73966 −0.959302 −0.479651 0.877459i \(-0.659237\pi\)
−0.479651 + 0.877459i \(0.659237\pi\)
\(84\) 0 0
\(85\) −2.63637 −0.285954
\(86\) 0 0
\(87\) −5.24028 −0.561816
\(88\) 0 0
\(89\) −2.27610 −0.241266 −0.120633 0.992697i \(-0.538492\pi\)
−0.120633 + 0.992697i \(0.538492\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 17.3469 1.79879
\(94\) 0 0
\(95\) −4.03871 −0.414363
\(96\) 0 0
\(97\) 1.24899 0.126815 0.0634077 0.997988i \(-0.479803\pi\)
0.0634077 + 0.997988i \(0.479803\pi\)
\(98\) 0 0
\(99\) 4.96736 0.499239
\(100\) 0 0
\(101\) −11.2461 −1.11903 −0.559515 0.828820i \(-0.689013\pi\)
−0.559515 + 0.828820i \(0.689013\pi\)
\(102\) 0 0
\(103\) 3.59297 0.354025 0.177013 0.984209i \(-0.443357\pi\)
0.177013 + 0.984209i \(0.443357\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.74632 −0.168823 −0.0844117 0.996431i \(-0.526901\pi\)
−0.0844117 + 0.996431i \(0.526901\pi\)
\(108\) 0 0
\(109\) −1.91848 −0.183757 −0.0918786 0.995770i \(-0.529287\pi\)
−0.0918786 + 0.995770i \(0.529287\pi\)
\(110\) 0 0
\(111\) 13.1150 1.24482
\(112\) 0 0
\(113\) −11.8303 −1.11290 −0.556451 0.830881i \(-0.687837\pi\)
−0.556451 + 0.830881i \(0.687837\pi\)
\(114\) 0 0
\(115\) −11.7820 −1.09867
\(116\) 0 0
\(117\) 9.78152 0.904301
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −8.43331 −0.766665
\(122\) 0 0
\(123\) 4.93986 0.445412
\(124\) 0 0
\(125\) −25.4892 −2.27982
\(126\) 0 0
\(127\) −15.3583 −1.36283 −0.681416 0.731896i \(-0.738636\pi\)
−0.681416 + 0.731896i \(0.738636\pi\)
\(128\) 0 0
\(129\) −19.6944 −1.73399
\(130\) 0 0
\(131\) −13.3828 −1.16926 −0.584631 0.811299i \(-0.698761\pi\)
−0.584631 + 0.811299i \(0.698761\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.00307 0.0863303
\(136\) 0 0
\(137\) −3.16704 −0.270579 −0.135289 0.990806i \(-0.543196\pi\)
−0.135289 + 0.990806i \(0.543196\pi\)
\(138\) 0 0
\(139\) −16.3904 −1.39021 −0.695106 0.718907i \(-0.744642\pi\)
−0.695106 + 0.718907i \(0.744642\pi\)
\(140\) 0 0
\(141\) 1.49520 0.125918
\(142\) 0 0
\(143\) 5.05421 0.422654
\(144\) 0 0
\(145\) −8.56865 −0.711588
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 14.0220 1.14873 0.574366 0.818599i \(-0.305249\pi\)
0.574366 + 0.818599i \(0.305249\pi\)
\(150\) 0 0
\(151\) 18.5461 1.50926 0.754632 0.656149i \(-0.227816\pi\)
0.754632 + 0.656149i \(0.227816\pi\)
\(152\) 0 0
\(153\) 2.02396 0.163628
\(154\) 0 0
\(155\) 28.3648 2.27831
\(156\) 0 0
\(157\) 23.5512 1.87959 0.939796 0.341735i \(-0.111014\pi\)
0.939796 + 0.341735i \(0.111014\pi\)
\(158\) 0 0
\(159\) −30.8307 −2.44503
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 9.07130 0.710519 0.355260 0.934768i \(-0.384392\pi\)
0.355260 + 0.934768i \(0.384392\pi\)
\(164\) 0 0
\(165\) 15.9814 1.24415
\(166\) 0 0
\(167\) −0.191778 −0.0148402 −0.00742011 0.999972i \(-0.502362\pi\)
−0.00742011 + 0.999972i \(0.502362\pi\)
\(168\) 0 0
\(169\) −3.04747 −0.234421
\(170\) 0 0
\(171\) 3.10055 0.237105
\(172\) 0 0
\(173\) −6.98927 −0.531384 −0.265692 0.964058i \(-0.585600\pi\)
−0.265692 + 0.964058i \(0.585600\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −35.6948 −2.68298
\(178\) 0 0
\(179\) −15.9087 −1.18907 −0.594534 0.804070i \(-0.702664\pi\)
−0.594534 + 0.804070i \(0.702664\pi\)
\(180\) 0 0
\(181\) 16.6258 1.23579 0.617894 0.786261i \(-0.287986\pi\)
0.617894 + 0.786261i \(0.287986\pi\)
\(182\) 0 0
\(183\) −23.0823 −1.70629
\(184\) 0 0
\(185\) 21.4450 1.57667
\(186\) 0 0
\(187\) 1.04580 0.0764766
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 24.0101 1.73731 0.868654 0.495419i \(-0.164985\pi\)
0.868654 + 0.495419i \(0.164985\pi\)
\(192\) 0 0
\(193\) 0.109875 0.00790894 0.00395447 0.999992i \(-0.498741\pi\)
0.00395447 + 0.999992i \(0.498741\pi\)
\(194\) 0 0
\(195\) 31.4698 2.25360
\(196\) 0 0
\(197\) −10.9282 −0.778601 −0.389301 0.921111i \(-0.627283\pi\)
−0.389301 + 0.921111i \(0.627283\pi\)
\(198\) 0 0
\(199\) 22.5372 1.59762 0.798810 0.601584i \(-0.205463\pi\)
0.798810 + 0.601584i \(0.205463\pi\)
\(200\) 0 0
\(201\) 6.87971 0.485258
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 8.07743 0.564152
\(206\) 0 0
\(207\) 9.04511 0.628679
\(208\) 0 0
\(209\) 1.60209 0.110819
\(210\) 0 0
\(211\) 23.7342 1.63393 0.816966 0.576685i \(-0.195654\pi\)
0.816966 + 0.576685i \(0.195654\pi\)
\(212\) 0 0
\(213\) 23.4661 1.60787
\(214\) 0 0
\(215\) −32.2033 −2.19625
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 41.0694 2.77522
\(220\) 0 0
\(221\) 2.05935 0.138527
\(222\) 0 0
\(223\) 4.36632 0.292390 0.146195 0.989256i \(-0.453297\pi\)
0.146195 + 0.989256i \(0.453297\pi\)
\(224\) 0 0
\(225\) 35.0710 2.33807
\(226\) 0 0
\(227\) 21.9914 1.45962 0.729810 0.683650i \(-0.239609\pi\)
0.729810 + 0.683650i \(0.239609\pi\)
\(228\) 0 0
\(229\) 4.40344 0.290988 0.145494 0.989359i \(-0.453523\pi\)
0.145494 + 0.989359i \(0.453523\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −20.0560 −1.31391 −0.656956 0.753929i \(-0.728156\pi\)
−0.656956 + 0.753929i \(0.728156\pi\)
\(234\) 0 0
\(235\) 2.44488 0.159486
\(236\) 0 0
\(237\) −11.9952 −0.779173
\(238\) 0 0
\(239\) 21.7477 1.40674 0.703370 0.710824i \(-0.251678\pi\)
0.703370 + 0.710824i \(0.251678\pi\)
\(240\) 0 0
\(241\) 30.9910 1.99630 0.998152 0.0607661i \(-0.0193544\pi\)
0.998152 + 0.0607661i \(0.0193544\pi\)
\(242\) 0 0
\(243\) 22.2044 1.42441
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.15476 0.200733
\(248\) 0 0
\(249\) 21.5863 1.36798
\(250\) 0 0
\(251\) 5.24483 0.331051 0.165525 0.986206i \(-0.447068\pi\)
0.165525 + 0.986206i \(0.447068\pi\)
\(252\) 0 0
\(253\) 4.67370 0.293833
\(254\) 0 0
\(255\) 6.51165 0.407775
\(256\) 0 0
\(257\) −28.5942 −1.78366 −0.891828 0.452374i \(-0.850577\pi\)
−0.891828 + 0.452374i \(0.850577\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 6.57823 0.407182
\(262\) 0 0
\(263\) 5.53993 0.341607 0.170803 0.985305i \(-0.445364\pi\)
0.170803 + 0.985305i \(0.445364\pi\)
\(264\) 0 0
\(265\) −50.4130 −3.09684
\(266\) 0 0
\(267\) 5.62181 0.344049
\(268\) 0 0
\(269\) −4.29154 −0.261660 −0.130830 0.991405i \(-0.541764\pi\)
−0.130830 + 0.991405i \(0.541764\pi\)
\(270\) 0 0
\(271\) −0.890669 −0.0541043 −0.0270521 0.999634i \(-0.508612\pi\)
−0.0270521 + 0.999634i \(0.508612\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 18.1216 1.09277
\(276\) 0 0
\(277\) −12.0106 −0.721648 −0.360824 0.932634i \(-0.617505\pi\)
−0.360824 + 0.932634i \(0.617505\pi\)
\(278\) 0 0
\(279\) −21.7759 −1.30369
\(280\) 0 0
\(281\) −17.4819 −1.04288 −0.521442 0.853287i \(-0.674606\pi\)
−0.521442 + 0.853287i \(0.674606\pi\)
\(282\) 0 0
\(283\) 20.4863 1.21778 0.608891 0.793254i \(-0.291615\pi\)
0.608891 + 0.793254i \(0.291615\pi\)
\(284\) 0 0
\(285\) 9.97534 0.590888
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.5739 −0.974934
\(290\) 0 0
\(291\) −3.08491 −0.180841
\(292\) 0 0
\(293\) −22.9489 −1.34069 −0.670346 0.742049i \(-0.733854\pi\)
−0.670346 + 0.742049i \(0.733854\pi\)
\(294\) 0 0
\(295\) −58.3664 −3.39822
\(296\) 0 0
\(297\) −0.397899 −0.0230885
\(298\) 0 0
\(299\) 9.20325 0.532238
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 27.7771 1.59575
\(304\) 0 0
\(305\) −37.7431 −2.16117
\(306\) 0 0
\(307\) 14.1287 0.806365 0.403183 0.915120i \(-0.367904\pi\)
0.403183 + 0.915120i \(0.367904\pi\)
\(308\) 0 0
\(309\) −8.87437 −0.504846
\(310\) 0 0
\(311\) −13.5304 −0.767240 −0.383620 0.923491i \(-0.625323\pi\)
−0.383620 + 0.923491i \(0.625323\pi\)
\(312\) 0 0
\(313\) 26.4488 1.49498 0.747489 0.664275i \(-0.231259\pi\)
0.747489 + 0.664275i \(0.231259\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.31283 −0.186067 −0.0930335 0.995663i \(-0.529656\pi\)
−0.0930335 + 0.995663i \(0.529656\pi\)
\(318\) 0 0
\(319\) 3.39904 0.190310
\(320\) 0 0
\(321\) 4.31329 0.240745
\(322\) 0 0
\(323\) 0.652775 0.0363213
\(324\) 0 0
\(325\) 35.6842 1.97940
\(326\) 0 0
\(327\) 4.73851 0.262040
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 11.7870 0.647874 0.323937 0.946079i \(-0.394993\pi\)
0.323937 + 0.946079i \(0.394993\pi\)
\(332\) 0 0
\(333\) −16.4635 −0.902194
\(334\) 0 0
\(335\) 11.2494 0.614620
\(336\) 0 0
\(337\) 11.3688 0.619298 0.309649 0.950851i \(-0.399789\pi\)
0.309649 + 0.950851i \(0.399789\pi\)
\(338\) 0 0
\(339\) 29.2200 1.58701
\(340\) 0 0
\(341\) −11.2518 −0.609320
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 29.1006 1.56672
\(346\) 0 0
\(347\) −0.0849530 −0.00456052 −0.00228026 0.999997i \(-0.500726\pi\)
−0.00228026 + 0.999997i \(0.500726\pi\)
\(348\) 0 0
\(349\) 10.5549 0.564989 0.282494 0.959269i \(-0.408838\pi\)
0.282494 + 0.959269i \(0.408838\pi\)
\(350\) 0 0
\(351\) −0.783526 −0.0418215
\(352\) 0 0
\(353\) −0.617246 −0.0328527 −0.0164263 0.999865i \(-0.505229\pi\)
−0.0164263 + 0.999865i \(0.505229\pi\)
\(354\) 0 0
\(355\) 38.3707 2.03651
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.59248 −0.189604 −0.0948020 0.995496i \(-0.530222\pi\)
−0.0948020 + 0.995496i \(0.530222\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 20.8297 1.09328
\(364\) 0 0
\(365\) 67.1548 3.51505
\(366\) 0 0
\(367\) −6.18758 −0.322989 −0.161494 0.986874i \(-0.551631\pi\)
−0.161494 + 0.986874i \(0.551631\pi\)
\(368\) 0 0
\(369\) −6.20111 −0.322817
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 18.2122 0.942992 0.471496 0.881868i \(-0.343714\pi\)
0.471496 + 0.881868i \(0.343714\pi\)
\(374\) 0 0
\(375\) 62.9566 3.25106
\(376\) 0 0
\(377\) 6.69324 0.344719
\(378\) 0 0
\(379\) 0.847819 0.0435495 0.0217748 0.999763i \(-0.493068\pi\)
0.0217748 + 0.999763i \(0.493068\pi\)
\(380\) 0 0
\(381\) 37.9340 1.94342
\(382\) 0 0
\(383\) 33.2555 1.69928 0.849639 0.527365i \(-0.176820\pi\)
0.849639 + 0.527365i \(0.176820\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 24.7227 1.25673
\(388\) 0 0
\(389\) −17.7449 −0.899703 −0.449852 0.893103i \(-0.648523\pi\)
−0.449852 + 0.893103i \(0.648523\pi\)
\(390\) 0 0
\(391\) 1.90431 0.0963051
\(392\) 0 0
\(393\) 33.0546 1.66739
\(394\) 0 0
\(395\) −19.6140 −0.986888
\(396\) 0 0
\(397\) −7.61524 −0.382198 −0.191099 0.981571i \(-0.561205\pi\)
−0.191099 + 0.981571i \(0.561205\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −34.8573 −1.74069 −0.870345 0.492442i \(-0.836104\pi\)
−0.870345 + 0.492442i \(0.836104\pi\)
\(402\) 0 0
\(403\) −22.1566 −1.10370
\(404\) 0 0
\(405\) 35.0893 1.74360
\(406\) 0 0
\(407\) −8.50685 −0.421669
\(408\) 0 0
\(409\) −3.21019 −0.158734 −0.0793668 0.996845i \(-0.525290\pi\)
−0.0793668 + 0.996845i \(0.525290\pi\)
\(410\) 0 0
\(411\) 7.82237 0.385849
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 35.2970 1.73266
\(416\) 0 0
\(417\) 40.4830 1.98246
\(418\) 0 0
\(419\) −16.7962 −0.820550 −0.410275 0.911962i \(-0.634567\pi\)
−0.410275 + 0.911962i \(0.634567\pi\)
\(420\) 0 0
\(421\) −20.3496 −0.991780 −0.495890 0.868385i \(-0.665158\pi\)
−0.495890 + 0.868385i \(0.665158\pi\)
\(422\) 0 0
\(423\) −1.87695 −0.0912606
\(424\) 0 0
\(425\) 7.38367 0.358161
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −12.4835 −0.602711
\(430\) 0 0
\(431\) −32.5259 −1.56672 −0.783358 0.621571i \(-0.786495\pi\)
−0.783358 + 0.621571i \(0.786495\pi\)
\(432\) 0 0
\(433\) 40.2853 1.93599 0.967994 0.250975i \(-0.0807512\pi\)
0.967994 + 0.250975i \(0.0807512\pi\)
\(434\) 0 0
\(435\) 21.1640 1.01474
\(436\) 0 0
\(437\) 2.91726 0.139551
\(438\) 0 0
\(439\) 6.28387 0.299913 0.149956 0.988693i \(-0.452087\pi\)
0.149956 + 0.988693i \(0.452087\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 25.6409 1.21824 0.609118 0.793079i \(-0.291523\pi\)
0.609118 + 0.793079i \(0.291523\pi\)
\(444\) 0 0
\(445\) 9.19253 0.435768
\(446\) 0 0
\(447\) −34.6335 −1.63811
\(448\) 0 0
\(449\) −28.7456 −1.35659 −0.678294 0.734791i \(-0.737280\pi\)
−0.678294 + 0.734791i \(0.737280\pi\)
\(450\) 0 0
\(451\) −3.20418 −0.150879
\(452\) 0 0
\(453\) −45.8077 −2.15223
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 27.9390 1.30693 0.653467 0.756955i \(-0.273314\pi\)
0.653467 + 0.756955i \(0.273314\pi\)
\(458\) 0 0
\(459\) −0.162125 −0.00756735
\(460\) 0 0
\(461\) 4.95920 0.230973 0.115486 0.993309i \(-0.463157\pi\)
0.115486 + 0.993309i \(0.463157\pi\)
\(462\) 0 0
\(463\) 13.4715 0.626072 0.313036 0.949741i \(-0.398654\pi\)
0.313036 + 0.949741i \(0.398654\pi\)
\(464\) 0 0
\(465\) −70.0590 −3.24891
\(466\) 0 0
\(467\) 30.9267 1.43112 0.715558 0.698553i \(-0.246173\pi\)
0.715558 + 0.698553i \(0.246173\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −58.1699 −2.68033
\(472\) 0 0
\(473\) 12.7745 0.587372
\(474\) 0 0
\(475\) 11.3112 0.518994
\(476\) 0 0
\(477\) 38.7024 1.77206
\(478\) 0 0
\(479\) 23.9952 1.09637 0.548183 0.836358i \(-0.315320\pi\)
0.548183 + 0.836358i \(0.315320\pi\)
\(480\) 0 0
\(481\) −16.7513 −0.763795
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5.04430 −0.229050
\(486\) 0 0
\(487\) 39.2762 1.77977 0.889887 0.456181i \(-0.150783\pi\)
0.889887 + 0.456181i \(0.150783\pi\)
\(488\) 0 0
\(489\) −22.4055 −1.01321
\(490\) 0 0
\(491\) 28.1575 1.27073 0.635365 0.772212i \(-0.280849\pi\)
0.635365 + 0.772212i \(0.280849\pi\)
\(492\) 0 0
\(493\) 1.38495 0.0623748
\(494\) 0 0
\(495\) −20.0618 −0.901709
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −32.3051 −1.44617 −0.723087 0.690757i \(-0.757278\pi\)
−0.723087 + 0.690757i \(0.757278\pi\)
\(500\) 0 0
\(501\) 0.473678 0.0211624
\(502\) 0 0
\(503\) 22.4333 1.00025 0.500125 0.865953i \(-0.333287\pi\)
0.500125 + 0.865953i \(0.333287\pi\)
\(504\) 0 0
\(505\) 45.4198 2.02116
\(506\) 0 0
\(507\) 7.52704 0.334288
\(508\) 0 0
\(509\) −2.56739 −0.113798 −0.0568988 0.998380i \(-0.518121\pi\)
−0.0568988 + 0.998380i \(0.518121\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −0.248363 −0.0109655
\(514\) 0 0
\(515\) −14.5110 −0.639429
\(516\) 0 0
\(517\) −0.969841 −0.0426536
\(518\) 0 0
\(519\) 17.2630 0.757762
\(520\) 0 0
\(521\) −28.2588 −1.23804 −0.619020 0.785376i \(-0.712470\pi\)
−0.619020 + 0.785376i \(0.712470\pi\)
\(522\) 0 0
\(523\) −12.4023 −0.542316 −0.271158 0.962535i \(-0.587407\pi\)
−0.271158 + 0.962535i \(0.587407\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.58458 −0.199707
\(528\) 0 0
\(529\) −14.4896 −0.629984
\(530\) 0 0
\(531\) 44.8084 1.94452
\(532\) 0 0
\(533\) −6.30953 −0.273296
\(534\) 0 0
\(535\) 7.05290 0.304923
\(536\) 0 0
\(537\) 39.2933 1.69563
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.18990 0.0511576 0.0255788 0.999673i \(-0.491857\pi\)
0.0255788 + 0.999673i \(0.491857\pi\)
\(542\) 0 0
\(543\) −41.0646 −1.76225
\(544\) 0 0
\(545\) 7.74820 0.331896
\(546\) 0 0
\(547\) −15.1927 −0.649593 −0.324797 0.945784i \(-0.605296\pi\)
−0.324797 + 0.945784i \(0.605296\pi\)
\(548\) 0 0
\(549\) 28.9757 1.23665
\(550\) 0 0
\(551\) 2.12163 0.0903844
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −52.9676 −2.24835
\(556\) 0 0
\(557\) −24.5874 −1.04180 −0.520902 0.853617i \(-0.674404\pi\)
−0.520902 + 0.853617i \(0.674404\pi\)
\(558\) 0 0
\(559\) 25.1550 1.06394
\(560\) 0 0
\(561\) −2.58306 −0.109057
\(562\) 0 0
\(563\) −33.8283 −1.42569 −0.712847 0.701319i \(-0.752595\pi\)
−0.712847 + 0.701319i \(0.752595\pi\)
\(564\) 0 0
\(565\) 47.7792 2.01009
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.85831 0.371360 0.185680 0.982610i \(-0.440551\pi\)
0.185680 + 0.982610i \(0.440551\pi\)
\(570\) 0 0
\(571\) −36.4577 −1.52571 −0.762854 0.646571i \(-0.776202\pi\)
−0.762854 + 0.646571i \(0.776202\pi\)
\(572\) 0 0
\(573\) −59.3032 −2.47743
\(574\) 0 0
\(575\) 32.9977 1.37610
\(576\) 0 0
\(577\) 42.2188 1.75759 0.878795 0.477199i \(-0.158348\pi\)
0.878795 + 0.477199i \(0.158348\pi\)
\(578\) 0 0
\(579\) −0.271382 −0.0112783
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 19.9979 0.828230
\(584\) 0 0
\(585\) −39.5048 −1.63332
\(586\) 0 0
\(587\) −24.3851 −1.00648 −0.503240 0.864146i \(-0.667859\pi\)
−0.503240 + 0.864146i \(0.667859\pi\)
\(588\) 0 0
\(589\) −7.02322 −0.289387
\(590\) 0 0
\(591\) 26.9919 1.11030
\(592\) 0 0
\(593\) −17.2356 −0.707783 −0.353892 0.935286i \(-0.615142\pi\)
−0.353892 + 0.935286i \(0.615142\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −55.6653 −2.27823
\(598\) 0 0
\(599\) −5.88690 −0.240532 −0.120266 0.992742i \(-0.538375\pi\)
−0.120266 + 0.992742i \(0.538375\pi\)
\(600\) 0 0
\(601\) −13.6088 −0.555114 −0.277557 0.960709i \(-0.589525\pi\)
−0.277557 + 0.960709i \(0.589525\pi\)
\(602\) 0 0
\(603\) −8.63625 −0.351695
\(604\) 0 0
\(605\) 34.0597 1.38473
\(606\) 0 0
\(607\) −13.6021 −0.552091 −0.276045 0.961145i \(-0.589024\pi\)
−0.276045 + 0.961145i \(0.589024\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.90977 −0.0772610
\(612\) 0 0
\(613\) −32.9386 −1.33038 −0.665188 0.746676i \(-0.731649\pi\)
−0.665188 + 0.746676i \(0.731649\pi\)
\(614\) 0 0
\(615\) −19.9507 −0.804489
\(616\) 0 0
\(617\) 39.2585 1.58049 0.790244 0.612792i \(-0.209954\pi\)
0.790244 + 0.612792i \(0.209954\pi\)
\(618\) 0 0
\(619\) −7.81918 −0.314279 −0.157140 0.987576i \(-0.550227\pi\)
−0.157140 + 0.987576i \(0.550227\pi\)
\(620\) 0 0
\(621\) −0.724538 −0.0290747
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 46.3876 1.85550
\(626\) 0 0
\(627\) −3.95705 −0.158029
\(628\) 0 0
\(629\) −3.46614 −0.138204
\(630\) 0 0
\(631\) −15.0926 −0.600828 −0.300414 0.953809i \(-0.597125\pi\)
−0.300414 + 0.953809i \(0.597125\pi\)
\(632\) 0 0
\(633\) −58.6219 −2.33001
\(634\) 0 0
\(635\) 62.0279 2.46150
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −29.4575 −1.16532
\(640\) 0 0
\(641\) −23.0518 −0.910493 −0.455247 0.890365i \(-0.650449\pi\)
−0.455247 + 0.890365i \(0.650449\pi\)
\(642\) 0 0
\(643\) 31.5297 1.24341 0.621706 0.783251i \(-0.286440\pi\)
0.621706 + 0.783251i \(0.286440\pi\)
\(644\) 0 0
\(645\) 79.5399 3.13188
\(646\) 0 0
\(647\) 6.44280 0.253293 0.126646 0.991948i \(-0.459579\pi\)
0.126646 + 0.991948i \(0.459579\pi\)
\(648\) 0 0
\(649\) 23.1529 0.908833
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 17.1146 0.669746 0.334873 0.942263i \(-0.391307\pi\)
0.334873 + 0.942263i \(0.391307\pi\)
\(654\) 0 0
\(655\) 54.0494 2.11188
\(656\) 0 0
\(657\) −51.5553 −2.01136
\(658\) 0 0
\(659\) 27.1362 1.05707 0.528537 0.848910i \(-0.322741\pi\)
0.528537 + 0.848910i \(0.322741\pi\)
\(660\) 0 0
\(661\) 9.45983 0.367945 0.183972 0.982931i \(-0.441104\pi\)
0.183972 + 0.982931i \(0.441104\pi\)
\(662\) 0 0
\(663\) −5.08645 −0.197541
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.18933 0.239652
\(668\) 0 0
\(669\) −10.7845 −0.416953
\(670\) 0 0
\(671\) 14.9721 0.577990
\(672\) 0 0
\(673\) −13.6374 −0.525682 −0.262841 0.964839i \(-0.584659\pi\)
−0.262841 + 0.964839i \(0.584659\pi\)
\(674\) 0 0
\(675\) −2.80929 −0.108130
\(676\) 0 0
\(677\) −2.50516 −0.0962810 −0.0481405 0.998841i \(-0.515330\pi\)
−0.0481405 + 0.998841i \(0.515330\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −54.3172 −2.08144
\(682\) 0 0
\(683\) −24.0553 −0.920449 −0.460224 0.887803i \(-0.652231\pi\)
−0.460224 + 0.887803i \(0.652231\pi\)
\(684\) 0 0
\(685\) 12.7908 0.488710
\(686\) 0 0
\(687\) −10.8762 −0.414953
\(688\) 0 0
\(689\) 39.3791 1.50022
\(690\) 0 0
\(691\) −10.5411 −0.401003 −0.200501 0.979693i \(-0.564257\pi\)
−0.200501 + 0.979693i \(0.564257\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 66.1960 2.51096
\(696\) 0 0
\(697\) −1.30555 −0.0494512
\(698\) 0 0
\(699\) 49.5369 1.87366
\(700\) 0 0
\(701\) −1.75242 −0.0661880 −0.0330940 0.999452i \(-0.510536\pi\)
−0.0330940 + 0.999452i \(0.510536\pi\)
\(702\) 0 0
\(703\) −5.30985 −0.200265
\(704\) 0 0
\(705\) −6.03868 −0.227430
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.89668 0.0712312 0.0356156 0.999366i \(-0.488661\pi\)
0.0356156 + 0.999366i \(0.488661\pi\)
\(710\) 0 0
\(711\) 15.0578 0.564713
\(712\) 0 0
\(713\) −20.4885 −0.767301
\(714\) 0 0
\(715\) −20.4125 −0.763384
\(716\) 0 0
\(717\) −53.7152 −2.00603
\(718\) 0 0
\(719\) 14.3276 0.534329 0.267164 0.963651i \(-0.413913\pi\)
0.267164 + 0.963651i \(0.413913\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −76.5455 −2.84676
\(724\) 0 0
\(725\) 23.9982 0.891271
\(726\) 0 0
\(727\) −42.5021 −1.57632 −0.788158 0.615472i \(-0.788965\pi\)
−0.788158 + 0.615472i \(0.788965\pi\)
\(728\) 0 0
\(729\) −28.7786 −1.06588
\(730\) 0 0
\(731\) 5.20500 0.192514
\(732\) 0 0
\(733\) 19.1811 0.708471 0.354235 0.935156i \(-0.384741\pi\)
0.354235 + 0.935156i \(0.384741\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.46244 −0.164376
\(738\) 0 0
\(739\) −12.2726 −0.451454 −0.225727 0.974191i \(-0.572476\pi\)
−0.225727 + 0.974191i \(0.572476\pi\)
\(740\) 0 0
\(741\) −7.79204 −0.286248
\(742\) 0 0
\(743\) 36.7738 1.34910 0.674549 0.738230i \(-0.264338\pi\)
0.674549 + 0.738230i \(0.264338\pi\)
\(744\) 0 0
\(745\) −56.6311 −2.07480
\(746\) 0 0
\(747\) −27.0978 −0.991456
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 37.4842 1.36782 0.683908 0.729568i \(-0.260279\pi\)
0.683908 + 0.729568i \(0.260279\pi\)
\(752\) 0 0
\(753\) −12.9544 −0.472083
\(754\) 0 0
\(755\) −74.9026 −2.72598
\(756\) 0 0
\(757\) 11.0641 0.402132 0.201066 0.979578i \(-0.435559\pi\)
0.201066 + 0.979578i \(0.435559\pi\)
\(758\) 0 0
\(759\) −11.5437 −0.419010
\(760\) 0 0
\(761\) −50.5192 −1.83132 −0.915659 0.401955i \(-0.868331\pi\)
−0.915659 + 0.401955i \(0.868331\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −8.17421 −0.295539
\(766\) 0 0
\(767\) 45.5918 1.64622
\(768\) 0 0
\(769\) −10.7883 −0.389037 −0.194518 0.980899i \(-0.562314\pi\)
−0.194518 + 0.980899i \(0.562314\pi\)
\(770\) 0 0
\(771\) 70.6257 2.54352
\(772\) 0 0
\(773\) 4.67288 0.168072 0.0840358 0.996463i \(-0.473219\pi\)
0.0840358 + 0.996463i \(0.473219\pi\)
\(774\) 0 0
\(775\) −79.4412 −2.85361
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.00000 −0.0716574
\(780\) 0 0
\(781\) −15.2210 −0.544650
\(782\) 0 0
\(783\) −0.526934 −0.0188311
\(784\) 0 0
\(785\) −95.1167 −3.39486
\(786\) 0 0
\(787\) 13.5788 0.484032 0.242016 0.970272i \(-0.422191\pi\)
0.242016 + 0.970272i \(0.422191\pi\)
\(788\) 0 0
\(789\) −13.6832 −0.487136
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 29.4823 1.04695
\(794\) 0 0
\(795\) 124.516 4.41614
\(796\) 0 0
\(797\) 25.3577 0.898214 0.449107 0.893478i \(-0.351742\pi\)
0.449107 + 0.893478i \(0.351742\pi\)
\(798\) 0 0
\(799\) −0.395164 −0.0139799
\(800\) 0 0
\(801\) −7.05718 −0.249353
\(802\) 0 0
\(803\) −26.6392 −0.940076
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 10.5998 0.373131
\(808\) 0 0
\(809\) 1.53872 0.0540985 0.0270493 0.999634i \(-0.491389\pi\)
0.0270493 + 0.999634i \(0.491389\pi\)
\(810\) 0 0
\(811\) 37.5288 1.31781 0.658907 0.752225i \(-0.271019\pi\)
0.658907 + 0.752225i \(0.271019\pi\)
\(812\) 0 0
\(813\) 2.19989 0.0771535
\(814\) 0 0
\(815\) −36.6364 −1.28332
\(816\) 0 0
\(817\) 7.97365 0.278963
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −8.83486 −0.308339 −0.154169 0.988044i \(-0.549270\pi\)
−0.154169 + 0.988044i \(0.549270\pi\)
\(822\) 0 0
\(823\) −30.8210 −1.07435 −0.537177 0.843470i \(-0.680509\pi\)
−0.537177 + 0.843470i \(0.680509\pi\)
\(824\) 0 0
\(825\) −44.7590 −1.55831
\(826\) 0 0
\(827\) 0.938262 0.0326266 0.0163133 0.999867i \(-0.494807\pi\)
0.0163133 + 0.999867i \(0.494807\pi\)
\(828\) 0 0
\(829\) −6.78457 −0.235638 −0.117819 0.993035i \(-0.537590\pi\)
−0.117819 + 0.993035i \(0.537590\pi\)
\(830\) 0 0
\(831\) 29.6654 1.02908
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0.774537 0.0268039
\(836\) 0 0
\(837\) 1.74431 0.0602921
\(838\) 0 0
\(839\) −11.6858 −0.403437 −0.201718 0.979444i \(-0.564653\pi\)
−0.201718 + 0.979444i \(0.564653\pi\)
\(840\) 0 0
\(841\) −24.4987 −0.844782
\(842\) 0 0
\(843\) 43.1791 1.48717
\(844\) 0 0
\(845\) 12.3079 0.423403
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −50.5996 −1.73657
\(850\) 0 0
\(851\) −15.4902 −0.530997
\(852\) 0 0
\(853\) 19.5533 0.669493 0.334746 0.942308i \(-0.391349\pi\)
0.334746 + 0.942308i \(0.391349\pi\)
\(854\) 0 0
\(855\) −12.5223 −0.428252
\(856\) 0 0
\(857\) 51.4154 1.75632 0.878159 0.478369i \(-0.158772\pi\)
0.878159 + 0.478369i \(0.158772\pi\)
\(858\) 0 0
\(859\) −27.8957 −0.951789 −0.475894 0.879502i \(-0.657876\pi\)
−0.475894 + 0.879502i \(0.657876\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 45.2264 1.53953 0.769763 0.638330i \(-0.220374\pi\)
0.769763 + 0.638330i \(0.220374\pi\)
\(864\) 0 0
\(865\) 28.2277 0.959769
\(866\) 0 0
\(867\) 40.9363 1.39027
\(868\) 0 0
\(869\) 7.78054 0.263937
\(870\) 0 0
\(871\) −8.78724 −0.297744
\(872\) 0 0
\(873\) 3.87255 0.131066
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 8.91265 0.300959 0.150479 0.988613i \(-0.451918\pi\)
0.150479 + 0.988613i \(0.451918\pi\)
\(878\) 0 0
\(879\) 56.6823 1.91185
\(880\) 0 0
\(881\) −45.9579 −1.54836 −0.774180 0.632965i \(-0.781837\pi\)
−0.774180 + 0.632965i \(0.781837\pi\)
\(882\) 0 0
\(883\) 28.6951 0.965666 0.482833 0.875712i \(-0.339608\pi\)
0.482833 + 0.875712i \(0.339608\pi\)
\(884\) 0 0
\(885\) 144.161 4.84592
\(886\) 0 0
\(887\) −24.1058 −0.809394 −0.404697 0.914451i \(-0.632623\pi\)
−0.404697 + 0.914451i \(0.632623\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −13.9193 −0.466314
\(892\) 0 0
\(893\) −0.605361 −0.0202576
\(894\) 0 0
\(895\) 64.2505 2.14766
\(896\) 0 0
\(897\) −22.7314 −0.758979
\(898\) 0 0
\(899\) −14.9007 −0.496965
\(900\) 0 0
\(901\) 8.14821 0.271456
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −67.1470 −2.23204
\(906\) 0 0
\(907\) 34.3249 1.13974 0.569869 0.821735i \(-0.306994\pi\)
0.569869 + 0.821735i \(0.306994\pi\)
\(908\) 0 0
\(909\) −34.8692 −1.15654
\(910\) 0 0
\(911\) 25.9008 0.858133 0.429066 0.903273i \(-0.358843\pi\)
0.429066 + 0.903273i \(0.358843\pi\)
\(912\) 0 0
\(913\) −14.0017 −0.463389
\(914\) 0 0
\(915\) 93.2229 3.08186
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 24.2185 0.798894 0.399447 0.916756i \(-0.369202\pi\)
0.399447 + 0.916756i \(0.369202\pi\)
\(920\) 0 0
\(921\) −34.8968 −1.14989
\(922\) 0 0
\(923\) −29.9725 −0.986558
\(924\) 0 0
\(925\) −60.0609 −1.97479
\(926\) 0 0
\(927\) 11.1402 0.365892
\(928\) 0 0
\(929\) −12.6889 −0.416310 −0.208155 0.978096i \(-0.566746\pi\)
−0.208155 + 0.978096i \(0.566746\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 33.4192 1.09410
\(934\) 0 0
\(935\) −4.22370 −0.138130
\(936\) 0 0
\(937\) 44.2503 1.44559 0.722797 0.691060i \(-0.242856\pi\)
0.722797 + 0.691060i \(0.242856\pi\)
\(938\) 0 0
\(939\) −65.3268 −2.13186
\(940\) 0 0
\(941\) −13.7250 −0.447421 −0.223710 0.974656i \(-0.571817\pi\)
−0.223710 + 0.974656i \(0.571817\pi\)
\(942\) 0 0
\(943\) −5.83451 −0.189998
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −20.6683 −0.671630 −0.335815 0.941928i \(-0.609012\pi\)
−0.335815 + 0.941928i \(0.609012\pi\)
\(948\) 0 0
\(949\) −52.4567 −1.70282
\(950\) 0 0
\(951\) 8.18246 0.265334
\(952\) 0 0
\(953\) 16.3518 0.529686 0.264843 0.964292i \(-0.414680\pi\)
0.264843 + 0.964292i \(0.414680\pi\)
\(954\) 0 0
\(955\) −96.9699 −3.13787
\(956\) 0 0
\(957\) −8.39538 −0.271384
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 18.3256 0.591150
\(962\) 0 0
\(963\) −5.41457 −0.174482
\(964\) 0 0
\(965\) −0.443752 −0.0142849
\(966\) 0 0
\(967\) 20.6838 0.665145 0.332573 0.943078i \(-0.392083\pi\)
0.332573 + 0.943078i \(0.392083\pi\)
\(968\) 0 0
\(969\) −1.61231 −0.0517948
\(970\) 0 0
\(971\) −2.05777 −0.0660368 −0.0330184 0.999455i \(-0.510512\pi\)
−0.0330184 + 0.999455i \(0.510512\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −88.1375 −2.82266
\(976\) 0 0
\(977\) 5.75307 0.184057 0.0920285 0.995756i \(-0.470665\pi\)
0.0920285 + 0.995756i \(0.470665\pi\)
\(978\) 0 0
\(979\) −3.64652 −0.116543
\(980\) 0 0
\(981\) −5.94835 −0.189916
\(982\) 0 0
\(983\) −26.9379 −0.859186 −0.429593 0.903023i \(-0.641343\pi\)
−0.429593 + 0.903023i \(0.641343\pi\)
\(984\) 0 0
\(985\) 44.1358 1.40628
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 23.2612 0.739662
\(990\) 0 0
\(991\) 41.9464 1.33247 0.666235 0.745742i \(-0.267905\pi\)
0.666235 + 0.745742i \(0.267905\pi\)
\(992\) 0 0
\(993\) −29.1132 −0.923878
\(994\) 0 0
\(995\) −91.0213 −2.88557
\(996\) 0 0
\(997\) −41.9695 −1.32919 −0.664593 0.747205i \(-0.731395\pi\)
−0.664593 + 0.747205i \(0.731395\pi\)
\(998\) 0 0
\(999\) 1.31877 0.0417240
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 7448.2.a.bq.1.2 8
7.2 even 3 1064.2.q.n.305.7 16
7.4 even 3 1064.2.q.n.457.7 yes 16
7.6 odd 2 7448.2.a.br.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.q.n.305.7 16 7.2 even 3
1064.2.q.n.457.7 yes 16 7.4 even 3
7448.2.a.bq.1.2 8 1.1 even 1 trivial
7448.2.a.br.1.7 8 7.6 odd 2