Properties

Label 7623.2.a.cy.1.7
Level 7623
Weight 2
Character 7623.1
Self dual yes
Analytic conductor 60.870
Analytic rank 0
Dimension 10
CM no
Inner twists 1

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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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 231)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.871604\)
Character \(\chi\) = 7623.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.871604 q^{2} -1.24031 q^{4} +4.06436 q^{5} +1.00000 q^{7} -2.82426 q^{8} +O(q^{10})\) \(q+0.871604 q^{2} -1.24031 q^{4} +4.06436 q^{5} +1.00000 q^{7} -2.82426 q^{8} +3.54252 q^{10} +6.09006 q^{13} +0.871604 q^{14} +0.0189705 q^{16} +1.70162 q^{17} -5.45712 q^{19} -5.04106 q^{20} +6.39153 q^{23} +11.5191 q^{25} +5.30813 q^{26} -1.24031 q^{28} +4.74935 q^{29} -4.36309 q^{31} +5.66506 q^{32} +1.48314 q^{34} +4.06436 q^{35} +2.43952 q^{37} -4.75645 q^{38} -11.4788 q^{40} -3.21037 q^{41} -0.127191 q^{43} +5.57089 q^{46} -8.46784 q^{47} +1.00000 q^{49} +10.0401 q^{50} -7.55354 q^{52} +4.71404 q^{53} -2.82426 q^{56} +4.13955 q^{58} -4.63368 q^{59} -5.31081 q^{61} -3.80289 q^{62} +4.89975 q^{64} +24.7522 q^{65} +14.0686 q^{67} -2.11054 q^{68} +3.54252 q^{70} -2.21883 q^{71} +5.57393 q^{73} +2.12630 q^{74} +6.76849 q^{76} -6.27134 q^{79} +0.0771030 q^{80} -2.79817 q^{82} -0.127722 q^{83} +6.91602 q^{85} -0.110860 q^{86} +8.12736 q^{89} +6.09006 q^{91} -7.92745 q^{92} -7.38061 q^{94} -22.1797 q^{95} -2.59721 q^{97} +0.871604 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 18q^{4} - 5q^{5} + 10q^{7} + 3q^{8} + O(q^{10}) \) \( 10q + 18q^{4} - 5q^{5} + 10q^{7} + 3q^{8} - 6q^{10} + 6q^{13} + 38q^{16} - 8q^{17} - 7q^{20} + 31q^{25} - q^{26} + 18q^{28} + 14q^{29} + 26q^{31} + 41q^{32} + 21q^{34} - 5q^{35} + 24q^{37} - 8q^{38} - 5q^{40} - 19q^{41} - 6q^{43} - q^{46} - 15q^{47} + 10q^{49} + q^{50} - 25q^{52} + q^{53} + 3q^{56} + 11q^{58} - 23q^{59} - 11q^{62} + 53q^{64} + 29q^{65} + 38q^{67} - 87q^{68} - 6q^{70} - 26q^{71} - q^{73} + 39q^{74} - 2q^{76} + 5q^{79} - 6q^{80} + 5q^{82} - 6q^{83} - q^{85} + 41q^{86} + 9q^{89} + 6q^{91} + 48q^{92} + 42q^{95} + 24q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.871604 0.616317 0.308159 0.951335i \(-0.400287\pi\)
0.308159 + 0.951335i \(0.400287\pi\)
\(3\) 0 0
\(4\) −1.24031 −0.620153
\(5\) 4.06436 1.81764 0.908820 0.417189i \(-0.136985\pi\)
0.908820 + 0.417189i \(0.136985\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.82426 −0.998528
\(9\) 0 0
\(10\) 3.54252 1.12024
\(11\) 0 0
\(12\) 0 0
\(13\) 6.09006 1.68908 0.844540 0.535492i \(-0.179874\pi\)
0.844540 + 0.535492i \(0.179874\pi\)
\(14\) 0.871604 0.232946
\(15\) 0 0
\(16\) 0.0189705 0.00474262
\(17\) 1.70162 0.412705 0.206352 0.978478i \(-0.433841\pi\)
0.206352 + 0.978478i \(0.433841\pi\)
\(18\) 0 0
\(19\) −5.45712 −1.25195 −0.625974 0.779844i \(-0.715298\pi\)
−0.625974 + 0.779844i \(0.715298\pi\)
\(20\) −5.04106 −1.12721
\(21\) 0 0
\(22\) 0 0
\(23\) 6.39153 1.33273 0.666363 0.745627i \(-0.267850\pi\)
0.666363 + 0.745627i \(0.267850\pi\)
\(24\) 0 0
\(25\) 11.5191 2.30381
\(26\) 5.30813 1.04101
\(27\) 0 0
\(28\) −1.24031 −0.234396
\(29\) 4.74935 0.881931 0.440966 0.897524i \(-0.354636\pi\)
0.440966 + 0.897524i \(0.354636\pi\)
\(30\) 0 0
\(31\) −4.36309 −0.783634 −0.391817 0.920043i \(-0.628153\pi\)
−0.391817 + 0.920043i \(0.628153\pi\)
\(32\) 5.66506 1.00145
\(33\) 0 0
\(34\) 1.48314 0.254357
\(35\) 4.06436 0.687003
\(36\) 0 0
\(37\) 2.43952 0.401055 0.200528 0.979688i \(-0.435734\pi\)
0.200528 + 0.979688i \(0.435734\pi\)
\(38\) −4.75645 −0.771598
\(39\) 0 0
\(40\) −11.4788 −1.81496
\(41\) −3.21037 −0.501375 −0.250688 0.968068i \(-0.580657\pi\)
−0.250688 + 0.968068i \(0.580657\pi\)
\(42\) 0 0
\(43\) −0.127191 −0.0193964 −0.00969821 0.999953i \(-0.503087\pi\)
−0.00969821 + 0.999953i \(0.503087\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 5.57089 0.821382
\(47\) −8.46784 −1.23516 −0.617581 0.786507i \(-0.711887\pi\)
−0.617581 + 0.786507i \(0.711887\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 10.0401 1.41988
\(51\) 0 0
\(52\) −7.55354 −1.04749
\(53\) 4.71404 0.647523 0.323761 0.946139i \(-0.395052\pi\)
0.323761 + 0.946139i \(0.395052\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.82426 −0.377408
\(57\) 0 0
\(58\) 4.13955 0.543550
\(59\) −4.63368 −0.603253 −0.301627 0.953426i \(-0.597530\pi\)
−0.301627 + 0.953426i \(0.597530\pi\)
\(60\) 0 0
\(61\) −5.31081 −0.679980 −0.339990 0.940429i \(-0.610424\pi\)
−0.339990 + 0.940429i \(0.610424\pi\)
\(62\) −3.80289 −0.482967
\(63\) 0 0
\(64\) 4.89975 0.612469
\(65\) 24.7522 3.07014
\(66\) 0 0
\(67\) 14.0686 1.71876 0.859379 0.511340i \(-0.170851\pi\)
0.859379 + 0.511340i \(0.170851\pi\)
\(68\) −2.11054 −0.255940
\(69\) 0 0
\(70\) 3.54252 0.423412
\(71\) −2.21883 −0.263327 −0.131664 0.991294i \(-0.542032\pi\)
−0.131664 + 0.991294i \(0.542032\pi\)
\(72\) 0 0
\(73\) 5.57393 0.652379 0.326189 0.945304i \(-0.394235\pi\)
0.326189 + 0.945304i \(0.394235\pi\)
\(74\) 2.12630 0.247177
\(75\) 0 0
\(76\) 6.76849 0.776400
\(77\) 0 0
\(78\) 0 0
\(79\) −6.27134 −0.705581 −0.352790 0.935702i \(-0.614767\pi\)
−0.352790 + 0.935702i \(0.614767\pi\)
\(80\) 0.0771030 0.00862037
\(81\) 0 0
\(82\) −2.79817 −0.309006
\(83\) −0.127722 −0.0140193 −0.00700965 0.999975i \(-0.502231\pi\)
−0.00700965 + 0.999975i \(0.502231\pi\)
\(84\) 0 0
\(85\) 6.91602 0.750148
\(86\) −0.110860 −0.0119543
\(87\) 0 0
\(88\) 0 0
\(89\) 8.12736 0.861498 0.430749 0.902472i \(-0.358249\pi\)
0.430749 + 0.902472i \(0.358249\pi\)
\(90\) 0 0
\(91\) 6.09006 0.638412
\(92\) −7.92745 −0.826494
\(93\) 0 0
\(94\) −7.38061 −0.761252
\(95\) −22.1797 −2.27559
\(96\) 0 0
\(97\) −2.59721 −0.263706 −0.131853 0.991269i \(-0.542093\pi\)
−0.131853 + 0.991269i \(0.542093\pi\)
\(98\) 0.871604 0.0880453
\(99\) 0 0
\(100\) −14.2872 −1.42872
\(101\) −6.02573 −0.599583 −0.299791 0.954005i \(-0.596917\pi\)
−0.299791 + 0.954005i \(0.596917\pi\)
\(102\) 0 0
\(103\) 12.8938 1.27046 0.635232 0.772322i \(-0.280905\pi\)
0.635232 + 0.772322i \(0.280905\pi\)
\(104\) −17.2000 −1.68659
\(105\) 0 0
\(106\) 4.10878 0.399080
\(107\) −5.34760 −0.516972 −0.258486 0.966015i \(-0.583224\pi\)
−0.258486 + 0.966015i \(0.583224\pi\)
\(108\) 0 0
\(109\) 1.44173 0.138093 0.0690465 0.997613i \(-0.478004\pi\)
0.0690465 + 0.997613i \(0.478004\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.0189705 0.00179254
\(113\) −19.5174 −1.83604 −0.918021 0.396532i \(-0.870214\pi\)
−0.918021 + 0.396532i \(0.870214\pi\)
\(114\) 0 0
\(115\) 25.9775 2.42242
\(116\) −5.89064 −0.546932
\(117\) 0 0
\(118\) −4.03873 −0.371795
\(119\) 1.70162 0.155988
\(120\) 0 0
\(121\) 0 0
\(122\) −4.62893 −0.419083
\(123\) 0 0
\(124\) 5.41156 0.485973
\(125\) 26.4958 2.36986
\(126\) 0 0
\(127\) 0.641713 0.0569428 0.0284714 0.999595i \(-0.490936\pi\)
0.0284714 + 0.999595i \(0.490936\pi\)
\(128\) −7.05948 −0.623976
\(129\) 0 0
\(130\) 21.5742 1.89218
\(131\) −13.9987 −1.22307 −0.611537 0.791216i \(-0.709448\pi\)
−0.611537 + 0.791216i \(0.709448\pi\)
\(132\) 0 0
\(133\) −5.45712 −0.473192
\(134\) 12.2623 1.05930
\(135\) 0 0
\(136\) −4.80584 −0.412097
\(137\) 2.70017 0.230691 0.115346 0.993325i \(-0.463202\pi\)
0.115346 + 0.993325i \(0.463202\pi\)
\(138\) 0 0
\(139\) 2.06192 0.174890 0.0874448 0.996169i \(-0.472130\pi\)
0.0874448 + 0.996169i \(0.472130\pi\)
\(140\) −5.04106 −0.426047
\(141\) 0 0
\(142\) −1.93395 −0.162293
\(143\) 0 0
\(144\) 0 0
\(145\) 19.3031 1.60303
\(146\) 4.85826 0.402072
\(147\) 0 0
\(148\) −3.02576 −0.248716
\(149\) 10.0829 0.826027 0.413013 0.910725i \(-0.364476\pi\)
0.413013 + 0.910725i \(0.364476\pi\)
\(150\) 0 0
\(151\) 14.9639 1.21775 0.608873 0.793268i \(-0.291622\pi\)
0.608873 + 0.793268i \(0.291622\pi\)
\(152\) 15.4123 1.25011
\(153\) 0 0
\(154\) 0 0
\(155\) −17.7332 −1.42436
\(156\) 0 0
\(157\) 19.4540 1.55260 0.776300 0.630364i \(-0.217094\pi\)
0.776300 + 0.630364i \(0.217094\pi\)
\(158\) −5.46613 −0.434862
\(159\) 0 0
\(160\) 23.0249 1.82028
\(161\) 6.39153 0.503723
\(162\) 0 0
\(163\) 12.1104 0.948562 0.474281 0.880374i \(-0.342708\pi\)
0.474281 + 0.880374i \(0.342708\pi\)
\(164\) 3.98184 0.310929
\(165\) 0 0
\(166\) −0.111323 −0.00864034
\(167\) −13.1680 −1.01897 −0.509484 0.860480i \(-0.670164\pi\)
−0.509484 + 0.860480i \(0.670164\pi\)
\(168\) 0 0
\(169\) 24.0889 1.85299
\(170\) 6.02804 0.462329
\(171\) 0 0
\(172\) 0.157755 0.0120287
\(173\) −14.7179 −1.11898 −0.559492 0.828836i \(-0.689004\pi\)
−0.559492 + 0.828836i \(0.689004\pi\)
\(174\) 0 0
\(175\) 11.5191 0.870759
\(176\) 0 0
\(177\) 0 0
\(178\) 7.08384 0.530956
\(179\) 11.6904 0.873780 0.436890 0.899515i \(-0.356080\pi\)
0.436890 + 0.899515i \(0.356080\pi\)
\(180\) 0 0
\(181\) 19.7002 1.46431 0.732154 0.681139i \(-0.238515\pi\)
0.732154 + 0.681139i \(0.238515\pi\)
\(182\) 5.30813 0.393465
\(183\) 0 0
\(184\) −18.0514 −1.33077
\(185\) 9.91511 0.728974
\(186\) 0 0
\(187\) 0 0
\(188\) 10.5027 0.765989
\(189\) 0 0
\(190\) −19.3319 −1.40249
\(191\) −6.96194 −0.503748 −0.251874 0.967760i \(-0.581047\pi\)
−0.251874 + 0.967760i \(0.581047\pi\)
\(192\) 0 0
\(193\) −16.8633 −1.21385 −0.606923 0.794761i \(-0.707596\pi\)
−0.606923 + 0.794761i \(0.707596\pi\)
\(194\) −2.26374 −0.162527
\(195\) 0 0
\(196\) −1.24031 −0.0885933
\(197\) 6.42145 0.457510 0.228755 0.973484i \(-0.426535\pi\)
0.228755 + 0.973484i \(0.426535\pi\)
\(198\) 0 0
\(199\) −13.2645 −0.940297 −0.470149 0.882587i \(-0.655800\pi\)
−0.470149 + 0.882587i \(0.655800\pi\)
\(200\) −32.5329 −2.30042
\(201\) 0 0
\(202\) −5.25205 −0.369533
\(203\) 4.74935 0.333339
\(204\) 0 0
\(205\) −13.0481 −0.911319
\(206\) 11.2383 0.783008
\(207\) 0 0
\(208\) 0.115531 0.00801067
\(209\) 0 0
\(210\) 0 0
\(211\) −2.91158 −0.200442 −0.100221 0.994965i \(-0.531955\pi\)
−0.100221 + 0.994965i \(0.531955\pi\)
\(212\) −5.84685 −0.401563
\(213\) 0 0
\(214\) −4.66099 −0.318619
\(215\) −0.516950 −0.0352557
\(216\) 0 0
\(217\) −4.36309 −0.296186
\(218\) 1.25662 0.0851091
\(219\) 0 0
\(220\) 0 0
\(221\) 10.3630 0.697091
\(222\) 0 0
\(223\) −3.35570 −0.224714 −0.112357 0.993668i \(-0.535840\pi\)
−0.112357 + 0.993668i \(0.535840\pi\)
\(224\) 5.66506 0.378513
\(225\) 0 0
\(226\) −17.0114 −1.13158
\(227\) 3.33791 0.221545 0.110772 0.993846i \(-0.464668\pi\)
0.110772 + 0.993846i \(0.464668\pi\)
\(228\) 0 0
\(229\) 6.80143 0.449451 0.224726 0.974422i \(-0.427851\pi\)
0.224726 + 0.974422i \(0.427851\pi\)
\(230\) 22.6421 1.49298
\(231\) 0 0
\(232\) −13.4134 −0.880634
\(233\) 6.18553 0.405228 0.202614 0.979259i \(-0.435056\pi\)
0.202614 + 0.979259i \(0.435056\pi\)
\(234\) 0 0
\(235\) −34.4164 −2.24508
\(236\) 5.74718 0.374109
\(237\) 0 0
\(238\) 1.48314 0.0961379
\(239\) 20.4784 1.32464 0.662319 0.749222i \(-0.269573\pi\)
0.662319 + 0.749222i \(0.269573\pi\)
\(240\) 0 0
\(241\) −1.04113 −0.0670653 −0.0335326 0.999438i \(-0.510676\pi\)
−0.0335326 + 0.999438i \(0.510676\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 6.58703 0.421691
\(245\) 4.06436 0.259663
\(246\) 0 0
\(247\) −33.2342 −2.11464
\(248\) 12.3225 0.782481
\(249\) 0 0
\(250\) 23.0939 1.46059
\(251\) −6.63300 −0.418672 −0.209336 0.977844i \(-0.567130\pi\)
−0.209336 + 0.977844i \(0.567130\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.559320 0.0350948
\(255\) 0 0
\(256\) −15.9526 −0.997036
\(257\) −2.88246 −0.179803 −0.0899015 0.995951i \(-0.528655\pi\)
−0.0899015 + 0.995951i \(0.528655\pi\)
\(258\) 0 0
\(259\) 2.43952 0.151585
\(260\) −30.7004 −1.90396
\(261\) 0 0
\(262\) −12.2013 −0.753801
\(263\) −21.1018 −1.30119 −0.650595 0.759425i \(-0.725480\pi\)
−0.650595 + 0.759425i \(0.725480\pi\)
\(264\) 0 0
\(265\) 19.1596 1.17696
\(266\) −4.75645 −0.291636
\(267\) 0 0
\(268\) −17.4494 −1.06589
\(269\) 17.1315 1.04453 0.522263 0.852784i \(-0.325088\pi\)
0.522263 + 0.852784i \(0.325088\pi\)
\(270\) 0 0
\(271\) −16.3599 −0.993790 −0.496895 0.867811i \(-0.665527\pi\)
−0.496895 + 0.867811i \(0.665527\pi\)
\(272\) 0.0322806 0.00195730
\(273\) 0 0
\(274\) 2.35348 0.142179
\(275\) 0 0
\(276\) 0 0
\(277\) 2.47852 0.148920 0.0744599 0.997224i \(-0.476277\pi\)
0.0744599 + 0.997224i \(0.476277\pi\)
\(278\) 1.79718 0.107787
\(279\) 0 0
\(280\) −11.4788 −0.685992
\(281\) 24.1948 1.44334 0.721671 0.692236i \(-0.243374\pi\)
0.721671 + 0.692236i \(0.243374\pi\)
\(282\) 0 0
\(283\) 29.1859 1.73492 0.867460 0.497508i \(-0.165751\pi\)
0.867460 + 0.497508i \(0.165751\pi\)
\(284\) 2.75203 0.163303
\(285\) 0 0
\(286\) 0 0
\(287\) −3.21037 −0.189502
\(288\) 0 0
\(289\) −14.1045 −0.829675
\(290\) 16.8246 0.987977
\(291\) 0 0
\(292\) −6.91338 −0.404575
\(293\) −27.1918 −1.58856 −0.794280 0.607551i \(-0.792152\pi\)
−0.794280 + 0.607551i \(0.792152\pi\)
\(294\) 0 0
\(295\) −18.8330 −1.09650
\(296\) −6.88986 −0.400465
\(297\) 0 0
\(298\) 8.78834 0.509095
\(299\) 38.9248 2.25108
\(300\) 0 0
\(301\) −0.127191 −0.00733115
\(302\) 13.0426 0.750518
\(303\) 0 0
\(304\) −0.103524 −0.00593752
\(305\) −21.5851 −1.23596
\(306\) 0 0
\(307\) 9.95364 0.568084 0.284042 0.958812i \(-0.408324\pi\)
0.284042 + 0.958812i \(0.408324\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −15.4563 −0.877860
\(311\) −16.2407 −0.920923 −0.460462 0.887680i \(-0.652316\pi\)
−0.460462 + 0.887680i \(0.652316\pi\)
\(312\) 0 0
\(313\) 16.6148 0.939125 0.469562 0.882899i \(-0.344412\pi\)
0.469562 + 0.882899i \(0.344412\pi\)
\(314\) 16.9562 0.956894
\(315\) 0 0
\(316\) 7.77838 0.437568
\(317\) −8.10002 −0.454942 −0.227471 0.973785i \(-0.573046\pi\)
−0.227471 + 0.973785i \(0.573046\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 19.9144 1.11325
\(321\) 0 0
\(322\) 5.57089 0.310453
\(323\) −9.28597 −0.516685
\(324\) 0 0
\(325\) 70.1518 3.89132
\(326\) 10.5555 0.584615
\(327\) 0 0
\(328\) 9.06693 0.500637
\(329\) −8.46784 −0.466847
\(330\) 0 0
\(331\) −6.64605 −0.365300 −0.182650 0.983178i \(-0.558468\pi\)
−0.182650 + 0.983178i \(0.558468\pi\)
\(332\) 0.158414 0.00869411
\(333\) 0 0
\(334\) −11.4773 −0.628008
\(335\) 57.1801 3.12408
\(336\) 0 0
\(337\) 20.9521 1.14133 0.570665 0.821183i \(-0.306685\pi\)
0.570665 + 0.821183i \(0.306685\pi\)
\(338\) 20.9960 1.14203
\(339\) 0 0
\(340\) −8.57798 −0.465207
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0.359220 0.0193679
\(345\) 0 0
\(346\) −12.8282 −0.689649
\(347\) −17.7871 −0.954862 −0.477431 0.878669i \(-0.658432\pi\)
−0.477431 + 0.878669i \(0.658432\pi\)
\(348\) 0 0
\(349\) −11.7341 −0.628110 −0.314055 0.949405i \(-0.601688\pi\)
−0.314055 + 0.949405i \(0.601688\pi\)
\(350\) 10.0401 0.536664
\(351\) 0 0
\(352\) 0 0
\(353\) −15.2682 −0.812642 −0.406321 0.913730i \(-0.633189\pi\)
−0.406321 + 0.913730i \(0.633189\pi\)
\(354\) 0 0
\(355\) −9.01815 −0.478634
\(356\) −10.0804 −0.534261
\(357\) 0 0
\(358\) 10.1894 0.538526
\(359\) 6.74198 0.355828 0.177914 0.984046i \(-0.443065\pi\)
0.177914 + 0.984046i \(0.443065\pi\)
\(360\) 0 0
\(361\) 10.7801 0.567375
\(362\) 17.1708 0.902478
\(363\) 0 0
\(364\) −7.55354 −0.395913
\(365\) 22.6545 1.18579
\(366\) 0 0
\(367\) −20.9743 −1.09485 −0.547424 0.836855i \(-0.684392\pi\)
−0.547424 + 0.836855i \(0.684392\pi\)
\(368\) 0.121250 0.00632062
\(369\) 0 0
\(370\) 8.64205 0.449279
\(371\) 4.71404 0.244741
\(372\) 0 0
\(373\) −29.1253 −1.50805 −0.754027 0.656844i \(-0.771891\pi\)
−0.754027 + 0.656844i \(0.771891\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 23.9154 1.23334
\(377\) 28.9238 1.48965
\(378\) 0 0
\(379\) 31.9353 1.64041 0.820203 0.572072i \(-0.193860\pi\)
0.820203 + 0.572072i \(0.193860\pi\)
\(380\) 27.5096 1.41121
\(381\) 0 0
\(382\) −6.06806 −0.310469
\(383\) −3.58968 −0.183424 −0.0917121 0.995786i \(-0.529234\pi\)
−0.0917121 + 0.995786i \(0.529234\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −14.6981 −0.748115
\(387\) 0 0
\(388\) 3.22133 0.163538
\(389\) −10.4710 −0.530901 −0.265451 0.964124i \(-0.585521\pi\)
−0.265451 + 0.964124i \(0.585521\pi\)
\(390\) 0 0
\(391\) 10.8760 0.550022
\(392\) −2.82426 −0.142647
\(393\) 0 0
\(394\) 5.59697 0.281971
\(395\) −25.4890 −1.28249
\(396\) 0 0
\(397\) 17.7269 0.889686 0.444843 0.895609i \(-0.353259\pi\)
0.444843 + 0.895609i \(0.353259\pi\)
\(398\) −11.5614 −0.579522
\(399\) 0 0
\(400\) 0.218522 0.0109261
\(401\) −8.08035 −0.403513 −0.201757 0.979436i \(-0.564665\pi\)
−0.201757 + 0.979436i \(0.564665\pi\)
\(402\) 0 0
\(403\) −26.5715 −1.32362
\(404\) 7.47375 0.371833
\(405\) 0 0
\(406\) 4.13955 0.205442
\(407\) 0 0
\(408\) 0 0
\(409\) −39.6889 −1.96249 −0.981245 0.192765i \(-0.938254\pi\)
−0.981245 + 0.192765i \(0.938254\pi\)
\(410\) −11.3728 −0.561662
\(411\) 0 0
\(412\) −15.9922 −0.787881
\(413\) −4.63368 −0.228008
\(414\) 0 0
\(415\) −0.519109 −0.0254820
\(416\) 34.5006 1.69153
\(417\) 0 0
\(418\) 0 0
\(419\) −16.1715 −0.790028 −0.395014 0.918675i \(-0.629260\pi\)
−0.395014 + 0.918675i \(0.629260\pi\)
\(420\) 0 0
\(421\) 24.8084 1.20909 0.604544 0.796572i \(-0.293355\pi\)
0.604544 + 0.796572i \(0.293355\pi\)
\(422\) −2.53775 −0.123536
\(423\) 0 0
\(424\) −13.3137 −0.646570
\(425\) 19.6011 0.950794
\(426\) 0 0
\(427\) −5.31081 −0.257008
\(428\) 6.63265 0.320601
\(429\) 0 0
\(430\) −0.450576 −0.0217287
\(431\) 21.8821 1.05402 0.527012 0.849858i \(-0.323312\pi\)
0.527012 + 0.849858i \(0.323312\pi\)
\(432\) 0 0
\(433\) 39.3439 1.89075 0.945374 0.325989i \(-0.105697\pi\)
0.945374 + 0.325989i \(0.105697\pi\)
\(434\) −3.80289 −0.182544
\(435\) 0 0
\(436\) −1.78819 −0.0856388
\(437\) −34.8793 −1.66850
\(438\) 0 0
\(439\) −9.59194 −0.457799 −0.228899 0.973450i \(-0.573513\pi\)
−0.228899 + 0.973450i \(0.573513\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 9.03244 0.429629
\(443\) 0.629136 0.0298911 0.0149456 0.999888i \(-0.495242\pi\)
0.0149456 + 0.999888i \(0.495242\pi\)
\(444\) 0 0
\(445\) 33.0325 1.56589
\(446\) −2.92484 −0.138495
\(447\) 0 0
\(448\) 4.89975 0.231492
\(449\) 17.3364 0.818154 0.409077 0.912500i \(-0.365851\pi\)
0.409077 + 0.912500i \(0.365851\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 24.2075 1.13863
\(453\) 0 0
\(454\) 2.90934 0.136542
\(455\) 24.7522 1.16040
\(456\) 0 0
\(457\) 29.1154 1.36196 0.680980 0.732302i \(-0.261554\pi\)
0.680980 + 0.732302i \(0.261554\pi\)
\(458\) 5.92816 0.277005
\(459\) 0 0
\(460\) −32.2201 −1.50227
\(461\) 15.1850 0.707236 0.353618 0.935390i \(-0.384951\pi\)
0.353618 + 0.935390i \(0.384951\pi\)
\(462\) 0 0
\(463\) 17.8886 0.831355 0.415677 0.909512i \(-0.363545\pi\)
0.415677 + 0.909512i \(0.363545\pi\)
\(464\) 0.0900974 0.00418267
\(465\) 0 0
\(466\) 5.39134 0.249749
\(467\) 30.3101 1.40259 0.701293 0.712874i \(-0.252607\pi\)
0.701293 + 0.712874i \(0.252607\pi\)
\(468\) 0 0
\(469\) 14.0686 0.649629
\(470\) −29.9975 −1.38368
\(471\) 0 0
\(472\) 13.0867 0.602366
\(473\) 0 0
\(474\) 0 0
\(475\) −62.8609 −2.88425
\(476\) −2.11054 −0.0967362
\(477\) 0 0
\(478\) 17.8491 0.816397
\(479\) −7.94750 −0.363130 −0.181565 0.983379i \(-0.558116\pi\)
−0.181565 + 0.983379i \(0.558116\pi\)
\(480\) 0 0
\(481\) 14.8569 0.677414
\(482\) −0.907456 −0.0413335
\(483\) 0 0
\(484\) 0 0
\(485\) −10.5560 −0.479323
\(486\) 0 0
\(487\) −10.1711 −0.460896 −0.230448 0.973085i \(-0.574019\pi\)
−0.230448 + 0.973085i \(0.574019\pi\)
\(488\) 14.9991 0.678979
\(489\) 0 0
\(490\) 3.54252 0.160035
\(491\) 1.07736 0.0486206 0.0243103 0.999704i \(-0.492261\pi\)
0.0243103 + 0.999704i \(0.492261\pi\)
\(492\) 0 0
\(493\) 8.08161 0.363977
\(494\) −28.9671 −1.30329
\(495\) 0 0
\(496\) −0.0827699 −0.00371648
\(497\) −2.21883 −0.0995283
\(498\) 0 0
\(499\) 34.6159 1.54962 0.774810 0.632194i \(-0.217845\pi\)
0.774810 + 0.632194i \(0.217845\pi\)
\(500\) −32.8629 −1.46968
\(501\) 0 0
\(502\) −5.78136 −0.258035
\(503\) 2.75919 0.123026 0.0615130 0.998106i \(-0.480407\pi\)
0.0615130 + 0.998106i \(0.480407\pi\)
\(504\) 0 0
\(505\) −24.4908 −1.08982
\(506\) 0 0
\(507\) 0 0
\(508\) −0.795920 −0.0353132
\(509\) −14.5914 −0.646753 −0.323377 0.946270i \(-0.604818\pi\)
−0.323377 + 0.946270i \(0.604818\pi\)
\(510\) 0 0
\(511\) 5.57393 0.246576
\(512\) 0.214624 0.00948514
\(513\) 0 0
\(514\) −2.51237 −0.110816
\(515\) 52.4051 2.30924
\(516\) 0 0
\(517\) 0 0
\(518\) 2.12630 0.0934242
\(519\) 0 0
\(520\) −69.9069 −3.06562
\(521\) 13.7317 0.601599 0.300799 0.953687i \(-0.402747\pi\)
0.300799 + 0.953687i \(0.402747\pi\)
\(522\) 0 0
\(523\) −7.54609 −0.329967 −0.164984 0.986296i \(-0.552757\pi\)
−0.164984 + 0.986296i \(0.552757\pi\)
\(524\) 17.3627 0.758493
\(525\) 0 0
\(526\) −18.3924 −0.801946
\(527\) −7.42434 −0.323409
\(528\) 0 0
\(529\) 17.8517 0.776160
\(530\) 16.6996 0.725383
\(531\) 0 0
\(532\) 6.76849 0.293451
\(533\) −19.5513 −0.846863
\(534\) 0 0
\(535\) −21.7346 −0.939668
\(536\) −39.7335 −1.71623
\(537\) 0 0
\(538\) 14.9319 0.643760
\(539\) 0 0
\(540\) 0 0
\(541\) 2.01679 0.0867084 0.0433542 0.999060i \(-0.486196\pi\)
0.0433542 + 0.999060i \(0.486196\pi\)
\(542\) −14.2593 −0.612490
\(543\) 0 0
\(544\) 9.63981 0.413304
\(545\) 5.85973 0.251003
\(546\) 0 0
\(547\) −41.1514 −1.75951 −0.879754 0.475429i \(-0.842293\pi\)
−0.879754 + 0.475429i \(0.842293\pi\)
\(548\) −3.34904 −0.143064
\(549\) 0 0
\(550\) 0 0
\(551\) −25.9177 −1.10413
\(552\) 0 0
\(553\) −6.27134 −0.266684
\(554\) 2.16029 0.0917818
\(555\) 0 0
\(556\) −2.55741 −0.108458
\(557\) −18.4609 −0.782214 −0.391107 0.920345i \(-0.627908\pi\)
−0.391107 + 0.920345i \(0.627908\pi\)
\(558\) 0 0
\(559\) −0.774600 −0.0327621
\(560\) 0.0771030 0.00325819
\(561\) 0 0
\(562\) 21.0883 0.889557
\(563\) −28.5154 −1.20178 −0.600890 0.799332i \(-0.705187\pi\)
−0.600890 + 0.799332i \(0.705187\pi\)
\(564\) 0 0
\(565\) −79.3258 −3.33726
\(566\) 25.4385 1.06926
\(567\) 0 0
\(568\) 6.26658 0.262940
\(569\) 17.7384 0.743631 0.371816 0.928307i \(-0.378735\pi\)
0.371816 + 0.928307i \(0.378735\pi\)
\(570\) 0 0
\(571\) 20.8488 0.872496 0.436248 0.899827i \(-0.356307\pi\)
0.436248 + 0.899827i \(0.356307\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −2.79817 −0.116793
\(575\) 73.6244 3.07035
\(576\) 0 0
\(577\) 21.2988 0.886680 0.443340 0.896353i \(-0.353793\pi\)
0.443340 + 0.896353i \(0.353793\pi\)
\(578\) −12.2935 −0.511343
\(579\) 0 0
\(580\) −23.9417 −0.994126
\(581\) −0.127722 −0.00529880
\(582\) 0 0
\(583\) 0 0
\(584\) −15.7422 −0.651419
\(585\) 0 0
\(586\) −23.7005 −0.979058
\(587\) −29.1874 −1.20469 −0.602346 0.798235i \(-0.705767\pi\)
−0.602346 + 0.798235i \(0.705767\pi\)
\(588\) 0 0
\(589\) 23.8099 0.981069
\(590\) −16.4149 −0.675790
\(591\) 0 0
\(592\) 0.0462789 0.00190205
\(593\) −37.3094 −1.53212 −0.766058 0.642772i \(-0.777784\pi\)
−0.766058 + 0.642772i \(0.777784\pi\)
\(594\) 0 0
\(595\) 6.91602 0.283529
\(596\) −12.5059 −0.512263
\(597\) 0 0
\(598\) 33.9271 1.38738
\(599\) 4.95368 0.202402 0.101201 0.994866i \(-0.467731\pi\)
0.101201 + 0.994866i \(0.467731\pi\)
\(600\) 0 0
\(601\) −29.4572 −1.20158 −0.600792 0.799405i \(-0.705148\pi\)
−0.600792 + 0.799405i \(0.705148\pi\)
\(602\) −0.110860 −0.00451832
\(603\) 0 0
\(604\) −18.5598 −0.755189
\(605\) 0 0
\(606\) 0 0
\(607\) 26.3426 1.06921 0.534606 0.845101i \(-0.320460\pi\)
0.534606 + 0.845101i \(0.320460\pi\)
\(608\) −30.9149 −1.25377
\(609\) 0 0
\(610\) −18.8136 −0.761742
\(611\) −51.5697 −2.08629
\(612\) 0 0
\(613\) −48.2089 −1.94714 −0.973569 0.228391i \(-0.926653\pi\)
−0.973569 + 0.228391i \(0.926653\pi\)
\(614\) 8.67563 0.350120
\(615\) 0 0
\(616\) 0 0
\(617\) 29.2376 1.17706 0.588532 0.808474i \(-0.299706\pi\)
0.588532 + 0.808474i \(0.299706\pi\)
\(618\) 0 0
\(619\) 6.14388 0.246943 0.123472 0.992348i \(-0.460597\pi\)
0.123472 + 0.992348i \(0.460597\pi\)
\(620\) 21.9946 0.883323
\(621\) 0 0
\(622\) −14.1554 −0.567581
\(623\) 8.12736 0.325616
\(624\) 0 0
\(625\) 50.0934 2.00374
\(626\) 14.4815 0.578799
\(627\) 0 0
\(628\) −24.1289 −0.962849
\(629\) 4.15115 0.165517
\(630\) 0 0
\(631\) 40.5646 1.61485 0.807425 0.589971i \(-0.200861\pi\)
0.807425 + 0.589971i \(0.200861\pi\)
\(632\) 17.7119 0.704542
\(633\) 0 0
\(634\) −7.06001 −0.280389
\(635\) 2.60815 0.103501
\(636\) 0 0
\(637\) 6.09006 0.241297
\(638\) 0 0
\(639\) 0 0
\(640\) −28.6923 −1.13416
\(641\) −23.5266 −0.929244 −0.464622 0.885509i \(-0.653810\pi\)
−0.464622 + 0.885509i \(0.653810\pi\)
\(642\) 0 0
\(643\) −21.0143 −0.828724 −0.414362 0.910112i \(-0.635995\pi\)
−0.414362 + 0.910112i \(0.635995\pi\)
\(644\) −7.92745 −0.312385
\(645\) 0 0
\(646\) −8.09369 −0.318442
\(647\) −0.452722 −0.0177983 −0.00889917 0.999960i \(-0.502833\pi\)
−0.00889917 + 0.999960i \(0.502833\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 61.1446 2.39829
\(651\) 0 0
\(652\) −15.0206 −0.588253
\(653\) 22.0408 0.862522 0.431261 0.902227i \(-0.358069\pi\)
0.431261 + 0.902227i \(0.358069\pi\)
\(654\) 0 0
\(655\) −56.8959 −2.22311
\(656\) −0.0609022 −0.00237783
\(657\) 0 0
\(658\) −7.38061 −0.287726
\(659\) 18.3859 0.716215 0.358107 0.933680i \(-0.383422\pi\)
0.358107 + 0.933680i \(0.383422\pi\)
\(660\) 0 0
\(661\) −45.9605 −1.78766 −0.893829 0.448408i \(-0.851991\pi\)
−0.893829 + 0.448408i \(0.851991\pi\)
\(662\) −5.79273 −0.225141
\(663\) 0 0
\(664\) 0.360721 0.0139987
\(665\) −22.1797 −0.860092
\(666\) 0 0
\(667\) 30.3556 1.17537
\(668\) 16.3323 0.631917
\(669\) 0 0
\(670\) 49.8384 1.92542
\(671\) 0 0
\(672\) 0 0
\(673\) −29.7402 −1.14640 −0.573200 0.819415i \(-0.694298\pi\)
−0.573200 + 0.819415i \(0.694298\pi\)
\(674\) 18.2619 0.703422
\(675\) 0 0
\(676\) −29.8776 −1.14914
\(677\) 27.7828 1.06778 0.533889 0.845554i \(-0.320730\pi\)
0.533889 + 0.845554i \(0.320730\pi\)
\(678\) 0 0
\(679\) −2.59721 −0.0996716
\(680\) −19.5327 −0.749044
\(681\) 0 0
\(682\) 0 0
\(683\) −40.8297 −1.56231 −0.781153 0.624339i \(-0.785368\pi\)
−0.781153 + 0.624339i \(0.785368\pi\)
\(684\) 0 0
\(685\) 10.9745 0.419313
\(686\) 0.871604 0.0332780
\(687\) 0 0
\(688\) −0.00241287 −9.19898e−5 0
\(689\) 28.7088 1.09372
\(690\) 0 0
\(691\) 37.8156 1.43857 0.719286 0.694714i \(-0.244469\pi\)
0.719286 + 0.694714i \(0.244469\pi\)
\(692\) 18.2547 0.693941
\(693\) 0 0
\(694\) −15.5033 −0.588498
\(695\) 8.38039 0.317886
\(696\) 0 0
\(697\) −5.46284 −0.206920
\(698\) −10.2275 −0.387115
\(699\) 0 0
\(700\) −14.2872 −0.540004
\(701\) 27.4256 1.03585 0.517926 0.855426i \(-0.326704\pi\)
0.517926 + 0.855426i \(0.326704\pi\)
\(702\) 0 0
\(703\) −13.3128 −0.502100
\(704\) 0 0
\(705\) 0 0
\(706\) −13.3078 −0.500845
\(707\) −6.02573 −0.226621
\(708\) 0 0
\(709\) −31.8439 −1.19592 −0.597962 0.801525i \(-0.704022\pi\)
−0.597962 + 0.801525i \(0.704022\pi\)
\(710\) −7.86026 −0.294990
\(711\) 0 0
\(712\) −22.9538 −0.860230
\(713\) −27.8868 −1.04437
\(714\) 0 0
\(715\) 0 0
\(716\) −14.4996 −0.541877
\(717\) 0 0
\(718\) 5.87633 0.219303
\(719\) 15.2468 0.568608 0.284304 0.958734i \(-0.408237\pi\)
0.284304 + 0.958734i \(0.408237\pi\)
\(720\) 0 0
\(721\) 12.8938 0.480190
\(722\) 9.39600 0.349683
\(723\) 0 0
\(724\) −24.4343 −0.908095
\(725\) 54.7080 2.03180
\(726\) 0 0
\(727\) −33.7158 −1.25045 −0.625225 0.780445i \(-0.714993\pi\)
−0.625225 + 0.780445i \(0.714993\pi\)
\(728\) −17.2000 −0.637473
\(729\) 0 0
\(730\) 19.7457 0.730823
\(731\) −0.216431 −0.00800499
\(732\) 0 0
\(733\) 4.51648 0.166820 0.0834101 0.996515i \(-0.473419\pi\)
0.0834101 + 0.996515i \(0.473419\pi\)
\(734\) −18.2813 −0.674774
\(735\) 0 0
\(736\) 36.2084 1.33466
\(737\) 0 0
\(738\) 0 0
\(739\) −10.0400 −0.369327 −0.184664 0.982802i \(-0.559120\pi\)
−0.184664 + 0.982802i \(0.559120\pi\)
\(740\) −12.2978 −0.452075
\(741\) 0 0
\(742\) 4.10878 0.150838
\(743\) −15.7027 −0.576076 −0.288038 0.957619i \(-0.593003\pi\)
−0.288038 + 0.957619i \(0.593003\pi\)
\(744\) 0 0
\(745\) 40.9808 1.50142
\(746\) −25.3858 −0.929439
\(747\) 0 0
\(748\) 0 0
\(749\) −5.34760 −0.195397
\(750\) 0 0
\(751\) 19.2780 0.703466 0.351733 0.936100i \(-0.385593\pi\)
0.351733 + 0.936100i \(0.385593\pi\)
\(752\) −0.160639 −0.00585790
\(753\) 0 0
\(754\) 25.2101 0.918099
\(755\) 60.8188 2.21342
\(756\) 0 0
\(757\) 37.5431 1.36453 0.682263 0.731106i \(-0.260996\pi\)
0.682263 + 0.731106i \(0.260996\pi\)
\(758\) 27.8350 1.01101
\(759\) 0 0
\(760\) 62.6414 2.27224
\(761\) −38.7469 −1.40458 −0.702288 0.711893i \(-0.747838\pi\)
−0.702288 + 0.711893i \(0.747838\pi\)
\(762\) 0 0
\(763\) 1.44173 0.0521942
\(764\) 8.63494 0.312401
\(765\) 0 0
\(766\) −3.12878 −0.113048
\(767\) −28.2194 −1.01894
\(768\) 0 0
\(769\) 24.0014 0.865513 0.432756 0.901511i \(-0.357541\pi\)
0.432756 + 0.901511i \(0.357541\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 20.9156 0.752770
\(773\) 39.2714 1.41250 0.706248 0.707965i \(-0.250387\pi\)
0.706248 + 0.707965i \(0.250387\pi\)
\(774\) 0 0
\(775\) −50.2587 −1.80534
\(776\) 7.33520 0.263318
\(777\) 0 0
\(778\) −9.12658 −0.327204
\(779\) 17.5194 0.627696
\(780\) 0 0
\(781\) 0 0
\(782\) 9.47956 0.338988
\(783\) 0 0
\(784\) 0.0189705 0.000677517 0
\(785\) 79.0682 2.82207
\(786\) 0 0
\(787\) −25.4235 −0.906251 −0.453125 0.891447i \(-0.649691\pi\)
−0.453125 + 0.891447i \(0.649691\pi\)
\(788\) −7.96457 −0.283726
\(789\) 0 0
\(790\) −22.2163 −0.790422
\(791\) −19.5174 −0.693959
\(792\) 0 0
\(793\) −32.3432 −1.14854
\(794\) 15.4508 0.548329
\(795\) 0 0
\(796\) 16.4521 0.583128
\(797\) 36.7626 1.30220 0.651099 0.758993i \(-0.274308\pi\)
0.651099 + 0.758993i \(0.274308\pi\)
\(798\) 0 0
\(799\) −14.4091 −0.509757
\(800\) 65.2562 2.30716
\(801\) 0 0
\(802\) −7.04287 −0.248692
\(803\) 0 0
\(804\) 0 0
\(805\) 25.9775 0.915587
\(806\) −23.1598 −0.815770
\(807\) 0 0
\(808\) 17.0183 0.598700
\(809\) −40.4785 −1.42315 −0.711574 0.702612i \(-0.752017\pi\)
−0.711574 + 0.702612i \(0.752017\pi\)
\(810\) 0 0
\(811\) 9.55021 0.335353 0.167677 0.985842i \(-0.446374\pi\)
0.167677 + 0.985842i \(0.446374\pi\)
\(812\) −5.89064 −0.206721
\(813\) 0 0
\(814\) 0 0
\(815\) 49.2212 1.72414
\(816\) 0 0
\(817\) 0.694095 0.0242833
\(818\) −34.5930 −1.20952
\(819\) 0 0
\(820\) 16.1836 0.565157
\(821\) −36.2589 −1.26544 −0.632722 0.774379i \(-0.718062\pi\)
−0.632722 + 0.774379i \(0.718062\pi\)
\(822\) 0 0
\(823\) −41.7383 −1.45491 −0.727454 0.686157i \(-0.759296\pi\)
−0.727454 + 0.686157i \(0.759296\pi\)
\(824\) −36.4155 −1.26859
\(825\) 0 0
\(826\) −4.03873 −0.140525
\(827\) 28.2659 0.982901 0.491450 0.870906i \(-0.336467\pi\)
0.491450 + 0.870906i \(0.336467\pi\)
\(828\) 0 0
\(829\) −2.01036 −0.0698226 −0.0349113 0.999390i \(-0.511115\pi\)
−0.0349113 + 0.999390i \(0.511115\pi\)
\(830\) −0.452457 −0.0157050
\(831\) 0 0
\(832\) 29.8398 1.03451
\(833\) 1.70162 0.0589578
\(834\) 0 0
\(835\) −53.5195 −1.85212
\(836\) 0 0
\(837\) 0 0
\(838\) −14.0951 −0.486908
\(839\) 24.2099 0.835818 0.417909 0.908489i \(-0.362763\pi\)
0.417909 + 0.908489i \(0.362763\pi\)
\(840\) 0 0
\(841\) −6.44371 −0.222197
\(842\) 21.6231 0.745182
\(843\) 0 0
\(844\) 3.61125 0.124304
\(845\) 97.9060 3.36807
\(846\) 0 0
\(847\) 0 0
\(848\) 0.0894276 0.00307096
\(849\) 0 0
\(850\) 17.0844 0.585991
\(851\) 15.5923 0.534497
\(852\) 0 0
\(853\) −20.1429 −0.689680 −0.344840 0.938662i \(-0.612067\pi\)
−0.344840 + 0.938662i \(0.612067\pi\)
\(854\) −4.62893 −0.158399
\(855\) 0 0
\(856\) 15.1030 0.516211
\(857\) −26.6092 −0.908953 −0.454477 0.890759i \(-0.650174\pi\)
−0.454477 + 0.890759i \(0.650174\pi\)
\(858\) 0 0
\(859\) 14.4645 0.493522 0.246761 0.969076i \(-0.420634\pi\)
0.246761 + 0.969076i \(0.420634\pi\)
\(860\) 0.641176 0.0218639
\(861\) 0 0
\(862\) 19.0725 0.649614
\(863\) −28.3624 −0.965466 −0.482733 0.875768i \(-0.660356\pi\)
−0.482733 + 0.875768i \(0.660356\pi\)
\(864\) 0 0
\(865\) −59.8190 −2.03391
\(866\) 34.2923 1.16530
\(867\) 0 0
\(868\) 5.41156 0.183680
\(869\) 0 0
\(870\) 0 0
\(871\) 85.6789 2.90312
\(872\) −4.07184 −0.137890
\(873\) 0 0
\(874\) −30.4010 −1.02833
\(875\) 26.4958 0.895723
\(876\) 0 0
\(877\) −10.1417 −0.342461 −0.171231 0.985231i \(-0.554774\pi\)
−0.171231 + 0.985231i \(0.554774\pi\)
\(878\) −8.36038 −0.282149
\(879\) 0 0
\(880\) 0 0
\(881\) 3.71883 0.125291 0.0626453 0.998036i \(-0.480046\pi\)
0.0626453 + 0.998036i \(0.480046\pi\)
\(882\) 0 0
\(883\) 17.3305 0.583218 0.291609 0.956538i \(-0.405809\pi\)
0.291609 + 0.956538i \(0.405809\pi\)
\(884\) −12.8533 −0.432303
\(885\) 0 0
\(886\) 0.548358 0.0184224
\(887\) −5.40696 −0.181548 −0.0907740 0.995872i \(-0.528934\pi\)
−0.0907740 + 0.995872i \(0.528934\pi\)
\(888\) 0 0
\(889\) 0.641713 0.0215224
\(890\) 28.7913 0.965087
\(891\) 0 0
\(892\) 4.16210 0.139357
\(893\) 46.2100 1.54636
\(894\) 0 0
\(895\) 47.5139 1.58822
\(896\) −7.05948 −0.235841
\(897\) 0 0
\(898\) 15.1105 0.504242
\(899\) −20.7218 −0.691111
\(900\) 0 0
\(901\) 8.02152 0.267236
\(902\) 0 0
\(903\) 0 0
\(904\) 55.1223 1.83334
\(905\) 80.0690 2.66158
\(906\) 0 0
\(907\) −10.7020 −0.355353 −0.177677 0.984089i \(-0.556858\pi\)
−0.177677 + 0.984089i \(0.556858\pi\)
\(908\) −4.14003 −0.137392
\(909\) 0 0
\(910\) 21.5742 0.715177
\(911\) 27.5708 0.913463 0.456732 0.889605i \(-0.349020\pi\)
0.456732 + 0.889605i \(0.349020\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 25.3771 0.839400
\(915\) 0 0
\(916\) −8.43586 −0.278729
\(917\) −13.9987 −0.462278
\(918\) 0 0
\(919\) −36.4021 −1.20080 −0.600398 0.799702i \(-0.704991\pi\)
−0.600398 + 0.799702i \(0.704991\pi\)
\(920\) −73.3674 −2.41885
\(921\) 0 0
\(922\) 13.2353 0.435882
\(923\) −13.5128 −0.444781
\(924\) 0 0
\(925\) 28.1010 0.923956
\(926\) 15.5918 0.512378
\(927\) 0 0
\(928\) 26.9054 0.883211
\(929\) −26.2401 −0.860910 −0.430455 0.902612i \(-0.641647\pi\)
−0.430455 + 0.902612i \(0.641647\pi\)
\(930\) 0 0
\(931\) −5.45712 −0.178850
\(932\) −7.67195 −0.251303
\(933\) 0 0
\(934\) 26.4184 0.864437
\(935\) 0 0
\(936\) 0 0
\(937\) −23.8799 −0.780121 −0.390061 0.920789i \(-0.627546\pi\)
−0.390061 + 0.920789i \(0.627546\pi\)
\(938\) 12.2623 0.400378
\(939\) 0 0
\(940\) 42.6869 1.39229
\(941\) 17.7793 0.579588 0.289794 0.957089i \(-0.406413\pi\)
0.289794 + 0.957089i \(0.406413\pi\)
\(942\) 0 0
\(943\) −20.5192 −0.668196
\(944\) −0.0879031 −0.00286100
\(945\) 0 0
\(946\) 0 0
\(947\) −31.7071 −1.03034 −0.515171 0.857088i \(-0.672271\pi\)
−0.515171 + 0.857088i \(0.672271\pi\)
\(948\) 0 0
\(949\) 33.9456 1.10192
\(950\) −54.7898 −1.77762
\(951\) 0 0
\(952\) −4.80584 −0.155758
\(953\) −3.28213 −0.106319 −0.0531593 0.998586i \(-0.516929\pi\)
−0.0531593 + 0.998586i \(0.516929\pi\)
\(954\) 0 0
\(955\) −28.2959 −0.915633
\(956\) −25.3995 −0.821478
\(957\) 0 0
\(958\) −6.92707 −0.223804
\(959\) 2.70017 0.0871931
\(960\) 0 0
\(961\) −11.9635 −0.385918
\(962\) 12.9493 0.417502
\(963\) 0 0
\(964\) 1.29132 0.0415907
\(965\) −68.5386 −2.20633
\(966\) 0 0
\(967\) 3.83683 0.123384 0.0616921 0.998095i \(-0.480350\pi\)
0.0616921 + 0.998095i \(0.480350\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −9.20065 −0.295415
\(971\) −44.3268 −1.42251 −0.711257 0.702932i \(-0.751874\pi\)
−0.711257 + 0.702932i \(0.751874\pi\)
\(972\) 0 0
\(973\) 2.06192 0.0661021
\(974\) −8.86517 −0.284058
\(975\) 0 0
\(976\) −0.100749 −0.00322489
\(977\) −9.69774 −0.310258 −0.155129 0.987894i \(-0.549579\pi\)
−0.155129 + 0.987894i \(0.549579\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −5.04106 −0.161031
\(981\) 0 0
\(982\) 0.939032 0.0299657
\(983\) −28.6752 −0.914597 −0.457298 0.889313i \(-0.651183\pi\)
−0.457298 + 0.889313i \(0.651183\pi\)
\(984\) 0 0
\(985\) 26.0991 0.831587
\(986\) 7.04396 0.224325
\(987\) 0 0
\(988\) 41.2206 1.31140
\(989\) −0.812944 −0.0258501
\(990\) 0 0
\(991\) −14.0455 −0.446170 −0.223085 0.974799i \(-0.571613\pi\)
−0.223085 + 0.974799i \(0.571613\pi\)
\(992\) −24.7172 −0.784771
\(993\) 0 0
\(994\) −1.93395 −0.0613410
\(995\) −53.9119 −1.70912
\(996\) 0 0
\(997\) 36.2102 1.14679 0.573394 0.819280i \(-0.305626\pi\)
0.573394 + 0.819280i \(0.305626\pi\)
\(998\) 30.1714 0.955058
\(999\) 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.cy.1.7 10
3.2 odd 2 2541.2.a.br.1.4 10
11.2 odd 10 693.2.m.j.631.4 20
11.6 odd 10 693.2.m.j.190.4 20
11.10 odd 2 7623.2.a.cx.1.4 10
33.2 even 10 231.2.j.g.169.2 20
33.17 even 10 231.2.j.g.190.2 yes 20
33.32 even 2 2541.2.a.bq.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.j.g.169.2 20 33.2 even 10
231.2.j.g.190.2 yes 20 33.17 even 10
693.2.m.j.190.4 20 11.6 odd 10
693.2.m.j.631.4 20 11.2 odd 10
2541.2.a.bq.1.7 10 33.32 even 2
2541.2.a.br.1.4 10 3.2 odd 2
7623.2.a.cx.1.4 10 11.10 odd 2
7623.2.a.cy.1.7 10 1.1 even 1 trivial