Properties

Label 7623.2.a.cy.1.10
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 1.10
Root \(2.79866\)
Character \(\chi\) = 7623.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.79866 q^{2} +5.83249 q^{4} +1.67767 q^{5} +1.00000 q^{7} +10.7258 q^{8} +O(q^{10})\) \(q+2.79866 q^{2} +5.83249 q^{4} +1.67767 q^{5} +1.00000 q^{7} +10.7258 q^{8} +4.69523 q^{10} -5.87113 q^{13} +2.79866 q^{14} +18.3530 q^{16} -0.304169 q^{17} +4.62860 q^{19} +9.78502 q^{20} +1.38164 q^{23} -2.18541 q^{25} -16.4313 q^{26} +5.83249 q^{28} +3.96868 q^{29} +0.764099 q^{31} +29.9121 q^{32} -0.851264 q^{34} +1.67767 q^{35} +3.21023 q^{37} +12.9539 q^{38} +17.9945 q^{40} -8.31274 q^{41} +1.01069 q^{43} +3.86674 q^{46} +2.58688 q^{47} +1.00000 q^{49} -6.11623 q^{50} -34.2434 q^{52} +1.45374 q^{53} +10.7258 q^{56} +11.1070 q^{58} +2.49444 q^{59} -3.39295 q^{61} +2.13845 q^{62} +47.0078 q^{64} -9.84984 q^{65} +6.16878 q^{67} -1.77406 q^{68} +4.69523 q^{70} -7.59943 q^{71} +12.7455 q^{73} +8.98434 q^{74} +26.9963 q^{76} +6.15519 q^{79} +30.7903 q^{80} -23.2645 q^{82} -2.01266 q^{83} -0.510295 q^{85} +2.82859 q^{86} -0.0843908 q^{89} -5.87113 q^{91} +8.05840 q^{92} +7.23980 q^{94} +7.76527 q^{95} +1.03775 q^{97} +2.79866 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 18q^{4} - 5q^{5} + 10q^{7} + 3q^{8} + O(q^{10}) \) \( 10q + 18q^{4} - 5q^{5} + 10q^{7} + 3q^{8} - 6q^{10} + 6q^{13} + 38q^{16} - 8q^{17} - 7q^{20} + 31q^{25} - q^{26} + 18q^{28} + 14q^{29} + 26q^{31} + 41q^{32} + 21q^{34} - 5q^{35} + 24q^{37} - 8q^{38} - 5q^{40} - 19q^{41} - 6q^{43} - q^{46} - 15q^{47} + 10q^{49} + q^{50} - 25q^{52} + q^{53} + 3q^{56} + 11q^{58} - 23q^{59} - 11q^{62} + 53q^{64} + 29q^{65} + 38q^{67} - 87q^{68} - 6q^{70} - 26q^{71} - q^{73} + 39q^{74} - 2q^{76} + 5q^{79} - 6q^{80} + 5q^{82} - 6q^{83} - q^{85} + 41q^{86} + 9q^{89} + 6q^{91} + 48q^{92} + 42q^{95} + 24q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.79866 1.97895 0.989476 0.144700i \(-0.0462218\pi\)
0.989476 + 0.144700i \(0.0462218\pi\)
\(3\) 0 0
\(4\) 5.83249 2.91625
\(5\) 1.67767 0.750278 0.375139 0.926969i \(-0.377595\pi\)
0.375139 + 0.926969i \(0.377595\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 10.7258 3.79216
\(9\) 0 0
\(10\) 4.69523 1.48476
\(11\) 0 0
\(12\) 0 0
\(13\) −5.87113 −1.62836 −0.814180 0.580613i \(-0.802813\pi\)
−0.814180 + 0.580613i \(0.802813\pi\)
\(14\) 2.79866 0.747973
\(15\) 0 0
\(16\) 18.3530 4.58825
\(17\) −0.304169 −0.0737717 −0.0368859 0.999319i \(-0.511744\pi\)
−0.0368859 + 0.999319i \(0.511744\pi\)
\(18\) 0 0
\(19\) 4.62860 1.06187 0.530937 0.847411i \(-0.321840\pi\)
0.530937 + 0.847411i \(0.321840\pi\)
\(20\) 9.78502 2.18800
\(21\) 0 0
\(22\) 0 0
\(23\) 1.38164 0.288092 0.144046 0.989571i \(-0.453989\pi\)
0.144046 + 0.989571i \(0.453989\pi\)
\(24\) 0 0
\(25\) −2.18541 −0.437083
\(26\) −16.4313 −3.22244
\(27\) 0 0
\(28\) 5.83249 1.10224
\(29\) 3.96868 0.736965 0.368483 0.929635i \(-0.379877\pi\)
0.368483 + 0.929635i \(0.379877\pi\)
\(30\) 0 0
\(31\) 0.764099 0.137236 0.0686181 0.997643i \(-0.478141\pi\)
0.0686181 + 0.997643i \(0.478141\pi\)
\(32\) 29.9121 5.28776
\(33\) 0 0
\(34\) −0.851264 −0.145991
\(35\) 1.67767 0.283578
\(36\) 0 0
\(37\) 3.21023 0.527759 0.263879 0.964556i \(-0.414998\pi\)
0.263879 + 0.964556i \(0.414998\pi\)
\(38\) 12.9539 2.10140
\(39\) 0 0
\(40\) 17.9945 2.84517
\(41\) −8.31274 −1.29823 −0.649116 0.760690i \(-0.724861\pi\)
−0.649116 + 0.760690i \(0.724861\pi\)
\(42\) 0 0
\(43\) 1.01069 0.154129 0.0770647 0.997026i \(-0.475445\pi\)
0.0770647 + 0.997026i \(0.475445\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 3.86674 0.570119
\(47\) 2.58688 0.377335 0.188668 0.982041i \(-0.439583\pi\)
0.188668 + 0.982041i \(0.439583\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −6.11623 −0.864966
\(51\) 0 0
\(52\) −34.2434 −4.74870
\(53\) 1.45374 0.199686 0.0998430 0.995003i \(-0.468166\pi\)
0.0998430 + 0.995003i \(0.468166\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 10.7258 1.43330
\(57\) 0 0
\(58\) 11.1070 1.45842
\(59\) 2.49444 0.324749 0.162374 0.986729i \(-0.448085\pi\)
0.162374 + 0.986729i \(0.448085\pi\)
\(60\) 0 0
\(61\) −3.39295 −0.434423 −0.217211 0.976125i \(-0.569696\pi\)
−0.217211 + 0.976125i \(0.569696\pi\)
\(62\) 2.13845 0.271584
\(63\) 0 0
\(64\) 47.0078 5.87598
\(65\) −9.84984 −1.22172
\(66\) 0 0
\(67\) 6.16878 0.753636 0.376818 0.926287i \(-0.377018\pi\)
0.376818 + 0.926287i \(0.377018\pi\)
\(68\) −1.77406 −0.215137
\(69\) 0 0
\(70\) 4.69523 0.561188
\(71\) −7.59943 −0.901886 −0.450943 0.892553i \(-0.648912\pi\)
−0.450943 + 0.892553i \(0.648912\pi\)
\(72\) 0 0
\(73\) 12.7455 1.49175 0.745877 0.666084i \(-0.232031\pi\)
0.745877 + 0.666084i \(0.232031\pi\)
\(74\) 8.98434 1.04441
\(75\) 0 0
\(76\) 26.9963 3.09669
\(77\) 0 0
\(78\) 0 0
\(79\) 6.15519 0.692512 0.346256 0.938140i \(-0.387453\pi\)
0.346256 + 0.938140i \(0.387453\pi\)
\(80\) 30.7903 3.44246
\(81\) 0 0
\(82\) −23.2645 −2.56914
\(83\) −2.01266 −0.220918 −0.110459 0.993881i \(-0.535232\pi\)
−0.110459 + 0.993881i \(0.535232\pi\)
\(84\) 0 0
\(85\) −0.510295 −0.0553493
\(86\) 2.82859 0.305014
\(87\) 0 0
\(88\) 0 0
\(89\) −0.0843908 −0.00894541 −0.00447270 0.999990i \(-0.501424\pi\)
−0.00447270 + 0.999990i \(0.501424\pi\)
\(90\) 0 0
\(91\) −5.87113 −0.615462
\(92\) 8.05840 0.840146
\(93\) 0 0
\(94\) 7.23980 0.746728
\(95\) 7.76527 0.796700
\(96\) 0 0
\(97\) 1.03775 0.105367 0.0526837 0.998611i \(-0.483223\pi\)
0.0526837 + 0.998611i \(0.483223\pi\)
\(98\) 2.79866 0.282707
\(99\) 0 0
\(100\) −12.7464 −1.27464
\(101\) −19.6972 −1.95994 −0.979971 0.199139i \(-0.936185\pi\)
−0.979971 + 0.199139i \(0.936185\pi\)
\(102\) 0 0
\(103\) −2.41267 −0.237727 −0.118864 0.992911i \(-0.537925\pi\)
−0.118864 + 0.992911i \(0.537925\pi\)
\(104\) −62.9729 −6.17500
\(105\) 0 0
\(106\) 4.06851 0.395169
\(107\) −9.26256 −0.895445 −0.447723 0.894172i \(-0.647765\pi\)
−0.447723 + 0.894172i \(0.647765\pi\)
\(108\) 0 0
\(109\) 8.30530 0.795503 0.397752 0.917493i \(-0.369791\pi\)
0.397752 + 0.917493i \(0.369791\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 18.3530 1.73420
\(113\) −5.47962 −0.515479 −0.257740 0.966214i \(-0.582978\pi\)
−0.257740 + 0.966214i \(0.582978\pi\)
\(114\) 0 0
\(115\) 2.31794 0.216149
\(116\) 23.1473 2.14917
\(117\) 0 0
\(118\) 6.98110 0.642662
\(119\) −0.304169 −0.0278831
\(120\) 0 0
\(121\) 0 0
\(122\) −9.49572 −0.859702
\(123\) 0 0
\(124\) 4.45660 0.400215
\(125\) −12.0548 −1.07821
\(126\) 0 0
\(127\) −20.0576 −1.77983 −0.889913 0.456130i \(-0.849235\pi\)
−0.889913 + 0.456130i \(0.849235\pi\)
\(128\) 71.7346 6.34050
\(129\) 0 0
\(130\) −27.5664 −2.41773
\(131\) 4.22096 0.368787 0.184394 0.982852i \(-0.440968\pi\)
0.184394 + 0.982852i \(0.440968\pi\)
\(132\) 0 0
\(133\) 4.62860 0.401350
\(134\) 17.2643 1.49141
\(135\) 0 0
\(136\) −3.26247 −0.279754
\(137\) 14.5361 1.24191 0.620953 0.783848i \(-0.286746\pi\)
0.620953 + 0.783848i \(0.286746\pi\)
\(138\) 0 0
\(139\) −6.94615 −0.589165 −0.294583 0.955626i \(-0.595181\pi\)
−0.294583 + 0.955626i \(0.595181\pi\)
\(140\) 9.78502 0.826985
\(141\) 0 0
\(142\) −21.2682 −1.78479
\(143\) 0 0
\(144\) 0 0
\(145\) 6.65814 0.552929
\(146\) 35.6704 2.95211
\(147\) 0 0
\(148\) 18.7236 1.53907
\(149\) −13.9640 −1.14398 −0.571989 0.820262i \(-0.693828\pi\)
−0.571989 + 0.820262i \(0.693828\pi\)
\(150\) 0 0
\(151\) 1.37080 0.111554 0.0557771 0.998443i \(-0.482236\pi\)
0.0557771 + 0.998443i \(0.482236\pi\)
\(152\) 49.6456 4.02679
\(153\) 0 0
\(154\) 0 0
\(155\) 1.28191 0.102965
\(156\) 0 0
\(157\) −15.8997 −1.26894 −0.634469 0.772949i \(-0.718781\pi\)
−0.634469 + 0.772949i \(0.718781\pi\)
\(158\) 17.2263 1.37045
\(159\) 0 0
\(160\) 50.1827 3.96729
\(161\) 1.38164 0.108888
\(162\) 0 0
\(163\) 10.4685 0.819957 0.409978 0.912095i \(-0.365536\pi\)
0.409978 + 0.912095i \(0.365536\pi\)
\(164\) −48.4840 −3.78596
\(165\) 0 0
\(166\) −5.63275 −0.437186
\(167\) 8.57355 0.663442 0.331721 0.943378i \(-0.392371\pi\)
0.331721 + 0.943378i \(0.392371\pi\)
\(168\) 0 0
\(169\) 21.4702 1.65156
\(170\) −1.42814 −0.109534
\(171\) 0 0
\(172\) 5.89486 0.449479
\(173\) −13.7471 −1.04517 −0.522586 0.852587i \(-0.675033\pi\)
−0.522586 + 0.852587i \(0.675033\pi\)
\(174\) 0 0
\(175\) −2.18541 −0.165202
\(176\) 0 0
\(177\) 0 0
\(178\) −0.236181 −0.0177025
\(179\) 3.85014 0.287773 0.143887 0.989594i \(-0.454040\pi\)
0.143887 + 0.989594i \(0.454040\pi\)
\(180\) 0 0
\(181\) −19.5568 −1.45365 −0.726823 0.686825i \(-0.759004\pi\)
−0.726823 + 0.686825i \(0.759004\pi\)
\(182\) −16.4313 −1.21797
\(183\) 0 0
\(184\) 14.8192 1.09249
\(185\) 5.38571 0.395966
\(186\) 0 0
\(187\) 0 0
\(188\) 15.0880 1.10040
\(189\) 0 0
\(190\) 21.7324 1.57663
\(191\) 2.54502 0.184151 0.0920755 0.995752i \(-0.470650\pi\)
0.0920755 + 0.995752i \(0.470650\pi\)
\(192\) 0 0
\(193\) −21.6282 −1.55683 −0.778415 0.627750i \(-0.783976\pi\)
−0.778415 + 0.627750i \(0.783976\pi\)
\(194\) 2.90430 0.208517
\(195\) 0 0
\(196\) 5.83249 0.416607
\(197\) −22.0693 −1.57237 −0.786187 0.617989i \(-0.787948\pi\)
−0.786187 + 0.617989i \(0.787948\pi\)
\(198\) 0 0
\(199\) −12.8315 −0.909598 −0.454799 0.890594i \(-0.650289\pi\)
−0.454799 + 0.890594i \(0.650289\pi\)
\(200\) −23.4404 −1.65749
\(201\) 0 0
\(202\) −55.1257 −3.87863
\(203\) 3.96868 0.278547
\(204\) 0 0
\(205\) −13.9461 −0.974035
\(206\) −6.75224 −0.470451
\(207\) 0 0
\(208\) −107.753 −7.47132
\(209\) 0 0
\(210\) 0 0
\(211\) 17.7406 1.22131 0.610655 0.791897i \(-0.290906\pi\)
0.610655 + 0.791897i \(0.290906\pi\)
\(212\) 8.47891 0.582334
\(213\) 0 0
\(214\) −25.9227 −1.77204
\(215\) 1.69561 0.115640
\(216\) 0 0
\(217\) 0.764099 0.0518704
\(218\) 23.2437 1.57426
\(219\) 0 0
\(220\) 0 0
\(221\) 1.78581 0.120127
\(222\) 0 0
\(223\) 17.1174 1.14627 0.573133 0.819462i \(-0.305728\pi\)
0.573133 + 0.819462i \(0.305728\pi\)
\(224\) 29.9121 1.99859
\(225\) 0 0
\(226\) −15.3356 −1.02011
\(227\) −20.4871 −1.35978 −0.679888 0.733316i \(-0.737971\pi\)
−0.679888 + 0.733316i \(0.737971\pi\)
\(228\) 0 0
\(229\) 24.4342 1.61466 0.807328 0.590103i \(-0.200913\pi\)
0.807328 + 0.590103i \(0.200913\pi\)
\(230\) 6.48712 0.427748
\(231\) 0 0
\(232\) 42.5674 2.79469
\(233\) −23.7053 −1.55298 −0.776491 0.630128i \(-0.783002\pi\)
−0.776491 + 0.630128i \(0.783002\pi\)
\(234\) 0 0
\(235\) 4.33994 0.283106
\(236\) 14.5488 0.947048
\(237\) 0 0
\(238\) −0.851264 −0.0551793
\(239\) −1.57997 −0.102200 −0.0510998 0.998694i \(-0.516273\pi\)
−0.0510998 + 0.998694i \(0.516273\pi\)
\(240\) 0 0
\(241\) 12.2382 0.788333 0.394167 0.919039i \(-0.371033\pi\)
0.394167 + 0.919039i \(0.371033\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −19.7894 −1.26688
\(245\) 1.67767 0.107183
\(246\) 0 0
\(247\) −27.1751 −1.72911
\(248\) 8.19561 0.520422
\(249\) 0 0
\(250\) −33.7372 −2.13373
\(251\) −19.4107 −1.22520 −0.612598 0.790395i \(-0.709875\pi\)
−0.612598 + 0.790395i \(0.709875\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −56.1345 −3.52219
\(255\) 0 0
\(256\) 106.745 6.67157
\(257\) 0.270104 0.0168486 0.00842431 0.999965i \(-0.497318\pi\)
0.00842431 + 0.999965i \(0.497318\pi\)
\(258\) 0 0
\(259\) 3.21023 0.199474
\(260\) −57.4491 −3.56284
\(261\) 0 0
\(262\) 11.8130 0.729812
\(263\) 27.9927 1.72611 0.863053 0.505113i \(-0.168549\pi\)
0.863053 + 0.505113i \(0.168549\pi\)
\(264\) 0 0
\(265\) 2.43889 0.149820
\(266\) 12.9539 0.794253
\(267\) 0 0
\(268\) 35.9794 2.19779
\(269\) −1.11686 −0.0680960 −0.0340480 0.999420i \(-0.510840\pi\)
−0.0340480 + 0.999420i \(0.510840\pi\)
\(270\) 0 0
\(271\) −24.8310 −1.50837 −0.754187 0.656660i \(-0.771969\pi\)
−0.754187 + 0.656660i \(0.771969\pi\)
\(272\) −5.58241 −0.338483
\(273\) 0 0
\(274\) 40.6817 2.45767
\(275\) 0 0
\(276\) 0 0
\(277\) 12.4335 0.747057 0.373528 0.927619i \(-0.378148\pi\)
0.373528 + 0.927619i \(0.378148\pi\)
\(278\) −19.4399 −1.16593
\(279\) 0 0
\(280\) 17.9945 1.07537
\(281\) −6.73560 −0.401812 −0.200906 0.979611i \(-0.564389\pi\)
−0.200906 + 0.979611i \(0.564389\pi\)
\(282\) 0 0
\(283\) 11.1606 0.663430 0.331715 0.943380i \(-0.392373\pi\)
0.331715 + 0.943380i \(0.392373\pi\)
\(284\) −44.3236 −2.63012
\(285\) 0 0
\(286\) 0 0
\(287\) −8.31274 −0.490685
\(288\) 0 0
\(289\) −16.9075 −0.994558
\(290\) 18.6339 1.09422
\(291\) 0 0
\(292\) 74.3383 4.35032
\(293\) −16.9009 −0.987363 −0.493682 0.869643i \(-0.664349\pi\)
−0.493682 + 0.869643i \(0.664349\pi\)
\(294\) 0 0
\(295\) 4.18486 0.243652
\(296\) 34.4324 2.00134
\(297\) 0 0
\(298\) −39.0805 −2.26388
\(299\) −8.11179 −0.469117
\(300\) 0 0
\(301\) 1.01069 0.0582554
\(302\) 3.83640 0.220760
\(303\) 0 0
\(304\) 84.9487 4.87214
\(305\) −5.69226 −0.325938
\(306\) 0 0
\(307\) 11.3453 0.647511 0.323755 0.946141i \(-0.395054\pi\)
0.323755 + 0.946141i \(0.395054\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 3.58762 0.203763
\(311\) −23.8487 −1.35234 −0.676169 0.736747i \(-0.736361\pi\)
−0.676169 + 0.736747i \(0.736361\pi\)
\(312\) 0 0
\(313\) 30.9666 1.75034 0.875169 0.483818i \(-0.160750\pi\)
0.875169 + 0.483818i \(0.160750\pi\)
\(314\) −44.4980 −2.51116
\(315\) 0 0
\(316\) 35.9001 2.01954
\(317\) −3.20875 −0.180221 −0.0901106 0.995932i \(-0.528722\pi\)
−0.0901106 + 0.995932i \(0.528722\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 78.8637 4.40862
\(321\) 0 0
\(322\) 3.86674 0.215485
\(323\) −1.40787 −0.0783362
\(324\) 0 0
\(325\) 12.8309 0.711728
\(326\) 29.2978 1.62265
\(327\) 0 0
\(328\) −89.1612 −4.92310
\(329\) 2.58688 0.142619
\(330\) 0 0
\(331\) −3.98424 −0.218994 −0.109497 0.993987i \(-0.534924\pi\)
−0.109497 + 0.993987i \(0.534924\pi\)
\(332\) −11.7388 −0.644252
\(333\) 0 0
\(334\) 23.9945 1.31292
\(335\) 10.3492 0.565437
\(336\) 0 0
\(337\) 11.3006 0.615582 0.307791 0.951454i \(-0.400410\pi\)
0.307791 + 0.951454i \(0.400410\pi\)
\(338\) 60.0878 3.26835
\(339\) 0 0
\(340\) −2.97629 −0.161412
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 10.8405 0.584483
\(345\) 0 0
\(346\) −38.4734 −2.06834
\(347\) 6.58840 0.353684 0.176842 0.984239i \(-0.443412\pi\)
0.176842 + 0.984239i \(0.443412\pi\)
\(348\) 0 0
\(349\) −20.4343 −1.09382 −0.546912 0.837190i \(-0.684197\pi\)
−0.546912 + 0.837190i \(0.684197\pi\)
\(350\) −6.11623 −0.326926
\(351\) 0 0
\(352\) 0 0
\(353\) −36.5457 −1.94513 −0.972565 0.232630i \(-0.925267\pi\)
−0.972565 + 0.232630i \(0.925267\pi\)
\(354\) 0 0
\(355\) −12.7494 −0.676665
\(356\) −0.492209 −0.0260870
\(357\) 0 0
\(358\) 10.7752 0.569489
\(359\) 0.314474 0.0165973 0.00829864 0.999966i \(-0.497358\pi\)
0.00829864 + 0.999966i \(0.497358\pi\)
\(360\) 0 0
\(361\) 2.42393 0.127575
\(362\) −54.7328 −2.87669
\(363\) 0 0
\(364\) −34.2434 −1.79484
\(365\) 21.3829 1.11923
\(366\) 0 0
\(367\) 22.6952 1.18468 0.592340 0.805688i \(-0.298204\pi\)
0.592340 + 0.805688i \(0.298204\pi\)
\(368\) 25.3572 1.32184
\(369\) 0 0
\(370\) 15.0728 0.783597
\(371\) 1.45374 0.0754742
\(372\) 0 0
\(373\) −32.8020 −1.69843 −0.849213 0.528051i \(-0.822923\pi\)
−0.849213 + 0.528051i \(0.822923\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 27.7465 1.43092
\(377\) −23.3006 −1.20004
\(378\) 0 0
\(379\) 25.4514 1.30735 0.653675 0.756776i \(-0.273227\pi\)
0.653675 + 0.756776i \(0.273227\pi\)
\(380\) 45.2909 2.32338
\(381\) 0 0
\(382\) 7.12264 0.364426
\(383\) 13.9526 0.712944 0.356472 0.934306i \(-0.383979\pi\)
0.356472 + 0.934306i \(0.383979\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −60.5299 −3.08089
\(387\) 0 0
\(388\) 6.05266 0.307277
\(389\) 9.06975 0.459855 0.229927 0.973208i \(-0.426151\pi\)
0.229927 + 0.973208i \(0.426151\pi\)
\(390\) 0 0
\(391\) −0.420251 −0.0212530
\(392\) 10.7258 0.541737
\(393\) 0 0
\(394\) −61.7645 −3.11165
\(395\) 10.3264 0.519577
\(396\) 0 0
\(397\) 24.1849 1.21381 0.606904 0.794775i \(-0.292411\pi\)
0.606904 + 0.794775i \(0.292411\pi\)
\(398\) −35.9109 −1.80005
\(399\) 0 0
\(400\) −40.1089 −2.00545
\(401\) −3.86368 −0.192943 −0.0964715 0.995336i \(-0.530756\pi\)
−0.0964715 + 0.995336i \(0.530756\pi\)
\(402\) 0 0
\(403\) −4.48613 −0.223470
\(404\) −114.884 −5.71568
\(405\) 0 0
\(406\) 11.1070 0.551230
\(407\) 0 0
\(408\) 0 0
\(409\) −20.0985 −0.993806 −0.496903 0.867806i \(-0.665530\pi\)
−0.496903 + 0.867806i \(0.665530\pi\)
\(410\) −39.0303 −1.92757
\(411\) 0 0
\(412\) −14.0719 −0.693272
\(413\) 2.49444 0.122744
\(414\) 0 0
\(415\) −3.37659 −0.165750
\(416\) −175.618 −8.61038
\(417\) 0 0
\(418\) 0 0
\(419\) 2.12825 0.103972 0.0519859 0.998648i \(-0.483445\pi\)
0.0519859 + 0.998648i \(0.483445\pi\)
\(420\) 0 0
\(421\) −3.84998 −0.187636 −0.0938182 0.995589i \(-0.529907\pi\)
−0.0938182 + 0.995589i \(0.529907\pi\)
\(422\) 49.6498 2.41691
\(423\) 0 0
\(424\) 15.5926 0.757242
\(425\) 0.664734 0.0322443
\(426\) 0 0
\(427\) −3.39295 −0.164196
\(428\) −54.0238 −2.61134
\(429\) 0 0
\(430\) 4.74544 0.228846
\(431\) −16.7030 −0.804555 −0.402278 0.915518i \(-0.631781\pi\)
−0.402278 + 0.915518i \(0.631781\pi\)
\(432\) 0 0
\(433\) 16.9215 0.813196 0.406598 0.913607i \(-0.366715\pi\)
0.406598 + 0.913607i \(0.366715\pi\)
\(434\) 2.13845 0.102649
\(435\) 0 0
\(436\) 48.4406 2.31988
\(437\) 6.39505 0.305917
\(438\) 0 0
\(439\) 26.7946 1.27883 0.639417 0.768860i \(-0.279176\pi\)
0.639417 + 0.768860i \(0.279176\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.99789 0.237725
\(443\) 3.92408 0.186439 0.0932194 0.995646i \(-0.470284\pi\)
0.0932194 + 0.995646i \(0.470284\pi\)
\(444\) 0 0
\(445\) −0.141580 −0.00671154
\(446\) 47.9058 2.26841
\(447\) 0 0
\(448\) 47.0078 2.22091
\(449\) −19.6785 −0.928686 −0.464343 0.885655i \(-0.653709\pi\)
−0.464343 + 0.885655i \(0.653709\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −31.9598 −1.50326
\(453\) 0 0
\(454\) −57.3364 −2.69093
\(455\) −9.84984 −0.461768
\(456\) 0 0
\(457\) −19.7725 −0.924921 −0.462460 0.886640i \(-0.653033\pi\)
−0.462460 + 0.886640i \(0.653033\pi\)
\(458\) 68.3830 3.19533
\(459\) 0 0
\(460\) 13.5194 0.630343
\(461\) 9.69184 0.451394 0.225697 0.974198i \(-0.427534\pi\)
0.225697 + 0.974198i \(0.427534\pi\)
\(462\) 0 0
\(463\) 7.21162 0.335152 0.167576 0.985859i \(-0.446406\pi\)
0.167576 + 0.985859i \(0.446406\pi\)
\(464\) 72.8372 3.38138
\(465\) 0 0
\(466\) −66.3429 −3.07328
\(467\) −36.5718 −1.69234 −0.846171 0.532912i \(-0.821098\pi\)
−0.846171 + 0.532912i \(0.821098\pi\)
\(468\) 0 0
\(469\) 6.16878 0.284848
\(470\) 12.1460 0.560253
\(471\) 0 0
\(472\) 26.7550 1.23150
\(473\) 0 0
\(474\) 0 0
\(475\) −10.1154 −0.464127
\(476\) −1.77406 −0.0813140
\(477\) 0 0
\(478\) −4.42179 −0.202248
\(479\) 38.9699 1.78058 0.890290 0.455394i \(-0.150502\pi\)
0.890290 + 0.455394i \(0.150502\pi\)
\(480\) 0 0
\(481\) −18.8477 −0.859381
\(482\) 34.2506 1.56007
\(483\) 0 0
\(484\) 0 0
\(485\) 1.74100 0.0790548
\(486\) 0 0
\(487\) −23.9835 −1.08679 −0.543397 0.839476i \(-0.682862\pi\)
−0.543397 + 0.839476i \(0.682862\pi\)
\(488\) −36.3923 −1.64740
\(489\) 0 0
\(490\) 4.69523 0.212109
\(491\) 3.19310 0.144103 0.0720513 0.997401i \(-0.477045\pi\)
0.0720513 + 0.997401i \(0.477045\pi\)
\(492\) 0 0
\(493\) −1.20715 −0.0543672
\(494\) −76.0539 −3.42183
\(495\) 0 0
\(496\) 14.0235 0.629674
\(497\) −7.59943 −0.340881
\(498\) 0 0
\(499\) 27.5331 1.23255 0.616275 0.787531i \(-0.288641\pi\)
0.616275 + 0.787531i \(0.288641\pi\)
\(500\) −70.3094 −3.14433
\(501\) 0 0
\(502\) −54.3241 −2.42460
\(503\) −33.1568 −1.47839 −0.739195 0.673492i \(-0.764794\pi\)
−0.739195 + 0.673492i \(0.764794\pi\)
\(504\) 0 0
\(505\) −33.0454 −1.47050
\(506\) 0 0
\(507\) 0 0
\(508\) −116.986 −5.19042
\(509\) 7.69479 0.341066 0.170533 0.985352i \(-0.445451\pi\)
0.170533 + 0.985352i \(0.445451\pi\)
\(510\) 0 0
\(511\) 12.7455 0.563830
\(512\) 155.274 6.86221
\(513\) 0 0
\(514\) 0.755929 0.0333426
\(515\) −4.04767 −0.178362
\(516\) 0 0
\(517\) 0 0
\(518\) 8.98434 0.394749
\(519\) 0 0
\(520\) −105.648 −4.63297
\(521\) 8.09827 0.354792 0.177396 0.984140i \(-0.443233\pi\)
0.177396 + 0.984140i \(0.443233\pi\)
\(522\) 0 0
\(523\) −19.3528 −0.846241 −0.423120 0.906073i \(-0.639065\pi\)
−0.423120 + 0.906073i \(0.639065\pi\)
\(524\) 24.6187 1.07547
\(525\) 0 0
\(526\) 78.3422 3.41588
\(527\) −0.232415 −0.0101241
\(528\) 0 0
\(529\) −21.0911 −0.917003
\(530\) 6.82563 0.296487
\(531\) 0 0
\(532\) 26.9963 1.17044
\(533\) 48.8052 2.11399
\(534\) 0 0
\(535\) −15.5395 −0.671833
\(536\) 66.1654 2.85791
\(537\) 0 0
\(538\) −3.12571 −0.134759
\(539\) 0 0
\(540\) 0 0
\(541\) 28.5883 1.22911 0.614554 0.788875i \(-0.289336\pi\)
0.614554 + 0.788875i \(0.289336\pi\)
\(542\) −69.4934 −2.98500
\(543\) 0 0
\(544\) −9.09832 −0.390087
\(545\) 13.9336 0.596849
\(546\) 0 0
\(547\) −23.3917 −1.00016 −0.500078 0.865980i \(-0.666695\pi\)
−0.500078 + 0.865980i \(0.666695\pi\)
\(548\) 84.7820 3.62171
\(549\) 0 0
\(550\) 0 0
\(551\) 18.3694 0.782564
\(552\) 0 0
\(553\) 6.15519 0.261745
\(554\) 34.7971 1.47839
\(555\) 0 0
\(556\) −40.5134 −1.71815
\(557\) 25.4361 1.07776 0.538881 0.842382i \(-0.318847\pi\)
0.538881 + 0.842382i \(0.318847\pi\)
\(558\) 0 0
\(559\) −5.93392 −0.250978
\(560\) 30.7903 1.30113
\(561\) 0 0
\(562\) −18.8506 −0.795167
\(563\) 39.8791 1.68070 0.840352 0.542041i \(-0.182348\pi\)
0.840352 + 0.542041i \(0.182348\pi\)
\(564\) 0 0
\(565\) −9.19301 −0.386753
\(566\) 31.2348 1.31290
\(567\) 0 0
\(568\) −81.5103 −3.42010
\(569\) 32.2487 1.35194 0.675968 0.736931i \(-0.263726\pi\)
0.675968 + 0.736931i \(0.263726\pi\)
\(570\) 0 0
\(571\) 20.6844 0.865615 0.432807 0.901486i \(-0.357523\pi\)
0.432807 + 0.901486i \(0.357523\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −23.2645 −0.971043
\(575\) −3.01945 −0.125920
\(576\) 0 0
\(577\) 15.7198 0.654424 0.327212 0.944951i \(-0.393891\pi\)
0.327212 + 0.944951i \(0.393891\pi\)
\(578\) −47.3183 −1.96818
\(579\) 0 0
\(580\) 38.8336 1.61248
\(581\) −2.01266 −0.0834993
\(582\) 0 0
\(583\) 0 0
\(584\) 136.707 5.65697
\(585\) 0 0
\(586\) −47.3000 −1.95394
\(587\) −20.5683 −0.848946 −0.424473 0.905441i \(-0.639541\pi\)
−0.424473 + 0.905441i \(0.639541\pi\)
\(588\) 0 0
\(589\) 3.53671 0.145727
\(590\) 11.7120 0.482175
\(591\) 0 0
\(592\) 58.9174 2.42149
\(593\) 21.1496 0.868511 0.434255 0.900790i \(-0.357012\pi\)
0.434255 + 0.900790i \(0.357012\pi\)
\(594\) 0 0
\(595\) −0.510295 −0.0209201
\(596\) −81.4451 −3.33612
\(597\) 0 0
\(598\) −22.7021 −0.928359
\(599\) 33.6993 1.37691 0.688457 0.725277i \(-0.258288\pi\)
0.688457 + 0.725277i \(0.258288\pi\)
\(600\) 0 0
\(601\) 36.7888 1.50065 0.750324 0.661070i \(-0.229897\pi\)
0.750324 + 0.661070i \(0.229897\pi\)
\(602\) 2.82859 0.115285
\(603\) 0 0
\(604\) 7.99519 0.325320
\(605\) 0 0
\(606\) 0 0
\(607\) −12.0614 −0.489558 −0.244779 0.969579i \(-0.578715\pi\)
−0.244779 + 0.969579i \(0.578715\pi\)
\(608\) 138.451 5.61494
\(609\) 0 0
\(610\) −15.9307 −0.645015
\(611\) −15.1879 −0.614437
\(612\) 0 0
\(613\) −8.57642 −0.346398 −0.173199 0.984887i \(-0.555410\pi\)
−0.173199 + 0.984887i \(0.555410\pi\)
\(614\) 31.7517 1.28139
\(615\) 0 0
\(616\) 0 0
\(617\) 0.0309560 0.00124624 0.000623121 1.00000i \(-0.499802\pi\)
0.000623121 1.00000i \(0.499802\pi\)
\(618\) 0 0
\(619\) −21.2938 −0.855869 −0.427934 0.903810i \(-0.640759\pi\)
−0.427934 + 0.903810i \(0.640759\pi\)
\(620\) 7.47672 0.300272
\(621\) 0 0
\(622\) −66.7445 −2.67621
\(623\) −0.0843908 −0.00338105
\(624\) 0 0
\(625\) −9.29689 −0.371876
\(626\) 86.6650 3.46383
\(627\) 0 0
\(628\) −92.7351 −3.70053
\(629\) −0.976451 −0.0389336
\(630\) 0 0
\(631\) 21.7895 0.867426 0.433713 0.901051i \(-0.357203\pi\)
0.433713 + 0.901051i \(0.357203\pi\)
\(632\) 66.0196 2.62612
\(633\) 0 0
\(634\) −8.98019 −0.356649
\(635\) −33.6501 −1.33536
\(636\) 0 0
\(637\) −5.87113 −0.232623
\(638\) 0 0
\(639\) 0 0
\(640\) 120.347 4.75714
\(641\) 39.8969 1.57583 0.787916 0.615783i \(-0.211160\pi\)
0.787916 + 0.615783i \(0.211160\pi\)
\(642\) 0 0
\(643\) 7.15604 0.282207 0.141103 0.989995i \(-0.454935\pi\)
0.141103 + 0.989995i \(0.454935\pi\)
\(644\) 8.05840 0.317546
\(645\) 0 0
\(646\) −3.94016 −0.155024
\(647\) 4.74897 0.186701 0.0933506 0.995633i \(-0.470242\pi\)
0.0933506 + 0.995633i \(0.470242\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 35.9092 1.40848
\(651\) 0 0
\(652\) 61.0575 2.39120
\(653\) 5.03380 0.196988 0.0984938 0.995138i \(-0.468598\pi\)
0.0984938 + 0.995138i \(0.468598\pi\)
\(654\) 0 0
\(655\) 7.08139 0.276693
\(656\) −152.564 −5.95661
\(657\) 0 0
\(658\) 7.23980 0.282237
\(659\) 6.55136 0.255205 0.127602 0.991825i \(-0.459272\pi\)
0.127602 + 0.991825i \(0.459272\pi\)
\(660\) 0 0
\(661\) 36.4255 1.41679 0.708394 0.705818i \(-0.249420\pi\)
0.708394 + 0.705818i \(0.249420\pi\)
\(662\) −11.1505 −0.433378
\(663\) 0 0
\(664\) −21.5875 −0.837757
\(665\) 7.76527 0.301124
\(666\) 0 0
\(667\) 5.48328 0.212313
\(668\) 50.0052 1.93476
\(669\) 0 0
\(670\) 28.9639 1.11897
\(671\) 0 0
\(672\) 0 0
\(673\) −31.9908 −1.23315 −0.616577 0.787295i \(-0.711481\pi\)
−0.616577 + 0.787295i \(0.711481\pi\)
\(674\) 31.6265 1.21821
\(675\) 0 0
\(676\) 125.225 4.81634
\(677\) −21.6417 −0.831760 −0.415880 0.909420i \(-0.636526\pi\)
−0.415880 + 0.909420i \(0.636526\pi\)
\(678\) 0 0
\(679\) 1.03775 0.0398251
\(680\) −5.47335 −0.209893
\(681\) 0 0
\(682\) 0 0
\(683\) 23.1587 0.886144 0.443072 0.896486i \(-0.353889\pi\)
0.443072 + 0.896486i \(0.353889\pi\)
\(684\) 0 0
\(685\) 24.3869 0.931775
\(686\) 2.79866 0.106853
\(687\) 0 0
\(688\) 18.5493 0.707184
\(689\) −8.53508 −0.325161
\(690\) 0 0
\(691\) 2.69598 0.102560 0.0512800 0.998684i \(-0.483670\pi\)
0.0512800 + 0.998684i \(0.483670\pi\)
\(692\) −80.1798 −3.04798
\(693\) 0 0
\(694\) 18.4387 0.699923
\(695\) −11.6534 −0.442038
\(696\) 0 0
\(697\) 2.52847 0.0957728
\(698\) −57.1887 −2.16463
\(699\) 0 0
\(700\) −12.7464 −0.481769
\(701\) 0.447285 0.0168937 0.00844686 0.999964i \(-0.497311\pi\)
0.00844686 + 0.999964i \(0.497311\pi\)
\(702\) 0 0
\(703\) 14.8589 0.560413
\(704\) 0 0
\(705\) 0 0
\(706\) −102.279 −3.84932
\(707\) −19.6972 −0.740789
\(708\) 0 0
\(709\) 11.2291 0.421718 0.210859 0.977517i \(-0.432374\pi\)
0.210859 + 0.977517i \(0.432374\pi\)
\(710\) −35.6811 −1.33909
\(711\) 0 0
\(712\) −0.905163 −0.0339224
\(713\) 1.05571 0.0395366
\(714\) 0 0
\(715\) 0 0
\(716\) 22.4559 0.839218
\(717\) 0 0
\(718\) 0.880105 0.0328452
\(719\) −9.04358 −0.337268 −0.168634 0.985679i \(-0.553936\pi\)
−0.168634 + 0.985679i \(0.553936\pi\)
\(720\) 0 0
\(721\) −2.41267 −0.0898525
\(722\) 6.78375 0.252465
\(723\) 0 0
\(724\) −114.065 −4.23919
\(725\) −8.67321 −0.322115
\(726\) 0 0
\(727\) −44.1368 −1.63694 −0.818471 0.574548i \(-0.805178\pi\)
−0.818471 + 0.574548i \(0.805178\pi\)
\(728\) −62.9729 −2.33393
\(729\) 0 0
\(730\) 59.8433 2.21490
\(731\) −0.307421 −0.0113704
\(732\) 0 0
\(733\) 28.0438 1.03582 0.517911 0.855435i \(-0.326710\pi\)
0.517911 + 0.855435i \(0.326710\pi\)
\(734\) 63.5161 2.34442
\(735\) 0 0
\(736\) 41.3277 1.52336
\(737\) 0 0
\(738\) 0 0
\(739\) 43.7065 1.60777 0.803886 0.594784i \(-0.202762\pi\)
0.803886 + 0.594784i \(0.202762\pi\)
\(740\) 31.4122 1.15473
\(741\) 0 0
\(742\) 4.06851 0.149360
\(743\) −21.3676 −0.783901 −0.391950 0.919986i \(-0.628199\pi\)
−0.391950 + 0.919986i \(0.628199\pi\)
\(744\) 0 0
\(745\) −23.4271 −0.858301
\(746\) −91.8017 −3.36110
\(747\) 0 0
\(748\) 0 0
\(749\) −9.26256 −0.338446
\(750\) 0 0
\(751\) 2.23940 0.0817169 0.0408585 0.999165i \(-0.486991\pi\)
0.0408585 + 0.999165i \(0.486991\pi\)
\(752\) 47.4770 1.73131
\(753\) 0 0
\(754\) −65.2106 −2.37483
\(755\) 2.29976 0.0836967
\(756\) 0 0
\(757\) 47.7090 1.73401 0.867007 0.498296i \(-0.166041\pi\)
0.867007 + 0.498296i \(0.166041\pi\)
\(758\) 71.2297 2.58718
\(759\) 0 0
\(760\) 83.2891 3.02121
\(761\) −35.6430 −1.29206 −0.646029 0.763313i \(-0.723572\pi\)
−0.646029 + 0.763313i \(0.723572\pi\)
\(762\) 0 0
\(763\) 8.30530 0.300672
\(764\) 14.8438 0.537030
\(765\) 0 0
\(766\) 39.0486 1.41088
\(767\) −14.6452 −0.528808
\(768\) 0 0
\(769\) −22.0645 −0.795665 −0.397832 0.917458i \(-0.630237\pi\)
−0.397832 + 0.917458i \(0.630237\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −126.146 −4.54010
\(773\) 18.9064 0.680016 0.340008 0.940423i \(-0.389570\pi\)
0.340008 + 0.940423i \(0.389570\pi\)
\(774\) 0 0
\(775\) −1.66987 −0.0599836
\(776\) 11.1307 0.399570
\(777\) 0 0
\(778\) 25.3832 0.910030
\(779\) −38.4763 −1.37856
\(780\) 0 0
\(781\) 0 0
\(782\) −1.17614 −0.0420587
\(783\) 0 0
\(784\) 18.3530 0.655464
\(785\) −26.6746 −0.952056
\(786\) 0 0
\(787\) −6.64396 −0.236832 −0.118416 0.992964i \(-0.537782\pi\)
−0.118416 + 0.992964i \(0.537782\pi\)
\(788\) −128.719 −4.58543
\(789\) 0 0
\(790\) 28.9000 1.02822
\(791\) −5.47962 −0.194833
\(792\) 0 0
\(793\) 19.9205 0.707397
\(794\) 67.6854 2.40207
\(795\) 0 0
\(796\) −74.8394 −2.65261
\(797\) 15.3017 0.542014 0.271007 0.962577i \(-0.412643\pi\)
0.271007 + 0.962577i \(0.412643\pi\)
\(798\) 0 0
\(799\) −0.786847 −0.0278367
\(800\) −65.3704 −2.31119
\(801\) 0 0
\(802\) −10.8131 −0.381825
\(803\) 0 0
\(804\) 0 0
\(805\) 2.31794 0.0816966
\(806\) −12.5551 −0.442236
\(807\) 0 0
\(808\) −211.269 −7.43241
\(809\) 24.7092 0.868728 0.434364 0.900737i \(-0.356973\pi\)
0.434364 + 0.900737i \(0.356973\pi\)
\(810\) 0 0
\(811\) −25.7880 −0.905539 −0.452770 0.891628i \(-0.649564\pi\)
−0.452770 + 0.891628i \(0.649564\pi\)
\(812\) 23.1473 0.812311
\(813\) 0 0
\(814\) 0 0
\(815\) 17.5627 0.615195
\(816\) 0 0
\(817\) 4.67810 0.163666
\(818\) −56.2488 −1.96669
\(819\) 0 0
\(820\) −81.3403 −2.84053
\(821\) −18.3066 −0.638905 −0.319452 0.947602i \(-0.603499\pi\)
−0.319452 + 0.947602i \(0.603499\pi\)
\(822\) 0 0
\(823\) −4.84388 −0.168847 −0.0844235 0.996430i \(-0.526905\pi\)
−0.0844235 + 0.996430i \(0.526905\pi\)
\(824\) −25.8779 −0.901500
\(825\) 0 0
\(826\) 6.98110 0.242903
\(827\) 25.8818 0.900000 0.450000 0.893029i \(-0.351424\pi\)
0.450000 + 0.893029i \(0.351424\pi\)
\(828\) 0 0
\(829\) 54.1465 1.88058 0.940292 0.340368i \(-0.110552\pi\)
0.940292 + 0.340368i \(0.110552\pi\)
\(830\) −9.44992 −0.328011
\(831\) 0 0
\(832\) −275.989 −9.56820
\(833\) −0.304169 −0.0105388
\(834\) 0 0
\(835\) 14.3836 0.497766
\(836\) 0 0
\(837\) 0 0
\(838\) 5.95625 0.205755
\(839\) −32.3629 −1.11729 −0.558645 0.829407i \(-0.688679\pi\)
−0.558645 + 0.829407i \(0.688679\pi\)
\(840\) 0 0
\(841\) −13.2496 −0.456882
\(842\) −10.7748 −0.371323
\(843\) 0 0
\(844\) 103.472 3.56164
\(845\) 36.0200 1.23913
\(846\) 0 0
\(847\) 0 0
\(848\) 26.6804 0.916210
\(849\) 0 0
\(850\) 1.86036 0.0638100
\(851\) 4.43538 0.152043
\(852\) 0 0
\(853\) −6.12615 −0.209755 −0.104878 0.994485i \(-0.533445\pi\)
−0.104878 + 0.994485i \(0.533445\pi\)
\(854\) −9.49572 −0.324937
\(855\) 0 0
\(856\) −99.3488 −3.39567
\(857\) −22.6396 −0.773354 −0.386677 0.922215i \(-0.626377\pi\)
−0.386677 + 0.922215i \(0.626377\pi\)
\(858\) 0 0
\(859\) −13.7204 −0.468134 −0.234067 0.972220i \(-0.575204\pi\)
−0.234067 + 0.972220i \(0.575204\pi\)
\(860\) 9.88965 0.337234
\(861\) 0 0
\(862\) −46.7460 −1.59218
\(863\) −43.6306 −1.48520 −0.742601 0.669734i \(-0.766408\pi\)
−0.742601 + 0.669734i \(0.766408\pi\)
\(864\) 0 0
\(865\) −23.0631 −0.784170
\(866\) 47.3575 1.60927
\(867\) 0 0
\(868\) 4.45660 0.151267
\(869\) 0 0
\(870\) 0 0
\(871\) −36.2177 −1.22719
\(872\) 89.0813 3.01667
\(873\) 0 0
\(874\) 17.8976 0.605394
\(875\) −12.0548 −0.407526
\(876\) 0 0
\(877\) −33.9122 −1.14513 −0.572567 0.819858i \(-0.694052\pi\)
−0.572567 + 0.819858i \(0.694052\pi\)
\(878\) 74.9889 2.53075
\(879\) 0 0
\(880\) 0 0
\(881\) −12.7514 −0.429605 −0.214803 0.976657i \(-0.568911\pi\)
−0.214803 + 0.976657i \(0.568911\pi\)
\(882\) 0 0
\(883\) 0.882229 0.0296894 0.0148447 0.999890i \(-0.495275\pi\)
0.0148447 + 0.999890i \(0.495275\pi\)
\(884\) 10.4158 0.350320
\(885\) 0 0
\(886\) 10.9822 0.368953
\(887\) 34.4245 1.15586 0.577931 0.816086i \(-0.303860\pi\)
0.577931 + 0.816086i \(0.303860\pi\)
\(888\) 0 0
\(889\) −20.0576 −0.672711
\(890\) −0.396235 −0.0132818
\(891\) 0 0
\(892\) 99.8372 3.34280
\(893\) 11.9736 0.400682
\(894\) 0 0
\(895\) 6.45928 0.215910
\(896\) 71.7346 2.39649
\(897\) 0 0
\(898\) −55.0734 −1.83782
\(899\) 3.03246 0.101138
\(900\) 0 0
\(901\) −0.442181 −0.0147312
\(902\) 0 0
\(903\) 0 0
\(904\) −58.7736 −1.95478
\(905\) −32.8099 −1.09064
\(906\) 0 0
\(907\) 37.1339 1.23301 0.616505 0.787351i \(-0.288548\pi\)
0.616505 + 0.787351i \(0.288548\pi\)
\(908\) −119.491 −3.96544
\(909\) 0 0
\(910\) −27.5664 −0.913816
\(911\) 38.9275 1.28973 0.644864 0.764298i \(-0.276914\pi\)
0.644864 + 0.764298i \(0.276914\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −55.3366 −1.83037
\(915\) 0 0
\(916\) 142.512 4.70874
\(917\) 4.22096 0.139388
\(918\) 0 0
\(919\) 29.1897 0.962881 0.481440 0.876479i \(-0.340114\pi\)
0.481440 + 0.876479i \(0.340114\pi\)
\(920\) 24.8618 0.819671
\(921\) 0 0
\(922\) 27.1242 0.893287
\(923\) 44.6173 1.46860
\(924\) 0 0
\(925\) −7.01568 −0.230674
\(926\) 20.1829 0.663250
\(927\) 0 0
\(928\) 118.712 3.89690
\(929\) −18.9850 −0.622879 −0.311440 0.950266i \(-0.600811\pi\)
−0.311440 + 0.950266i \(0.600811\pi\)
\(930\) 0 0
\(931\) 4.62860 0.151696
\(932\) −138.261 −4.52888
\(933\) 0 0
\(934\) −102.352 −3.34906
\(935\) 0 0
\(936\) 0 0
\(937\) 19.8921 0.649847 0.324924 0.945740i \(-0.394661\pi\)
0.324924 + 0.945740i \(0.394661\pi\)
\(938\) 17.2643 0.563700
\(939\) 0 0
\(940\) 25.3127 0.825608
\(941\) −10.9695 −0.357595 −0.178797 0.983886i \(-0.557221\pi\)
−0.178797 + 0.983886i \(0.557221\pi\)
\(942\) 0 0
\(943\) −11.4852 −0.374010
\(944\) 45.7805 1.49003
\(945\) 0 0
\(946\) 0 0
\(947\) 40.5321 1.31712 0.658558 0.752530i \(-0.271167\pi\)
0.658558 + 0.752530i \(0.271167\pi\)
\(948\) 0 0
\(949\) −74.8308 −2.42911
\(950\) −28.3096 −0.918484
\(951\) 0 0
\(952\) −3.26247 −0.105737
\(953\) −46.6243 −1.51031 −0.755154 0.655547i \(-0.772438\pi\)
−0.755154 + 0.655547i \(0.772438\pi\)
\(954\) 0 0
\(955\) 4.26971 0.138164
\(956\) −9.21516 −0.298039
\(957\) 0 0
\(958\) 109.063 3.52368
\(959\) 14.5361 0.469396
\(960\) 0 0
\(961\) −30.4162 −0.981166
\(962\) −52.7483 −1.70067
\(963\) 0 0
\(964\) 71.3794 2.29897
\(965\) −36.2850 −1.16806
\(966\) 0 0
\(967\) −27.2512 −0.876338 −0.438169 0.898893i \(-0.644373\pi\)
−0.438169 + 0.898893i \(0.644373\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 4.87247 0.156446
\(971\) −23.2361 −0.745683 −0.372842 0.927895i \(-0.621617\pi\)
−0.372842 + 0.927895i \(0.621617\pi\)
\(972\) 0 0
\(973\) −6.94615 −0.222684
\(974\) −67.1215 −2.15071
\(975\) 0 0
\(976\) −62.2709 −1.99324
\(977\) 28.7747 0.920583 0.460292 0.887768i \(-0.347745\pi\)
0.460292 + 0.887768i \(0.347745\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 9.78502 0.312571
\(981\) 0 0
\(982\) 8.93640 0.285172
\(983\) 28.1922 0.899192 0.449596 0.893232i \(-0.351568\pi\)
0.449596 + 0.893232i \(0.351568\pi\)
\(984\) 0 0
\(985\) −37.0251 −1.17972
\(986\) −3.37839 −0.107590
\(987\) 0 0
\(988\) −158.499 −5.04252
\(989\) 1.39641 0.0444034
\(990\) 0 0
\(991\) −47.6676 −1.51421 −0.757106 0.653293i \(-0.773387\pi\)
−0.757106 + 0.653293i \(0.773387\pi\)
\(992\) 22.8558 0.725673
\(993\) 0 0
\(994\) −21.2682 −0.674587
\(995\) −21.5270 −0.682451
\(996\) 0 0
\(997\) 18.6624 0.591046 0.295523 0.955336i \(-0.404506\pi\)
0.295523 + 0.955336i \(0.404506\pi\)
\(998\) 77.0557 2.43916
\(999\) 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.1.10 10
3.2 odd 2 2541.2.a.br.1.1 10
11.7 odd 10 693.2.m.j.379.1 20
11.8 odd 10 693.2.m.j.64.1 20
11.10 odd 2 7623.2.a.cx.1.1 10
33.8 even 10 231.2.j.g.64.5 20
33.29 even 10 231.2.j.g.148.5 yes 20
33.32 even 2 2541.2.a.bq.1.10 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.j.g.64.5 20 33.8 even 10
231.2.j.g.148.5 yes 20 33.29 even 10
693.2.m.j.64.1 20 11.8 odd 10
693.2.m.j.379.1 20 11.7 odd 10
2541.2.a.bq.1.10 10 33.32 even 2
2541.2.a.br.1.1 10 3.2 odd 2
7623.2.a.cx.1.1 10 11.10 odd 2
7623.2.a.cy.1.10 10 1.1 even 1 trivial