Properties

Label 7623.2.a.db.1.7
Level 7623
Weight 2
Character 7623.1
Self dual yes
Analytic conductor 60.870
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7623.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.8699614608\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 693)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.759363\)
Character \(\chi\) = 7623.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.759363 q^{2} -1.42337 q^{4} -2.86525 q^{5} -1.00000 q^{7} +2.59958 q^{8} +O(q^{10})\) \(q-0.759363 q^{2} -1.42337 q^{4} -2.86525 q^{5} -1.00000 q^{7} +2.59958 q^{8} +2.17577 q^{10} +6.96619 q^{13} +0.759363 q^{14} +0.872709 q^{16} +6.65872 q^{17} +5.75106 q^{19} +4.07830 q^{20} +0.724581 q^{23} +3.20966 q^{25} -5.28987 q^{26} +1.42337 q^{28} +7.56740 q^{29} +2.81968 q^{31} -5.86186 q^{32} -5.05639 q^{34} +2.86525 q^{35} -1.72211 q^{37} -4.36715 q^{38} -7.44844 q^{40} +1.12086 q^{41} +11.7092 q^{43} -0.550220 q^{46} -5.18956 q^{47} +1.00000 q^{49} -2.43729 q^{50} -9.91544 q^{52} +6.25771 q^{53} -2.59958 q^{56} -5.74641 q^{58} -3.98228 q^{59} +5.97074 q^{61} -2.14116 q^{62} +2.70587 q^{64} -19.9599 q^{65} +10.3611 q^{67} -9.47781 q^{68} -2.17577 q^{70} +0.995183 q^{71} -3.53684 q^{73} +1.30771 q^{74} -8.18588 q^{76} +0.669794 q^{79} -2.50053 q^{80} -0.851138 q^{82} +13.4240 q^{83} -19.0789 q^{85} -8.89157 q^{86} -16.6006 q^{89} -6.96619 q^{91} -1.03135 q^{92} +3.94076 q^{94} -16.4782 q^{95} +10.1121 q^{97} -0.759363 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 20q^{4} - 16q^{7} + O(q^{10}) \) \( 16q + 20q^{4} - 16q^{7} + 6q^{10} + 32q^{16} - 10q^{19} + 44q^{25} - 20q^{28} + 30q^{31} + 12q^{34} + 38q^{37} + 68q^{40} - 16q^{43} - 80q^{46} + 16q^{49} - 2q^{52} + 18q^{58} + 28q^{61} + 34q^{64} + 52q^{67} - 6q^{70} + 14q^{73} + 14q^{76} - 54q^{79} + 64q^{82} - 30q^{85} + 60q^{94} + 108q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.759363 −0.536951 −0.268475 0.963287i \(-0.586520\pi\)
−0.268475 + 0.963287i \(0.586520\pi\)
\(3\) 0 0
\(4\) −1.42337 −0.711684
\(5\) −2.86525 −1.28138 −0.640689 0.767800i \(-0.721351\pi\)
−0.640689 + 0.767800i \(0.721351\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 2.59958 0.919090
\(9\) 0 0
\(10\) 2.17577 0.688038
\(11\) 0 0
\(12\) 0 0
\(13\) 6.96619 1.93207 0.966036 0.258407i \(-0.0831974\pi\)
0.966036 + 0.258407i \(0.0831974\pi\)
\(14\) 0.759363 0.202948
\(15\) 0 0
\(16\) 0.872709 0.218177
\(17\) 6.65872 1.61498 0.807489 0.589883i \(-0.200826\pi\)
0.807489 + 0.589883i \(0.200826\pi\)
\(18\) 0 0
\(19\) 5.75106 1.31938 0.659692 0.751536i \(-0.270687\pi\)
0.659692 + 0.751536i \(0.270687\pi\)
\(20\) 4.07830 0.911936
\(21\) 0 0
\(22\) 0 0
\(23\) 0.724581 0.151086 0.0755428 0.997143i \(-0.475931\pi\)
0.0755428 + 0.997143i \(0.475931\pi\)
\(24\) 0 0
\(25\) 3.20966 0.641931
\(26\) −5.28987 −1.03743
\(27\) 0 0
\(28\) 1.42337 0.268991
\(29\) 7.56740 1.40523 0.702616 0.711570i \(-0.252015\pi\)
0.702616 + 0.711570i \(0.252015\pi\)
\(30\) 0 0
\(31\) 2.81968 0.506430 0.253215 0.967410i \(-0.418512\pi\)
0.253215 + 0.967410i \(0.418512\pi\)
\(32\) −5.86186 −1.03624
\(33\) 0 0
\(34\) −5.05639 −0.867164
\(35\) 2.86525 0.484316
\(36\) 0 0
\(37\) −1.72211 −0.283113 −0.141557 0.989930i \(-0.545211\pi\)
−0.141557 + 0.989930i \(0.545211\pi\)
\(38\) −4.36715 −0.708445
\(39\) 0 0
\(40\) −7.44844 −1.17770
\(41\) 1.12086 0.175048 0.0875242 0.996162i \(-0.472104\pi\)
0.0875242 + 0.996162i \(0.472104\pi\)
\(42\) 0 0
\(43\) 11.7092 1.78564 0.892821 0.450411i \(-0.148723\pi\)
0.892821 + 0.450411i \(0.148723\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.550220 −0.0811256
\(47\) −5.18956 −0.756975 −0.378488 0.925606i \(-0.623556\pi\)
−0.378488 + 0.925606i \(0.623556\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −2.43729 −0.344686
\(51\) 0 0
\(52\) −9.91544 −1.37502
\(53\) 6.25771 0.859562 0.429781 0.902933i \(-0.358591\pi\)
0.429781 + 0.902933i \(0.358591\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.59958 −0.347383
\(57\) 0 0
\(58\) −5.74641 −0.754540
\(59\) −3.98228 −0.518448 −0.259224 0.965817i \(-0.583467\pi\)
−0.259224 + 0.965817i \(0.583467\pi\)
\(60\) 0 0
\(61\) 5.97074 0.764475 0.382237 0.924064i \(-0.375154\pi\)
0.382237 + 0.924064i \(0.375154\pi\)
\(62\) −2.14116 −0.271928
\(63\) 0 0
\(64\) 2.70587 0.338233
\(65\) −19.9599 −2.47572
\(66\) 0 0
\(67\) 10.3611 1.26581 0.632906 0.774229i \(-0.281862\pi\)
0.632906 + 0.774229i \(0.281862\pi\)
\(68\) −9.47781 −1.14935
\(69\) 0 0
\(70\) −2.17577 −0.260054
\(71\) 0.995183 0.118107 0.0590533 0.998255i \(-0.481192\pi\)
0.0590533 + 0.998255i \(0.481192\pi\)
\(72\) 0 0
\(73\) −3.53684 −0.413956 −0.206978 0.978346i \(-0.566363\pi\)
−0.206978 + 0.978346i \(0.566363\pi\)
\(74\) 1.30771 0.152018
\(75\) 0 0
\(76\) −8.18588 −0.938984
\(77\) 0 0
\(78\) 0 0
\(79\) 0.669794 0.0753578 0.0376789 0.999290i \(-0.488004\pi\)
0.0376789 + 0.999290i \(0.488004\pi\)
\(80\) −2.50053 −0.279568
\(81\) 0 0
\(82\) −0.851138 −0.0939924
\(83\) 13.4240 1.47348 0.736739 0.676177i \(-0.236365\pi\)
0.736739 + 0.676177i \(0.236365\pi\)
\(84\) 0 0
\(85\) −19.0789 −2.06940
\(86\) −8.89157 −0.958803
\(87\) 0 0
\(88\) 0 0
\(89\) −16.6006 −1.75966 −0.879828 0.475292i \(-0.842343\pi\)
−0.879828 + 0.475292i \(0.842343\pi\)
\(90\) 0 0
\(91\) −6.96619 −0.730255
\(92\) −1.03135 −0.107525
\(93\) 0 0
\(94\) 3.94076 0.406459
\(95\) −16.4782 −1.69063
\(96\) 0 0
\(97\) 10.1121 1.02672 0.513362 0.858172i \(-0.328400\pi\)
0.513362 + 0.858172i \(0.328400\pi\)
\(98\) −0.759363 −0.0767073
\(99\) 0 0
\(100\) −4.56852 −0.456852
\(101\) 6.42353 0.639165 0.319582 0.947559i \(-0.396457\pi\)
0.319582 + 0.947559i \(0.396457\pi\)
\(102\) 0 0
\(103\) −8.95787 −0.882645 −0.441323 0.897348i \(-0.645491\pi\)
−0.441323 + 0.897348i \(0.645491\pi\)
\(104\) 18.1092 1.77575
\(105\) 0 0
\(106\) −4.75188 −0.461543
\(107\) 4.52891 0.437826 0.218913 0.975744i \(-0.429749\pi\)
0.218913 + 0.975744i \(0.429749\pi\)
\(108\) 0 0
\(109\) 1.02744 0.0984106 0.0492053 0.998789i \(-0.484331\pi\)
0.0492053 + 0.998789i \(0.484331\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.872709 −0.0824632
\(113\) −13.2380 −1.24533 −0.622664 0.782490i \(-0.713950\pi\)
−0.622664 + 0.782490i \(0.713950\pi\)
\(114\) 0 0
\(115\) −2.07611 −0.193598
\(116\) −10.7712 −1.00008
\(117\) 0 0
\(118\) 3.02399 0.278381
\(119\) −6.65872 −0.610404
\(120\) 0 0
\(121\) 0 0
\(122\) −4.53396 −0.410486
\(123\) 0 0
\(124\) −4.01344 −0.360418
\(125\) 5.12978 0.458822
\(126\) 0 0
\(127\) −16.2934 −1.44581 −0.722903 0.690949i \(-0.757193\pi\)
−0.722903 + 0.690949i \(0.757193\pi\)
\(128\) 9.66899 0.854626
\(129\) 0 0
\(130\) 15.1568 1.32934
\(131\) 6.19831 0.541549 0.270774 0.962643i \(-0.412720\pi\)
0.270774 + 0.962643i \(0.412720\pi\)
\(132\) 0 0
\(133\) −5.75106 −0.498680
\(134\) −7.86785 −0.679679
\(135\) 0 0
\(136\) 17.3099 1.48431
\(137\) −16.0095 −1.36779 −0.683893 0.729582i \(-0.739714\pi\)
−0.683893 + 0.729582i \(0.739714\pi\)
\(138\) 0 0
\(139\) −4.61401 −0.391355 −0.195678 0.980668i \(-0.562691\pi\)
−0.195678 + 0.980668i \(0.562691\pi\)
\(140\) −4.07830 −0.344679
\(141\) 0 0
\(142\) −0.755706 −0.0634174
\(143\) 0 0
\(144\) 0 0
\(145\) −21.6825 −1.80063
\(146\) 2.68575 0.222274
\(147\) 0 0
\(148\) 2.45119 0.201487
\(149\) −7.21841 −0.591355 −0.295678 0.955288i \(-0.595545\pi\)
−0.295678 + 0.955288i \(0.595545\pi\)
\(150\) 0 0
\(151\) −0.626349 −0.0509716 −0.0254858 0.999675i \(-0.508113\pi\)
−0.0254858 + 0.999675i \(0.508113\pi\)
\(152\) 14.9503 1.21263
\(153\) 0 0
\(154\) 0 0
\(155\) −8.07909 −0.648928
\(156\) 0 0
\(157\) −6.14752 −0.490626 −0.245313 0.969444i \(-0.578891\pi\)
−0.245313 + 0.969444i \(0.578891\pi\)
\(158\) −0.508617 −0.0404634
\(159\) 0 0
\(160\) 16.7957 1.32782
\(161\) −0.724581 −0.0571050
\(162\) 0 0
\(163\) 21.6415 1.69510 0.847548 0.530719i \(-0.178078\pi\)
0.847548 + 0.530719i \(0.178078\pi\)
\(164\) −1.59539 −0.124579
\(165\) 0 0
\(166\) −10.1937 −0.791186
\(167\) −23.9947 −1.85677 −0.928384 0.371622i \(-0.878802\pi\)
−0.928384 + 0.371622i \(0.878802\pi\)
\(168\) 0 0
\(169\) 35.5278 2.73290
\(170\) 14.4878 1.11117
\(171\) 0 0
\(172\) −16.6666 −1.27081
\(173\) −10.8109 −0.821935 −0.410968 0.911650i \(-0.634809\pi\)
−0.410968 + 0.911650i \(0.634809\pi\)
\(174\) 0 0
\(175\) −3.20966 −0.242627
\(176\) 0 0
\(177\) 0 0
\(178\) 12.6059 0.944849
\(179\) −5.92839 −0.443109 −0.221554 0.975148i \(-0.571113\pi\)
−0.221554 + 0.975148i \(0.571113\pi\)
\(180\) 0 0
\(181\) −4.84617 −0.360213 −0.180106 0.983647i \(-0.557644\pi\)
−0.180106 + 0.983647i \(0.557644\pi\)
\(182\) 5.28987 0.392111
\(183\) 0 0
\(184\) 1.88361 0.138861
\(185\) 4.93427 0.362775
\(186\) 0 0
\(187\) 0 0
\(188\) 7.38665 0.538727
\(189\) 0 0
\(190\) 12.5130 0.907786
\(191\) 15.6923 1.13546 0.567729 0.823216i \(-0.307822\pi\)
0.567729 + 0.823216i \(0.307822\pi\)
\(192\) 0 0
\(193\) 22.7548 1.63793 0.818963 0.573846i \(-0.194549\pi\)
0.818963 + 0.573846i \(0.194549\pi\)
\(194\) −7.67873 −0.551301
\(195\) 0 0
\(196\) −1.42337 −0.101669
\(197\) 15.3025 1.09026 0.545129 0.838352i \(-0.316481\pi\)
0.545129 + 0.838352i \(0.316481\pi\)
\(198\) 0 0
\(199\) −0.547814 −0.0388335 −0.0194168 0.999811i \(-0.506181\pi\)
−0.0194168 + 0.999811i \(0.506181\pi\)
\(200\) 8.34376 0.589993
\(201\) 0 0
\(202\) −4.87779 −0.343200
\(203\) −7.56740 −0.531128
\(204\) 0 0
\(205\) −3.21153 −0.224303
\(206\) 6.80228 0.473937
\(207\) 0 0
\(208\) 6.07945 0.421534
\(209\) 0 0
\(210\) 0 0
\(211\) 13.8726 0.955030 0.477515 0.878624i \(-0.341538\pi\)
0.477515 + 0.878624i \(0.341538\pi\)
\(212\) −8.90702 −0.611737
\(213\) 0 0
\(214\) −3.43908 −0.235091
\(215\) −33.5499 −2.28808
\(216\) 0 0
\(217\) −2.81968 −0.191412
\(218\) −0.780198 −0.0528416
\(219\) 0 0
\(220\) 0 0
\(221\) 46.3859 3.12025
\(222\) 0 0
\(223\) −7.60179 −0.509053 −0.254527 0.967066i \(-0.581920\pi\)
−0.254527 + 0.967066i \(0.581920\pi\)
\(224\) 5.86186 0.391662
\(225\) 0 0
\(226\) 10.0525 0.668680
\(227\) −0.295156 −0.0195902 −0.00979511 0.999952i \(-0.503118\pi\)
−0.00979511 + 0.999952i \(0.503118\pi\)
\(228\) 0 0
\(229\) 7.11072 0.469890 0.234945 0.972009i \(-0.424509\pi\)
0.234945 + 0.972009i \(0.424509\pi\)
\(230\) 1.57652 0.103953
\(231\) 0 0
\(232\) 19.6721 1.29153
\(233\) 10.2537 0.671743 0.335872 0.941908i \(-0.390969\pi\)
0.335872 + 0.941908i \(0.390969\pi\)
\(234\) 0 0
\(235\) 14.8694 0.969972
\(236\) 5.66824 0.368971
\(237\) 0 0
\(238\) 5.05639 0.327757
\(239\) −19.8042 −1.28103 −0.640513 0.767947i \(-0.721278\pi\)
−0.640513 + 0.767947i \(0.721278\pi\)
\(240\) 0 0
\(241\) 20.0305 1.29028 0.645138 0.764066i \(-0.276800\pi\)
0.645138 + 0.764066i \(0.276800\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −8.49856 −0.544064
\(245\) −2.86525 −0.183054
\(246\) 0 0
\(247\) 40.0630 2.54915
\(248\) 7.32999 0.465455
\(249\) 0 0
\(250\) −3.89537 −0.246365
\(251\) 2.69309 0.169986 0.0849932 0.996382i \(-0.472913\pi\)
0.0849932 + 0.996382i \(0.472913\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 12.3726 0.776327
\(255\) 0 0
\(256\) −12.7540 −0.797126
\(257\) −25.3591 −1.58186 −0.790929 0.611908i \(-0.790402\pi\)
−0.790929 + 0.611908i \(0.790402\pi\)
\(258\) 0 0
\(259\) 1.72211 0.107007
\(260\) 28.4102 1.76193
\(261\) 0 0
\(262\) −4.70677 −0.290785
\(263\) −9.04980 −0.558034 −0.279017 0.960286i \(-0.590009\pi\)
−0.279017 + 0.960286i \(0.590009\pi\)
\(264\) 0 0
\(265\) −17.9299 −1.10142
\(266\) 4.36715 0.267767
\(267\) 0 0
\(268\) −14.7477 −0.900857
\(269\) −2.73289 −0.166627 −0.0833136 0.996523i \(-0.526550\pi\)
−0.0833136 + 0.996523i \(0.526550\pi\)
\(270\) 0 0
\(271\) −17.9520 −1.09051 −0.545254 0.838271i \(-0.683567\pi\)
−0.545254 + 0.838271i \(0.683567\pi\)
\(272\) 5.81113 0.352351
\(273\) 0 0
\(274\) 12.1570 0.734434
\(275\) 0 0
\(276\) 0 0
\(277\) 11.1503 0.669958 0.334979 0.942226i \(-0.391271\pi\)
0.334979 + 0.942226i \(0.391271\pi\)
\(278\) 3.50371 0.210139
\(279\) 0 0
\(280\) 7.44844 0.445130
\(281\) 3.96239 0.236377 0.118188 0.992991i \(-0.462291\pi\)
0.118188 + 0.992991i \(0.462291\pi\)
\(282\) 0 0
\(283\) −5.74911 −0.341749 −0.170875 0.985293i \(-0.554659\pi\)
−0.170875 + 0.985293i \(0.554659\pi\)
\(284\) −1.41651 −0.0840545
\(285\) 0 0
\(286\) 0 0
\(287\) −1.12086 −0.0661621
\(288\) 0 0
\(289\) 27.3386 1.60815
\(290\) 16.4649 0.966852
\(291\) 0 0
\(292\) 5.03422 0.294606
\(293\) 23.2438 1.35792 0.678958 0.734177i \(-0.262432\pi\)
0.678958 + 0.734177i \(0.262432\pi\)
\(294\) 0 0
\(295\) 11.4102 0.664328
\(296\) −4.47676 −0.260206
\(297\) 0 0
\(298\) 5.48140 0.317529
\(299\) 5.04757 0.291908
\(300\) 0 0
\(301\) −11.7092 −0.674909
\(302\) 0.475627 0.0273692
\(303\) 0 0
\(304\) 5.01900 0.287860
\(305\) −17.1077 −0.979582
\(306\) 0 0
\(307\) −3.87940 −0.221409 −0.110705 0.993853i \(-0.535311\pi\)
−0.110705 + 0.993853i \(0.535311\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 6.13497 0.348443
\(311\) −3.74658 −0.212449 −0.106225 0.994342i \(-0.533876\pi\)
−0.106225 + 0.994342i \(0.533876\pi\)
\(312\) 0 0
\(313\) 18.0642 1.02105 0.510523 0.859864i \(-0.329452\pi\)
0.510523 + 0.859864i \(0.329452\pi\)
\(314\) 4.66820 0.263442
\(315\) 0 0
\(316\) −0.953364 −0.0536309
\(317\) −7.41444 −0.416436 −0.208218 0.978082i \(-0.566766\pi\)
−0.208218 + 0.978082i \(0.566766\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −7.75298 −0.433405
\(321\) 0 0
\(322\) 0.550220 0.0306626
\(323\) 38.2947 2.13078
\(324\) 0 0
\(325\) 22.3591 1.24026
\(326\) −16.4338 −0.910183
\(327\) 0 0
\(328\) 2.91376 0.160885
\(329\) 5.18956 0.286110
\(330\) 0 0
\(331\) 14.5172 0.797937 0.398968 0.916965i \(-0.369368\pi\)
0.398968 + 0.916965i \(0.369368\pi\)
\(332\) −19.1073 −1.04865
\(333\) 0 0
\(334\) 18.2207 0.996993
\(335\) −29.6872 −1.62198
\(336\) 0 0
\(337\) −10.5543 −0.574930 −0.287465 0.957791i \(-0.592813\pi\)
−0.287465 + 0.957791i \(0.592813\pi\)
\(338\) −26.9785 −1.46744
\(339\) 0 0
\(340\) 27.1563 1.47276
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 30.4391 1.64117
\(345\) 0 0
\(346\) 8.20938 0.441339
\(347\) −22.5100 −1.20840 −0.604199 0.796833i \(-0.706507\pi\)
−0.604199 + 0.796833i \(0.706507\pi\)
\(348\) 0 0
\(349\) 20.7206 1.10915 0.554574 0.832135i \(-0.312881\pi\)
0.554574 + 0.832135i \(0.312881\pi\)
\(350\) 2.43729 0.130279
\(351\) 0 0
\(352\) 0 0
\(353\) −6.01460 −0.320125 −0.160062 0.987107i \(-0.551170\pi\)
−0.160062 + 0.987107i \(0.551170\pi\)
\(354\) 0 0
\(355\) −2.85145 −0.151339
\(356\) 23.6287 1.25232
\(357\) 0 0
\(358\) 4.50180 0.237928
\(359\) −18.4700 −0.974810 −0.487405 0.873176i \(-0.662056\pi\)
−0.487405 + 0.873176i \(0.662056\pi\)
\(360\) 0 0
\(361\) 14.0747 0.740775
\(362\) 3.68000 0.193417
\(363\) 0 0
\(364\) 9.91544 0.519710
\(365\) 10.1339 0.530434
\(366\) 0 0
\(367\) −4.02990 −0.210359 −0.105180 0.994453i \(-0.533542\pi\)
−0.105180 + 0.994453i \(0.533542\pi\)
\(368\) 0.632349 0.0329634
\(369\) 0 0
\(370\) −3.74691 −0.194792
\(371\) −6.25771 −0.324884
\(372\) 0 0
\(373\) −5.06561 −0.262287 −0.131144 0.991363i \(-0.541865\pi\)
−0.131144 + 0.991363i \(0.541865\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −13.4907 −0.695728
\(377\) 52.7159 2.71501
\(378\) 0 0
\(379\) 2.19657 0.112830 0.0564152 0.998407i \(-0.482033\pi\)
0.0564152 + 0.998407i \(0.482033\pi\)
\(380\) 23.4546 1.20319
\(381\) 0 0
\(382\) −11.9162 −0.609685
\(383\) 24.4857 1.25116 0.625579 0.780161i \(-0.284863\pi\)
0.625579 + 0.780161i \(0.284863\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −17.2792 −0.879487
\(387\) 0 0
\(388\) −14.3932 −0.730703
\(389\) −34.3208 −1.74013 −0.870066 0.492936i \(-0.835924\pi\)
−0.870066 + 0.492936i \(0.835924\pi\)
\(390\) 0 0
\(391\) 4.82479 0.244000
\(392\) 2.59958 0.131299
\(393\) 0 0
\(394\) −11.6202 −0.585415
\(395\) −1.91913 −0.0965618
\(396\) 0 0
\(397\) 8.46742 0.424968 0.212484 0.977165i \(-0.431845\pi\)
0.212484 + 0.977165i \(0.431845\pi\)
\(398\) 0.415990 0.0208517
\(399\) 0 0
\(400\) 2.80110 0.140055
\(401\) −28.9079 −1.44359 −0.721797 0.692105i \(-0.756684\pi\)
−0.721797 + 0.692105i \(0.756684\pi\)
\(402\) 0 0
\(403\) 19.6424 0.978459
\(404\) −9.14304 −0.454883
\(405\) 0 0
\(406\) 5.74641 0.285189
\(407\) 0 0
\(408\) 0 0
\(409\) 1.59556 0.0788955 0.0394478 0.999222i \(-0.487440\pi\)
0.0394478 + 0.999222i \(0.487440\pi\)
\(410\) 2.43872 0.120440
\(411\) 0 0
\(412\) 12.7503 0.628164
\(413\) 3.98228 0.195955
\(414\) 0 0
\(415\) −38.4632 −1.88808
\(416\) −40.8348 −2.00209
\(417\) 0 0
\(418\) 0 0
\(419\) 0.224640 0.0109744 0.00548719 0.999985i \(-0.498253\pi\)
0.00548719 + 0.999985i \(0.498253\pi\)
\(420\) 0 0
\(421\) 11.5297 0.561924 0.280962 0.959719i \(-0.409346\pi\)
0.280962 + 0.959719i \(0.409346\pi\)
\(422\) −10.5344 −0.512804
\(423\) 0 0
\(424\) 16.2674 0.790015
\(425\) 21.3722 1.03670
\(426\) 0 0
\(427\) −5.97074 −0.288944
\(428\) −6.44630 −0.311593
\(429\) 0 0
\(430\) 25.4766 1.22859
\(431\) 27.8911 1.34347 0.671733 0.740794i \(-0.265550\pi\)
0.671733 + 0.740794i \(0.265550\pi\)
\(432\) 0 0
\(433\) 25.9669 1.24789 0.623944 0.781469i \(-0.285529\pi\)
0.623944 + 0.781469i \(0.285529\pi\)
\(434\) 2.14116 0.102779
\(435\) 0 0
\(436\) −1.46242 −0.0700372
\(437\) 4.16711 0.199340
\(438\) 0 0
\(439\) −23.5551 −1.12422 −0.562112 0.827061i \(-0.690011\pi\)
−0.562112 + 0.827061i \(0.690011\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −35.2238 −1.67542
\(443\) −24.8412 −1.18024 −0.590120 0.807315i \(-0.700920\pi\)
−0.590120 + 0.807315i \(0.700920\pi\)
\(444\) 0 0
\(445\) 47.5648 2.25479
\(446\) 5.77252 0.273337
\(447\) 0 0
\(448\) −2.70587 −0.127840
\(449\) 18.4127 0.868947 0.434473 0.900685i \(-0.356935\pi\)
0.434473 + 0.900685i \(0.356935\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 18.8426 0.886279
\(453\) 0 0
\(454\) 0.224131 0.0105190
\(455\) 19.9599 0.935733
\(456\) 0 0
\(457\) −4.61369 −0.215820 −0.107910 0.994161i \(-0.534416\pi\)
−0.107910 + 0.994161i \(0.534416\pi\)
\(458\) −5.39962 −0.252308
\(459\) 0 0
\(460\) 2.95506 0.137780
\(461\) 33.5148 1.56094 0.780470 0.625193i \(-0.214980\pi\)
0.780470 + 0.625193i \(0.214980\pi\)
\(462\) 0 0
\(463\) −16.5338 −0.768392 −0.384196 0.923252i \(-0.625521\pi\)
−0.384196 + 0.923252i \(0.625521\pi\)
\(464\) 6.60414 0.306590
\(465\) 0 0
\(466\) −7.78630 −0.360693
\(467\) 19.4446 0.899788 0.449894 0.893082i \(-0.351462\pi\)
0.449894 + 0.893082i \(0.351462\pi\)
\(468\) 0 0
\(469\) −10.3611 −0.478432
\(470\) −11.2913 −0.520827
\(471\) 0 0
\(472\) −10.3522 −0.476501
\(473\) 0 0
\(474\) 0 0
\(475\) 18.4589 0.846954
\(476\) 9.47781 0.434415
\(477\) 0 0
\(478\) 15.0386 0.687848
\(479\) 39.2757 1.79455 0.897276 0.441469i \(-0.145543\pi\)
0.897276 + 0.441469i \(0.145543\pi\)
\(480\) 0 0
\(481\) −11.9965 −0.546995
\(482\) −15.2104 −0.692815
\(483\) 0 0
\(484\) 0 0
\(485\) −28.9736 −1.31562
\(486\) 0 0
\(487\) −17.1008 −0.774911 −0.387455 0.921889i \(-0.626646\pi\)
−0.387455 + 0.921889i \(0.626646\pi\)
\(488\) 15.5214 0.702621
\(489\) 0 0
\(490\) 2.17577 0.0982911
\(491\) −34.7859 −1.56986 −0.784932 0.619582i \(-0.787302\pi\)
−0.784932 + 0.619582i \(0.787302\pi\)
\(492\) 0 0
\(493\) 50.3892 2.26942
\(494\) −30.4224 −1.36877
\(495\) 0 0
\(496\) 2.46076 0.110491
\(497\) −0.995183 −0.0446401
\(498\) 0 0
\(499\) 15.6577 0.700935 0.350467 0.936575i \(-0.386023\pi\)
0.350467 + 0.936575i \(0.386023\pi\)
\(500\) −7.30157 −0.326536
\(501\) 0 0
\(502\) −2.04504 −0.0912744
\(503\) 21.8981 0.976386 0.488193 0.872736i \(-0.337656\pi\)
0.488193 + 0.872736i \(0.337656\pi\)
\(504\) 0 0
\(505\) −18.4050 −0.819012
\(506\) 0 0
\(507\) 0 0
\(508\) 23.1915 1.02896
\(509\) −26.8438 −1.18983 −0.594915 0.803789i \(-0.702814\pi\)
−0.594915 + 0.803789i \(0.702814\pi\)
\(510\) 0 0
\(511\) 3.53684 0.156461
\(512\) −9.65305 −0.426609
\(513\) 0 0
\(514\) 19.2568 0.849380
\(515\) 25.6665 1.13100
\(516\) 0 0
\(517\) 0 0
\(518\) −1.30771 −0.0574574
\(519\) 0 0
\(520\) −51.8873 −2.27541
\(521\) −15.9670 −0.699528 −0.349764 0.936838i \(-0.613738\pi\)
−0.349764 + 0.936838i \(0.613738\pi\)
\(522\) 0 0
\(523\) −13.2422 −0.579040 −0.289520 0.957172i \(-0.593496\pi\)
−0.289520 + 0.957172i \(0.593496\pi\)
\(524\) −8.82247 −0.385411
\(525\) 0 0
\(526\) 6.87208 0.299637
\(527\) 18.7755 0.817873
\(528\) 0 0
\(529\) −22.4750 −0.977173
\(530\) 13.6153 0.591411
\(531\) 0 0
\(532\) 8.18588 0.354903
\(533\) 7.80810 0.338206
\(534\) 0 0
\(535\) −12.9764 −0.561021
\(536\) 26.9345 1.16339
\(537\) 0 0
\(538\) 2.07526 0.0894706
\(539\) 0 0
\(540\) 0 0
\(541\) 25.5950 1.10042 0.550209 0.835027i \(-0.314548\pi\)
0.550209 + 0.835027i \(0.314548\pi\)
\(542\) 13.6321 0.585550
\(543\) 0 0
\(544\) −39.0325 −1.67351
\(545\) −2.94386 −0.126101
\(546\) 0 0
\(547\) −30.1551 −1.28934 −0.644670 0.764461i \(-0.723005\pi\)
−0.644670 + 0.764461i \(0.723005\pi\)
\(548\) 22.7874 0.973431
\(549\) 0 0
\(550\) 0 0
\(551\) 43.5206 1.85404
\(552\) 0 0
\(553\) −0.669794 −0.0284826
\(554\) −8.46715 −0.359735
\(555\) 0 0
\(556\) 6.56743 0.278521
\(557\) −0.733579 −0.0310827 −0.0155414 0.999879i \(-0.504947\pi\)
−0.0155414 + 0.999879i \(0.504947\pi\)
\(558\) 0 0
\(559\) 81.5688 3.44999
\(560\) 2.50053 0.105667
\(561\) 0 0
\(562\) −3.00890 −0.126923
\(563\) −20.9036 −0.880982 −0.440491 0.897757i \(-0.645196\pi\)
−0.440491 + 0.897757i \(0.645196\pi\)
\(564\) 0 0
\(565\) 37.9302 1.59574
\(566\) 4.36566 0.183502
\(567\) 0 0
\(568\) 2.58706 0.108551
\(569\) 28.2526 1.18441 0.592205 0.805787i \(-0.298258\pi\)
0.592205 + 0.805787i \(0.298258\pi\)
\(570\) 0 0
\(571\) −38.7512 −1.62169 −0.810843 0.585264i \(-0.800991\pi\)
−0.810843 + 0.585264i \(0.800991\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.851138 0.0355258
\(575\) 2.32566 0.0969866
\(576\) 0 0
\(577\) 12.7178 0.529450 0.264725 0.964324i \(-0.414719\pi\)
0.264725 + 0.964324i \(0.414719\pi\)
\(578\) −20.7599 −0.863499
\(579\) 0 0
\(580\) 30.8622 1.28148
\(581\) −13.4240 −0.556922
\(582\) 0 0
\(583\) 0 0
\(584\) −9.19430 −0.380463
\(585\) 0 0
\(586\) −17.6505 −0.729134
\(587\) −7.77003 −0.320704 −0.160352 0.987060i \(-0.551263\pi\)
−0.160352 + 0.987060i \(0.551263\pi\)
\(588\) 0 0
\(589\) 16.2162 0.668175
\(590\) −8.66450 −0.356712
\(591\) 0 0
\(592\) −1.50290 −0.0617688
\(593\) −25.2949 −1.03874 −0.519368 0.854551i \(-0.673832\pi\)
−0.519368 + 0.854551i \(0.673832\pi\)
\(594\) 0 0
\(595\) 19.0789 0.782159
\(596\) 10.2744 0.420858
\(597\) 0 0
\(598\) −3.83294 −0.156740
\(599\) 11.9194 0.487014 0.243507 0.969899i \(-0.421702\pi\)
0.243507 + 0.969899i \(0.421702\pi\)
\(600\) 0 0
\(601\) −21.0106 −0.857041 −0.428521 0.903532i \(-0.640965\pi\)
−0.428521 + 0.903532i \(0.640965\pi\)
\(602\) 8.89157 0.362393
\(603\) 0 0
\(604\) 0.891525 0.0362756
\(605\) 0 0
\(606\) 0 0
\(607\) −25.7817 −1.04645 −0.523223 0.852196i \(-0.675271\pi\)
−0.523223 + 0.852196i \(0.675271\pi\)
\(608\) −33.7119 −1.36720
\(609\) 0 0
\(610\) 12.9909 0.525987
\(611\) −36.1514 −1.46253
\(612\) 0 0
\(613\) 31.9173 1.28913 0.644563 0.764551i \(-0.277039\pi\)
0.644563 + 0.764551i \(0.277039\pi\)
\(614\) 2.94588 0.118886
\(615\) 0 0
\(616\) 0 0
\(617\) −13.9772 −0.562701 −0.281350 0.959605i \(-0.590782\pi\)
−0.281350 + 0.959605i \(0.590782\pi\)
\(618\) 0 0
\(619\) 22.4745 0.903326 0.451663 0.892189i \(-0.350831\pi\)
0.451663 + 0.892189i \(0.350831\pi\)
\(620\) 11.4995 0.461832
\(621\) 0 0
\(622\) 2.84502 0.114075
\(623\) 16.6006 0.665088
\(624\) 0 0
\(625\) −30.7464 −1.22986
\(626\) −13.7173 −0.548252
\(627\) 0 0
\(628\) 8.75018 0.349170
\(629\) −11.4671 −0.457221
\(630\) 0 0
\(631\) −41.0383 −1.63371 −0.816854 0.576845i \(-0.804284\pi\)
−0.816854 + 0.576845i \(0.804284\pi\)
\(632\) 1.74118 0.0692606
\(633\) 0 0
\(634\) 5.63025 0.223606
\(635\) 46.6847 1.85262
\(636\) 0 0
\(637\) 6.96619 0.276010
\(638\) 0 0
\(639\) 0 0
\(640\) −27.7041 −1.09510
\(641\) −13.8318 −0.546323 −0.273162 0.961968i \(-0.588069\pi\)
−0.273162 + 0.961968i \(0.588069\pi\)
\(642\) 0 0
\(643\) −33.5125 −1.32161 −0.660803 0.750560i \(-0.729784\pi\)
−0.660803 + 0.750560i \(0.729784\pi\)
\(644\) 1.03135 0.0406407
\(645\) 0 0
\(646\) −29.0796 −1.14412
\(647\) 8.58616 0.337557 0.168778 0.985654i \(-0.446018\pi\)
0.168778 + 0.985654i \(0.446018\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −16.9787 −0.665957
\(651\) 0 0
\(652\) −30.8039 −1.20637
\(653\) −47.4478 −1.85678 −0.928388 0.371613i \(-0.878805\pi\)
−0.928388 + 0.371613i \(0.878805\pi\)
\(654\) 0 0
\(655\) −17.7597 −0.693929
\(656\) 0.978182 0.0381916
\(657\) 0 0
\(658\) −3.94076 −0.153627
\(659\) 47.4501 1.84839 0.924197 0.381916i \(-0.124736\pi\)
0.924197 + 0.381916i \(0.124736\pi\)
\(660\) 0 0
\(661\) −24.3627 −0.947599 −0.473800 0.880633i \(-0.657118\pi\)
−0.473800 + 0.880633i \(0.657118\pi\)
\(662\) −11.0238 −0.428453
\(663\) 0 0
\(664\) 34.8968 1.35426
\(665\) 16.4782 0.638998
\(666\) 0 0
\(667\) 5.48320 0.212310
\(668\) 34.1533 1.32143
\(669\) 0 0
\(670\) 22.5433 0.870926
\(671\) 0 0
\(672\) 0 0
\(673\) −31.9467 −1.23146 −0.615728 0.787959i \(-0.711138\pi\)
−0.615728 + 0.787959i \(0.711138\pi\)
\(674\) 8.01456 0.308709
\(675\) 0 0
\(676\) −50.5690 −1.94496
\(677\) 1.01464 0.0389957 0.0194979 0.999810i \(-0.493793\pi\)
0.0194979 + 0.999810i \(0.493793\pi\)
\(678\) 0 0
\(679\) −10.1121 −0.388065
\(680\) −49.5971 −1.90196
\(681\) 0 0
\(682\) 0 0
\(683\) 0.904878 0.0346242 0.0173121 0.999850i \(-0.494489\pi\)
0.0173121 + 0.999850i \(0.494489\pi\)
\(684\) 0 0
\(685\) 45.8713 1.75265
\(686\) 0.759363 0.0289926
\(687\) 0 0
\(688\) 10.2188 0.389587
\(689\) 43.5924 1.66074
\(690\) 0 0
\(691\) −21.4535 −0.816130 −0.408065 0.912953i \(-0.633796\pi\)
−0.408065 + 0.912953i \(0.633796\pi\)
\(692\) 15.3878 0.584958
\(693\) 0 0
\(694\) 17.0932 0.648851
\(695\) 13.2203 0.501474
\(696\) 0 0
\(697\) 7.46347 0.282699
\(698\) −15.7345 −0.595558
\(699\) 0 0
\(700\) 4.56852 0.172674
\(701\) 19.0750 0.720453 0.360227 0.932865i \(-0.382699\pi\)
0.360227 + 0.932865i \(0.382699\pi\)
\(702\) 0 0
\(703\) −9.90396 −0.373535
\(704\) 0 0
\(705\) 0 0
\(706\) 4.56727 0.171891
\(707\) −6.42353 −0.241582
\(708\) 0 0
\(709\) −9.71578 −0.364884 −0.182442 0.983217i \(-0.558400\pi\)
−0.182442 + 0.983217i \(0.558400\pi\)
\(710\) 2.16529 0.0812617
\(711\) 0 0
\(712\) −43.1545 −1.61728
\(713\) 2.04309 0.0765142
\(714\) 0 0
\(715\) 0 0
\(716\) 8.43828 0.315353
\(717\) 0 0
\(718\) 14.0255 0.523425
\(719\) −12.2204 −0.455743 −0.227871 0.973691i \(-0.573177\pi\)
−0.227871 + 0.973691i \(0.573177\pi\)
\(720\) 0 0
\(721\) 8.95787 0.333609
\(722\) −10.6878 −0.397760
\(723\) 0 0
\(724\) 6.89788 0.256358
\(725\) 24.2888 0.902062
\(726\) 0 0
\(727\) 0.0225849 0.000837628 0 0.000418814 1.00000i \(-0.499867\pi\)
0.000418814 1.00000i \(0.499867\pi\)
\(728\) −18.1092 −0.671170
\(729\) 0 0
\(730\) −7.69534 −0.284817
\(731\) 77.9686 2.88377
\(732\) 0 0
\(733\) −5.28222 −0.195103 −0.0975516 0.995230i \(-0.531101\pi\)
−0.0975516 + 0.995230i \(0.531101\pi\)
\(734\) 3.06016 0.112953
\(735\) 0 0
\(736\) −4.24740 −0.156561
\(737\) 0 0
\(738\) 0 0
\(739\) 36.0831 1.32734 0.663670 0.748025i \(-0.268998\pi\)
0.663670 + 0.748025i \(0.268998\pi\)
\(740\) −7.02329 −0.258181
\(741\) 0 0
\(742\) 4.75188 0.174447
\(743\) 34.2049 1.25486 0.627429 0.778674i \(-0.284107\pi\)
0.627429 + 0.778674i \(0.284107\pi\)
\(744\) 0 0
\(745\) 20.6825 0.757750
\(746\) 3.84664 0.140835
\(747\) 0 0
\(748\) 0 0
\(749\) −4.52891 −0.165483
\(750\) 0 0
\(751\) 7.33500 0.267658 0.133829 0.991004i \(-0.457273\pi\)
0.133829 + 0.991004i \(0.457273\pi\)
\(752\) −4.52898 −0.165155
\(753\) 0 0
\(754\) −40.0306 −1.45783
\(755\) 1.79465 0.0653139
\(756\) 0 0
\(757\) −34.8941 −1.26825 −0.634124 0.773231i \(-0.718639\pi\)
−0.634124 + 0.773231i \(0.718639\pi\)
\(758\) −1.66800 −0.0605844
\(759\) 0 0
\(760\) −42.8365 −1.55384
\(761\) −2.28870 −0.0829655 −0.0414827 0.999139i \(-0.513208\pi\)
−0.0414827 + 0.999139i \(0.513208\pi\)
\(762\) 0 0
\(763\) −1.02744 −0.0371957
\(764\) −22.3360 −0.808087
\(765\) 0 0
\(766\) −18.5935 −0.671811
\(767\) −27.7413 −1.00168
\(768\) 0 0
\(769\) 9.59977 0.346176 0.173088 0.984906i \(-0.444625\pi\)
0.173088 + 0.984906i \(0.444625\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −32.3885 −1.16569
\(773\) 13.7761 0.495492 0.247746 0.968825i \(-0.420310\pi\)
0.247746 + 0.968825i \(0.420310\pi\)
\(774\) 0 0
\(775\) 9.05021 0.325093
\(776\) 26.2871 0.943652
\(777\) 0 0
\(778\) 26.0619 0.934365
\(779\) 6.44612 0.230956
\(780\) 0 0
\(781\) 0 0
\(782\) −3.66377 −0.131016
\(783\) 0 0
\(784\) 0.872709 0.0311682
\(785\) 17.6142 0.628677
\(786\) 0 0
\(787\) 2.24272 0.0799443 0.0399721 0.999201i \(-0.487273\pi\)
0.0399721 + 0.999201i \(0.487273\pi\)
\(788\) −21.7811 −0.775919
\(789\) 0 0
\(790\) 1.45732 0.0518490
\(791\) 13.2380 0.470689
\(792\) 0 0
\(793\) 41.5933 1.47702
\(794\) −6.42985 −0.228187
\(795\) 0 0
\(796\) 0.779741 0.0276372
\(797\) −18.1909 −0.644353 −0.322177 0.946680i \(-0.604414\pi\)
−0.322177 + 0.946680i \(0.604414\pi\)
\(798\) 0 0
\(799\) −34.5558 −1.22250
\(800\) −18.8146 −0.665195
\(801\) 0 0
\(802\) 21.9516 0.775139
\(803\) 0 0
\(804\) 0 0
\(805\) 2.07611 0.0731731
\(806\) −14.9157 −0.525384
\(807\) 0 0
\(808\) 16.6985 0.587450
\(809\) −31.2009 −1.09696 −0.548482 0.836162i \(-0.684794\pi\)
−0.548482 + 0.836162i \(0.684794\pi\)
\(810\) 0 0
\(811\) 25.2002 0.884899 0.442449 0.896793i \(-0.354110\pi\)
0.442449 + 0.896793i \(0.354110\pi\)
\(812\) 10.7712 0.377995
\(813\) 0 0
\(814\) 0 0
\(815\) −62.0084 −2.17206
\(816\) 0 0
\(817\) 67.3406 2.35595
\(818\) −1.21161 −0.0423630
\(819\) 0 0
\(820\) 4.57119 0.159633
\(821\) −11.8863 −0.414836 −0.207418 0.978252i \(-0.566506\pi\)
−0.207418 + 0.978252i \(0.566506\pi\)
\(822\) 0 0
\(823\) 7.62865 0.265918 0.132959 0.991122i \(-0.457552\pi\)
0.132959 + 0.991122i \(0.457552\pi\)
\(824\) −23.2867 −0.811231
\(825\) 0 0
\(826\) −3.02399 −0.105218
\(827\) −11.4070 −0.396661 −0.198330 0.980135i \(-0.563552\pi\)
−0.198330 + 0.980135i \(0.563552\pi\)
\(828\) 0 0
\(829\) −44.6474 −1.55067 −0.775334 0.631552i \(-0.782418\pi\)
−0.775334 + 0.631552i \(0.782418\pi\)
\(830\) 29.2075 1.01381
\(831\) 0 0
\(832\) 18.8496 0.653491
\(833\) 6.65872 0.230711
\(834\) 0 0
\(835\) 68.7509 2.37922
\(836\) 0 0
\(837\) 0 0
\(838\) −0.170583 −0.00589270
\(839\) −10.0848 −0.348166 −0.174083 0.984731i \(-0.555696\pi\)
−0.174083 + 0.984731i \(0.555696\pi\)
\(840\) 0 0
\(841\) 28.2656 0.974675
\(842\) −8.75525 −0.301726
\(843\) 0 0
\(844\) −19.7458 −0.679679
\(845\) −101.796 −3.50188
\(846\) 0 0
\(847\) 0 0
\(848\) 5.46116 0.187537
\(849\) 0 0
\(850\) −16.2293 −0.556659
\(851\) −1.24781 −0.0427743
\(852\) 0 0
\(853\) 19.0126 0.650981 0.325490 0.945545i \(-0.394471\pi\)
0.325490 + 0.945545i \(0.394471\pi\)
\(854\) 4.53396 0.155149
\(855\) 0 0
\(856\) 11.7733 0.402401
\(857\) −29.8781 −1.02062 −0.510308 0.859992i \(-0.670469\pi\)
−0.510308 + 0.859992i \(0.670469\pi\)
\(858\) 0 0
\(859\) −16.6976 −0.569714 −0.284857 0.958570i \(-0.591946\pi\)
−0.284857 + 0.958570i \(0.591946\pi\)
\(860\) 47.7538 1.62839
\(861\) 0 0
\(862\) −21.1795 −0.721375
\(863\) −16.7819 −0.571261 −0.285631 0.958340i \(-0.592203\pi\)
−0.285631 + 0.958340i \(0.592203\pi\)
\(864\) 0 0
\(865\) 30.9758 1.05321
\(866\) −19.7183 −0.670055
\(867\) 0 0
\(868\) 4.01344 0.136225
\(869\) 0 0
\(870\) 0 0
\(871\) 72.1774 2.44564
\(872\) 2.67090 0.0904482
\(873\) 0 0
\(874\) −3.16435 −0.107036
\(875\) −5.12978 −0.173418
\(876\) 0 0
\(877\) −5.53815 −0.187010 −0.0935050 0.995619i \(-0.529807\pi\)
−0.0935050 + 0.995619i \(0.529807\pi\)
\(878\) 17.8869 0.603653
\(879\) 0 0
\(880\) 0 0
\(881\) 6.77615 0.228294 0.114147 0.993464i \(-0.463586\pi\)
0.114147 + 0.993464i \(0.463586\pi\)
\(882\) 0 0
\(883\) −23.9604 −0.806331 −0.403165 0.915127i \(-0.632090\pi\)
−0.403165 + 0.915127i \(0.632090\pi\)
\(884\) −66.0242 −2.22063
\(885\) 0 0
\(886\) 18.8635 0.633731
\(887\) −27.6881 −0.929676 −0.464838 0.885396i \(-0.653887\pi\)
−0.464838 + 0.885396i \(0.653887\pi\)
\(888\) 0 0
\(889\) 16.2934 0.546463
\(890\) −36.1189 −1.21071
\(891\) 0 0
\(892\) 10.8201 0.362285
\(893\) −29.8455 −0.998741
\(894\) 0 0
\(895\) 16.9863 0.567790
\(896\) −9.66899 −0.323018
\(897\) 0 0
\(898\) −13.9819 −0.466582
\(899\) 21.3377 0.711651
\(900\) 0 0
\(901\) 41.6684 1.38817
\(902\) 0 0
\(903\) 0 0
\(904\) −34.4133 −1.14457
\(905\) 13.8855 0.461569
\(906\) 0 0
\(907\) 14.9565 0.496623 0.248311 0.968680i \(-0.420124\pi\)
0.248311 + 0.968680i \(0.420124\pi\)
\(908\) 0.420116 0.0139420
\(909\) 0 0
\(910\) −15.1568 −0.502443
\(911\) −25.1916 −0.834635 −0.417318 0.908761i \(-0.637030\pi\)
−0.417318 + 0.908761i \(0.637030\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 3.50347 0.115884
\(915\) 0 0
\(916\) −10.1212 −0.334413
\(917\) −6.19831 −0.204686
\(918\) 0 0
\(919\) −26.7796 −0.883378 −0.441689 0.897168i \(-0.645621\pi\)
−0.441689 + 0.897168i \(0.645621\pi\)
\(920\) −5.39700 −0.177934
\(921\) 0 0
\(922\) −25.4499 −0.838148
\(923\) 6.93263 0.228190
\(924\) 0 0
\(925\) −5.52738 −0.181739
\(926\) 12.5552 0.412589
\(927\) 0 0
\(928\) −44.3591 −1.45616
\(929\) 5.65027 0.185379 0.0926896 0.995695i \(-0.470454\pi\)
0.0926896 + 0.995695i \(0.470454\pi\)
\(930\) 0 0
\(931\) 5.75106 0.188483
\(932\) −14.5948 −0.478069
\(933\) 0 0
\(934\) −14.7655 −0.483142
\(935\) 0 0
\(936\) 0 0
\(937\) 45.2807 1.47925 0.739627 0.673017i \(-0.235002\pi\)
0.739627 + 0.673017i \(0.235002\pi\)
\(938\) 7.86785 0.256894
\(939\) 0 0
\(940\) −21.1646 −0.690313
\(941\) 32.6876 1.06558 0.532792 0.846246i \(-0.321143\pi\)
0.532792 + 0.846246i \(0.321143\pi\)
\(942\) 0 0
\(943\) 0.812152 0.0264473
\(944\) −3.47537 −0.113114
\(945\) 0 0
\(946\) 0 0
\(947\) −39.8004 −1.29334 −0.646669 0.762771i \(-0.723838\pi\)
−0.646669 + 0.762771i \(0.723838\pi\)
\(948\) 0 0
\(949\) −24.6383 −0.799793
\(950\) −14.0170 −0.454773
\(951\) 0 0
\(952\) −17.3099 −0.561016
\(953\) 12.5174 0.405479 0.202739 0.979233i \(-0.435016\pi\)
0.202739 + 0.979233i \(0.435016\pi\)
\(954\) 0 0
\(955\) −44.9625 −1.45495
\(956\) 28.1886 0.911686
\(957\) 0 0
\(958\) −29.8245 −0.963587
\(959\) 16.0095 0.516974
\(960\) 0 0
\(961\) −23.0494 −0.743529
\(962\) 9.10973 0.293710
\(963\) 0 0
\(964\) −28.5107 −0.918269
\(965\) −65.1982 −2.09880
\(966\) 0 0
\(967\) −12.7139 −0.408850 −0.204425 0.978882i \(-0.565532\pi\)
−0.204425 + 0.978882i \(0.565532\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 22.0015 0.706425
\(971\) 22.6126 0.725673 0.362837 0.931853i \(-0.381808\pi\)
0.362837 + 0.931853i \(0.381808\pi\)
\(972\) 0 0
\(973\) 4.61401 0.147918
\(974\) 12.9857 0.416089
\(975\) 0 0
\(976\) 5.21072 0.166791
\(977\) 17.9694 0.574893 0.287446 0.957797i \(-0.407194\pi\)
0.287446 + 0.957797i \(0.407194\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 4.07830 0.130277
\(981\) 0 0
\(982\) 26.4151 0.842940
\(983\) −48.2065 −1.53755 −0.768775 0.639520i \(-0.779133\pi\)
−0.768775 + 0.639520i \(0.779133\pi\)
\(984\) 0 0
\(985\) −43.8455 −1.39703
\(986\) −38.2637 −1.21857
\(987\) 0 0
\(988\) −57.0243 −1.81419
\(989\) 8.48430 0.269785
\(990\) 0 0
\(991\) −6.62493 −0.210448 −0.105224 0.994449i \(-0.533556\pi\)
−0.105224 + 0.994449i \(0.533556\pi\)
\(992\) −16.5286 −0.524783
\(993\) 0 0
\(994\) 0.755706 0.0239695
\(995\) 1.56962 0.0497605
\(996\) 0 0
\(997\) 28.1261 0.890762 0.445381 0.895341i \(-0.353068\pi\)
0.445381 + 0.895341i \(0.353068\pi\)
\(998\) −11.8899 −0.376368
\(999\) 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 7623.2.a.db.1.7 16
3.2 odd 2 inner 7623.2.a.db.1.10 16
11.2 odd 10 693.2.m.k.631.4 yes 32
11.6 odd 10 693.2.m.k.190.4 32
11.10 odd 2 7623.2.a.dc.1.10 16
33.2 even 10 693.2.m.k.631.5 yes 32
33.17 even 10 693.2.m.k.190.5 yes 32
33.32 even 2 7623.2.a.dc.1.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
693.2.m.k.190.4 32 11.6 odd 10
693.2.m.k.190.5 yes 32 33.17 even 10
693.2.m.k.631.4 yes 32 11.2 odd 10
693.2.m.k.631.5 yes 32 33.2 even 10
7623.2.a.db.1.7 16 1.1 even 1 trivial
7623.2.a.db.1.10 16 3.2 odd 2 inner
7623.2.a.dc.1.7 16 33.32 even 2
7623.2.a.dc.1.10 16 11.10 odd 2