Properties

Label 4730.2.a.bb.1.1
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 11
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.87555\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.87555 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.87555 q^{6} -0.638121 q^{7} -1.00000 q^{8} +5.26880 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.87555 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.87555 q^{6} -0.638121 q^{7} -1.00000 q^{8} +5.26880 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.87555 q^{12} -4.59700 q^{13} +0.638121 q^{14} +2.87555 q^{15} +1.00000 q^{16} +2.19981 q^{17} -5.26880 q^{18} +8.48677 q^{19} -1.00000 q^{20} +1.83495 q^{21} +1.00000 q^{22} -6.59700 q^{23} +2.87555 q^{24} +1.00000 q^{25} +4.59700 q^{26} -6.52406 q^{27} -0.638121 q^{28} -7.34651 q^{29} -2.87555 q^{30} -2.58878 q^{31} -1.00000 q^{32} +2.87555 q^{33} -2.19981 q^{34} +0.638121 q^{35} +5.26880 q^{36} +8.68495 q^{37} -8.48677 q^{38} +13.2189 q^{39} +1.00000 q^{40} +5.97606 q^{41} -1.83495 q^{42} +1.00000 q^{43} -1.00000 q^{44} -5.26880 q^{45} +6.59700 q^{46} -7.43235 q^{47} -2.87555 q^{48} -6.59280 q^{49} -1.00000 q^{50} -6.32566 q^{51} -4.59700 q^{52} -1.66793 q^{53} +6.52406 q^{54} +1.00000 q^{55} +0.638121 q^{56} -24.4042 q^{57} +7.34651 q^{58} +9.08082 q^{59} +2.87555 q^{60} -7.07567 q^{61} +2.58878 q^{62} -3.36213 q^{63} +1.00000 q^{64} +4.59700 q^{65} -2.87555 q^{66} +3.07549 q^{67} +2.19981 q^{68} +18.9700 q^{69} -0.638121 q^{70} -2.59759 q^{71} -5.26880 q^{72} -16.2362 q^{73} -8.68495 q^{74} -2.87555 q^{75} +8.48677 q^{76} +0.638121 q^{77} -13.2189 q^{78} +6.29306 q^{79} -1.00000 q^{80} +2.95388 q^{81} -5.97606 q^{82} -2.36375 q^{83} +1.83495 q^{84} -2.19981 q^{85} -1.00000 q^{86} +21.1253 q^{87} +1.00000 q^{88} +3.41566 q^{89} +5.26880 q^{90} +2.93344 q^{91} -6.59700 q^{92} +7.44416 q^{93} +7.43235 q^{94} -8.48677 q^{95} +2.87555 q^{96} +6.87292 q^{97} +6.59280 q^{98} -5.26880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + O(q^{10}) \) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + 11q^{10} - 11q^{11} - q^{12} + 4q^{13} - 6q^{14} + q^{15} + 11q^{16} - 10q^{17} - 12q^{18} + 14q^{19} - 11q^{20} - 2q^{21} + 11q^{22} - 18q^{23} + q^{24} + 11q^{25} - 4q^{26} + 2q^{27} + 6q^{28} - 6q^{29} - q^{30} + 13q^{31} - 11q^{32} + q^{33} + 10q^{34} - 6q^{35} + 12q^{36} + q^{37} - 14q^{38} + 12q^{39} + 11q^{40} + 12q^{41} + 2q^{42} + 11q^{43} - 11q^{44} - 12q^{45} + 18q^{46} - 5q^{47} - q^{48} + 31q^{49} - 11q^{50} + q^{51} + 4q^{52} - 27q^{53} - 2q^{54} + 11q^{55} - 6q^{56} - 5q^{57} + 6q^{58} + 11q^{59} + q^{60} + 36q^{61} - 13q^{62} + 17q^{63} + 11q^{64} - 4q^{65} - q^{66} + 18q^{67} - 10q^{68} + 14q^{69} + 6q^{70} - 14q^{71} - 12q^{72} - 11q^{73} - q^{74} - q^{75} + 14q^{76} - 6q^{77} - 12q^{78} + 28q^{79} - 11q^{80} + 7q^{81} - 12q^{82} - 4q^{83} - 2q^{84} + 10q^{85} - 11q^{86} + 38q^{87} + 11q^{88} - 7q^{89} + 12q^{90} + 14q^{91} - 18q^{92} - 3q^{93} + 5q^{94} - 14q^{95} + q^{96} - q^{97} - 31q^{98} - 12q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.87555 −1.66020 −0.830101 0.557614i \(-0.811717\pi\)
−0.830101 + 0.557614i \(0.811717\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 2.87555 1.17394
\(7\) −0.638121 −0.241187 −0.120594 0.992702i \(-0.538480\pi\)
−0.120594 + 0.992702i \(0.538480\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.26880 1.75627
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) −2.87555 −0.830101
\(13\) −4.59700 −1.27498 −0.637489 0.770460i \(-0.720027\pi\)
−0.637489 + 0.770460i \(0.720027\pi\)
\(14\) 0.638121 0.170545
\(15\) 2.87555 0.742465
\(16\) 1.00000 0.250000
\(17\) 2.19981 0.533531 0.266766 0.963761i \(-0.414045\pi\)
0.266766 + 0.963761i \(0.414045\pi\)
\(18\) −5.26880 −1.24187
\(19\) 8.48677 1.94700 0.973499 0.228690i \(-0.0734442\pi\)
0.973499 + 0.228690i \(0.0734442\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.83495 0.400419
\(22\) 1.00000 0.213201
\(23\) −6.59700 −1.37557 −0.687785 0.725915i \(-0.741417\pi\)
−0.687785 + 0.725915i \(0.741417\pi\)
\(24\) 2.87555 0.586970
\(25\) 1.00000 0.200000
\(26\) 4.59700 0.901545
\(27\) −6.52406 −1.25556
\(28\) −0.638121 −0.120594
\(29\) −7.34651 −1.36421 −0.682107 0.731253i \(-0.738936\pi\)
−0.682107 + 0.731253i \(0.738936\pi\)
\(30\) −2.87555 −0.525002
\(31\) −2.58878 −0.464958 −0.232479 0.972601i \(-0.574684\pi\)
−0.232479 + 0.972601i \(0.574684\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.87555 0.500569
\(34\) −2.19981 −0.377264
\(35\) 0.638121 0.107862
\(36\) 5.26880 0.878134
\(37\) 8.68495 1.42780 0.713899 0.700249i \(-0.246928\pi\)
0.713899 + 0.700249i \(0.246928\pi\)
\(38\) −8.48677 −1.37674
\(39\) 13.2189 2.11672
\(40\) 1.00000 0.158114
\(41\) 5.97606 0.933304 0.466652 0.884441i \(-0.345460\pi\)
0.466652 + 0.884441i \(0.345460\pi\)
\(42\) −1.83495 −0.283139
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) −5.26880 −0.785427
\(46\) 6.59700 0.972674
\(47\) −7.43235 −1.08412 −0.542060 0.840340i \(-0.682355\pi\)
−0.542060 + 0.840340i \(0.682355\pi\)
\(48\) −2.87555 −0.415050
\(49\) −6.59280 −0.941829
\(50\) −1.00000 −0.141421
\(51\) −6.32566 −0.885769
\(52\) −4.59700 −0.637489
\(53\) −1.66793 −0.229108 −0.114554 0.993417i \(-0.536544\pi\)
−0.114554 + 0.993417i \(0.536544\pi\)
\(54\) 6.52406 0.887813
\(55\) 1.00000 0.134840
\(56\) 0.638121 0.0852725
\(57\) −24.4042 −3.23241
\(58\) 7.34651 0.964644
\(59\) 9.08082 1.18222 0.591111 0.806590i \(-0.298689\pi\)
0.591111 + 0.806590i \(0.298689\pi\)
\(60\) 2.87555 0.371232
\(61\) −7.07567 −0.905947 −0.452973 0.891524i \(-0.649637\pi\)
−0.452973 + 0.891524i \(0.649637\pi\)
\(62\) 2.58878 0.328775
\(63\) −3.36213 −0.423589
\(64\) 1.00000 0.125000
\(65\) 4.59700 0.570187
\(66\) −2.87555 −0.353956
\(67\) 3.07549 0.375731 0.187866 0.982195i \(-0.439843\pi\)
0.187866 + 0.982195i \(0.439843\pi\)
\(68\) 2.19981 0.266766
\(69\) 18.9700 2.28372
\(70\) −0.638121 −0.0762701
\(71\) −2.59759 −0.308278 −0.154139 0.988049i \(-0.549260\pi\)
−0.154139 + 0.988049i \(0.549260\pi\)
\(72\) −5.26880 −0.620934
\(73\) −16.2362 −1.90030 −0.950149 0.311796i \(-0.899070\pi\)
−0.950149 + 0.311796i \(0.899070\pi\)
\(74\) −8.68495 −1.00961
\(75\) −2.87555 −0.332040
\(76\) 8.48677 0.973499
\(77\) 0.638121 0.0727207
\(78\) −13.2189 −1.49675
\(79\) 6.29306 0.708024 0.354012 0.935241i \(-0.384817\pi\)
0.354012 + 0.935241i \(0.384817\pi\)
\(80\) −1.00000 −0.111803
\(81\) 2.95388 0.328209
\(82\) −5.97606 −0.659946
\(83\) −2.36375 −0.259455 −0.129728 0.991550i \(-0.541410\pi\)
−0.129728 + 0.991550i \(0.541410\pi\)
\(84\) 1.83495 0.200210
\(85\) −2.19981 −0.238602
\(86\) −1.00000 −0.107833
\(87\) 21.1253 2.26487
\(88\) 1.00000 0.106600
\(89\) 3.41566 0.362059 0.181030 0.983478i \(-0.442057\pi\)
0.181030 + 0.983478i \(0.442057\pi\)
\(90\) 5.26880 0.555381
\(91\) 2.93344 0.307508
\(92\) −6.59700 −0.687785
\(93\) 7.44416 0.771924
\(94\) 7.43235 0.766588
\(95\) −8.48677 −0.870724
\(96\) 2.87555 0.293485
\(97\) 6.87292 0.697840 0.348920 0.937153i \(-0.386549\pi\)
0.348920 + 0.937153i \(0.386549\pi\)
\(98\) 6.59280 0.665974
\(99\) −5.26880 −0.529535
\(100\) 1.00000 0.100000
\(101\) −3.48201 −0.346473 −0.173237 0.984880i \(-0.555423\pi\)
−0.173237 + 0.984880i \(0.555423\pi\)
\(102\) 6.32566 0.626333
\(103\) −2.39572 −0.236057 −0.118028 0.993010i \(-0.537657\pi\)
−0.118028 + 0.993010i \(0.537657\pi\)
\(104\) 4.59700 0.450773
\(105\) −1.83495 −0.179073
\(106\) 1.66793 0.162004
\(107\) −2.44388 −0.236259 −0.118130 0.992998i \(-0.537690\pi\)
−0.118130 + 0.992998i \(0.537690\pi\)
\(108\) −6.52406 −0.627778
\(109\) −17.0063 −1.62891 −0.814453 0.580229i \(-0.802963\pi\)
−0.814453 + 0.580229i \(0.802963\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −24.9740 −2.37043
\(112\) −0.638121 −0.0602968
\(113\) −19.3050 −1.81606 −0.908031 0.418903i \(-0.862415\pi\)
−0.908031 + 0.418903i \(0.862415\pi\)
\(114\) 24.4042 2.28566
\(115\) 6.59700 0.615173
\(116\) −7.34651 −0.682107
\(117\) −24.2207 −2.23920
\(118\) −9.08082 −0.835958
\(119\) −1.40374 −0.128681
\(120\) −2.87555 −0.262501
\(121\) 1.00000 0.0909091
\(122\) 7.07567 0.640601
\(123\) −17.1845 −1.54947
\(124\) −2.58878 −0.232479
\(125\) −1.00000 −0.0894427
\(126\) 3.36213 0.299523
\(127\) 14.3223 1.27089 0.635447 0.772144i \(-0.280816\pi\)
0.635447 + 0.772144i \(0.280816\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.87555 −0.253178
\(130\) −4.59700 −0.403183
\(131\) −20.3247 −1.77577 −0.887887 0.460062i \(-0.847827\pi\)
−0.887887 + 0.460062i \(0.847827\pi\)
\(132\) 2.87555 0.250285
\(133\) −5.41559 −0.469591
\(134\) −3.07549 −0.265682
\(135\) 6.52406 0.561502
\(136\) −2.19981 −0.188632
\(137\) −1.83433 −0.156717 −0.0783586 0.996925i \(-0.524968\pi\)
−0.0783586 + 0.996925i \(0.524968\pi\)
\(138\) −18.9700 −1.61483
\(139\) 19.0091 1.61233 0.806167 0.591688i \(-0.201538\pi\)
0.806167 + 0.591688i \(0.201538\pi\)
\(140\) 0.638121 0.0539311
\(141\) 21.3721 1.79986
\(142\) 2.59759 0.217985
\(143\) 4.59700 0.384420
\(144\) 5.26880 0.439067
\(145\) 7.34651 0.610095
\(146\) 16.2362 1.34371
\(147\) 18.9579 1.56363
\(148\) 8.68495 0.713899
\(149\) −5.64636 −0.462568 −0.231284 0.972886i \(-0.574293\pi\)
−0.231284 + 0.972886i \(0.574293\pi\)
\(150\) 2.87555 0.234788
\(151\) −12.7081 −1.03417 −0.517084 0.855935i \(-0.672982\pi\)
−0.517084 + 0.855935i \(0.672982\pi\)
\(152\) −8.48677 −0.688368
\(153\) 11.5903 0.937024
\(154\) −0.638121 −0.0514213
\(155\) 2.58878 0.207936
\(156\) 13.2189 1.05836
\(157\) −8.30966 −0.663183 −0.331592 0.943423i \(-0.607586\pi\)
−0.331592 + 0.943423i \(0.607586\pi\)
\(158\) −6.29306 −0.500649
\(159\) 4.79623 0.380366
\(160\) 1.00000 0.0790569
\(161\) 4.20968 0.331770
\(162\) −2.95388 −0.232079
\(163\) 1.36870 0.107205 0.0536025 0.998562i \(-0.482930\pi\)
0.0536025 + 0.998562i \(0.482930\pi\)
\(164\) 5.97606 0.466652
\(165\) −2.87555 −0.223861
\(166\) 2.36375 0.183463
\(167\) −0.269910 −0.0208863 −0.0104431 0.999945i \(-0.503324\pi\)
−0.0104431 + 0.999945i \(0.503324\pi\)
\(168\) −1.83495 −0.141570
\(169\) 8.13238 0.625568
\(170\) 2.19981 0.168717
\(171\) 44.7151 3.41945
\(172\) 1.00000 0.0762493
\(173\) 0.646448 0.0491486 0.0245743 0.999698i \(-0.492177\pi\)
0.0245743 + 0.999698i \(0.492177\pi\)
\(174\) −21.1253 −1.60150
\(175\) −0.638121 −0.0482374
\(176\) −1.00000 −0.0753778
\(177\) −26.1124 −1.96273
\(178\) −3.41566 −0.256014
\(179\) −9.33927 −0.698050 −0.349025 0.937113i \(-0.613487\pi\)
−0.349025 + 0.937113i \(0.613487\pi\)
\(180\) −5.26880 −0.392713
\(181\) 23.1945 1.72403 0.862017 0.506879i \(-0.169201\pi\)
0.862017 + 0.506879i \(0.169201\pi\)
\(182\) −2.93344 −0.217441
\(183\) 20.3465 1.50405
\(184\) 6.59700 0.486337
\(185\) −8.68495 −0.638530
\(186\) −7.44416 −0.545832
\(187\) −2.19981 −0.160866
\(188\) −7.43235 −0.542060
\(189\) 4.16314 0.302824
\(190\) 8.48677 0.615695
\(191\) 1.40312 0.101526 0.0507631 0.998711i \(-0.483835\pi\)
0.0507631 + 0.998711i \(0.483835\pi\)
\(192\) −2.87555 −0.207525
\(193\) −12.2988 −0.885287 −0.442644 0.896698i \(-0.645959\pi\)
−0.442644 + 0.896698i \(0.645959\pi\)
\(194\) −6.87292 −0.493447
\(195\) −13.2189 −0.946626
\(196\) −6.59280 −0.470914
\(197\) 11.3866 0.811260 0.405630 0.914037i \(-0.367052\pi\)
0.405630 + 0.914037i \(0.367052\pi\)
\(198\) 5.26880 0.374438
\(199\) −0.348978 −0.0247384 −0.0123692 0.999923i \(-0.503937\pi\)
−0.0123692 + 0.999923i \(0.503937\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −8.84375 −0.623790
\(202\) 3.48201 0.244994
\(203\) 4.68797 0.329031
\(204\) −6.32566 −0.442885
\(205\) −5.97606 −0.417386
\(206\) 2.39572 0.166917
\(207\) −34.7583 −2.41587
\(208\) −4.59700 −0.318744
\(209\) −8.48677 −0.587042
\(210\) 1.83495 0.126624
\(211\) 16.2045 1.11556 0.557781 0.829988i \(-0.311653\pi\)
0.557781 + 0.829988i \(0.311653\pi\)
\(212\) −1.66793 −0.114554
\(213\) 7.46952 0.511803
\(214\) 2.44388 0.167060
\(215\) −1.00000 −0.0681994
\(216\) 6.52406 0.443906
\(217\) 1.65195 0.112142
\(218\) 17.0063 1.15181
\(219\) 46.6879 3.15488
\(220\) 1.00000 0.0674200
\(221\) −10.1125 −0.680240
\(222\) 24.9740 1.67615
\(223\) −7.27004 −0.486838 −0.243419 0.969921i \(-0.578269\pi\)
−0.243419 + 0.969921i \(0.578269\pi\)
\(224\) 0.638121 0.0426363
\(225\) 5.26880 0.351254
\(226\) 19.3050 1.28415
\(227\) −22.9239 −1.52151 −0.760756 0.649038i \(-0.775172\pi\)
−0.760756 + 0.649038i \(0.775172\pi\)
\(228\) −24.4042 −1.61620
\(229\) −17.3301 −1.14520 −0.572602 0.819834i \(-0.694066\pi\)
−0.572602 + 0.819834i \(0.694066\pi\)
\(230\) −6.59700 −0.434993
\(231\) −1.83495 −0.120731
\(232\) 7.34651 0.482322
\(233\) 16.5045 1.08124 0.540622 0.841265i \(-0.318189\pi\)
0.540622 + 0.841265i \(0.318189\pi\)
\(234\) 24.2207 1.58335
\(235\) 7.43235 0.484833
\(236\) 9.08082 0.591111
\(237\) −18.0960 −1.17546
\(238\) 1.40374 0.0909911
\(239\) 19.8684 1.28518 0.642591 0.766209i \(-0.277859\pi\)
0.642591 + 0.766209i \(0.277859\pi\)
\(240\) 2.87555 0.185616
\(241\) −26.6728 −1.71814 −0.859072 0.511855i \(-0.828959\pi\)
−0.859072 + 0.511855i \(0.828959\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 11.0782 0.710664
\(244\) −7.07567 −0.452973
\(245\) 6.59280 0.421199
\(246\) 17.1845 1.09564
\(247\) −39.0137 −2.48238
\(248\) 2.58878 0.164387
\(249\) 6.79709 0.430748
\(250\) 1.00000 0.0632456
\(251\) 4.27840 0.270050 0.135025 0.990842i \(-0.456889\pi\)
0.135025 + 0.990842i \(0.456889\pi\)
\(252\) −3.36213 −0.211795
\(253\) 6.59700 0.414750
\(254\) −14.3223 −0.898658
\(255\) 6.32566 0.396128
\(256\) 1.00000 0.0625000
\(257\) 14.5985 0.910628 0.455314 0.890331i \(-0.349527\pi\)
0.455314 + 0.890331i \(0.349527\pi\)
\(258\) 2.87555 0.179024
\(259\) −5.54205 −0.344366
\(260\) 4.59700 0.285094
\(261\) −38.7073 −2.39592
\(262\) 20.3247 1.25566
\(263\) 0.0322302 0.00198740 0.000993700 1.00000i \(-0.499684\pi\)
0.000993700 1.00000i \(0.499684\pi\)
\(264\) −2.87555 −0.176978
\(265\) 1.66793 0.102460
\(266\) 5.41559 0.332051
\(267\) −9.82191 −0.601091
\(268\) 3.07549 0.187866
\(269\) −0.394595 −0.0240589 −0.0120294 0.999928i \(-0.503829\pi\)
−0.0120294 + 0.999928i \(0.503829\pi\)
\(270\) −6.52406 −0.397042
\(271\) 28.5263 1.73285 0.866423 0.499310i \(-0.166413\pi\)
0.866423 + 0.499310i \(0.166413\pi\)
\(272\) 2.19981 0.133383
\(273\) −8.43526 −0.510525
\(274\) 1.83433 0.110816
\(275\) −1.00000 −0.0603023
\(276\) 18.9700 1.14186
\(277\) 30.2610 1.81821 0.909105 0.416567i \(-0.136767\pi\)
0.909105 + 0.416567i \(0.136767\pi\)
\(278\) −19.0091 −1.14009
\(279\) −13.6398 −0.816591
\(280\) −0.638121 −0.0381350
\(281\) 15.4840 0.923695 0.461848 0.886959i \(-0.347187\pi\)
0.461848 + 0.886959i \(0.347187\pi\)
\(282\) −21.3721 −1.27269
\(283\) −10.0140 −0.595271 −0.297636 0.954680i \(-0.596198\pi\)
−0.297636 + 0.954680i \(0.596198\pi\)
\(284\) −2.59759 −0.154139
\(285\) 24.4042 1.44558
\(286\) −4.59700 −0.271826
\(287\) −3.81345 −0.225101
\(288\) −5.26880 −0.310467
\(289\) −12.1609 −0.715344
\(290\) −7.34651 −0.431402
\(291\) −19.7635 −1.15855
\(292\) −16.2362 −0.950149
\(293\) 10.6641 0.623002 0.311501 0.950246i \(-0.399168\pi\)
0.311501 + 0.950246i \(0.399168\pi\)
\(294\) −18.9579 −1.10565
\(295\) −9.08082 −0.528706
\(296\) −8.68495 −0.504803
\(297\) 6.52406 0.378565
\(298\) 5.64636 0.327085
\(299\) 30.3264 1.75382
\(300\) −2.87555 −0.166020
\(301\) −0.638121 −0.0367807
\(302\) 12.7081 0.731267
\(303\) 10.0127 0.575215
\(304\) 8.48677 0.486750
\(305\) 7.07567 0.405152
\(306\) −11.5903 −0.662576
\(307\) 15.1916 0.867029 0.433515 0.901147i \(-0.357273\pi\)
0.433515 + 0.901147i \(0.357273\pi\)
\(308\) 0.638121 0.0363603
\(309\) 6.88901 0.391902
\(310\) −2.58878 −0.147033
\(311\) −21.3131 −1.20855 −0.604277 0.796774i \(-0.706538\pi\)
−0.604277 + 0.796774i \(0.706538\pi\)
\(312\) −13.2189 −0.748373
\(313\) 3.96895 0.224339 0.112169 0.993689i \(-0.464220\pi\)
0.112169 + 0.993689i \(0.464220\pi\)
\(314\) 8.30966 0.468941
\(315\) 3.36213 0.189435
\(316\) 6.29306 0.354012
\(317\) 1.66920 0.0937514 0.0468757 0.998901i \(-0.485074\pi\)
0.0468757 + 0.998901i \(0.485074\pi\)
\(318\) −4.79623 −0.268959
\(319\) 7.34651 0.411326
\(320\) −1.00000 −0.0559017
\(321\) 7.02752 0.392238
\(322\) −4.20968 −0.234596
\(323\) 18.6692 1.03878
\(324\) 2.95388 0.164104
\(325\) −4.59700 −0.254996
\(326\) −1.36870 −0.0758054
\(327\) 48.9025 2.70431
\(328\) −5.97606 −0.329973
\(329\) 4.74274 0.261476
\(330\) 2.87555 0.158294
\(331\) 28.2235 1.55131 0.775653 0.631160i \(-0.217421\pi\)
0.775653 + 0.631160i \(0.217421\pi\)
\(332\) −2.36375 −0.129728
\(333\) 45.7593 2.50759
\(334\) 0.269910 0.0147688
\(335\) −3.07549 −0.168032
\(336\) 1.83495 0.100105
\(337\) −19.2662 −1.04950 −0.524750 0.851257i \(-0.675841\pi\)
−0.524750 + 0.851257i \(0.675841\pi\)
\(338\) −8.13238 −0.442343
\(339\) 55.5126 3.01503
\(340\) −2.19981 −0.119301
\(341\) 2.58878 0.140190
\(342\) −44.7151 −2.41792
\(343\) 8.67385 0.468344
\(344\) −1.00000 −0.0539164
\(345\) −18.9700 −1.02131
\(346\) −0.646448 −0.0347533
\(347\) 28.1125 1.50916 0.754580 0.656208i \(-0.227840\pi\)
0.754580 + 0.656208i \(0.227840\pi\)
\(348\) 21.1253 1.13243
\(349\) −18.4755 −0.988972 −0.494486 0.869186i \(-0.664644\pi\)
−0.494486 + 0.869186i \(0.664644\pi\)
\(350\) 0.638121 0.0341090
\(351\) 29.9911 1.60081
\(352\) 1.00000 0.0533002
\(353\) 35.2433 1.87581 0.937905 0.346893i \(-0.112763\pi\)
0.937905 + 0.346893i \(0.112763\pi\)
\(354\) 26.1124 1.38786
\(355\) 2.59759 0.137866
\(356\) 3.41566 0.181030
\(357\) 4.03654 0.213636
\(358\) 9.33927 0.493596
\(359\) −7.85867 −0.414765 −0.207382 0.978260i \(-0.566494\pi\)
−0.207382 + 0.978260i \(0.566494\pi\)
\(360\) 5.26880 0.277690
\(361\) 53.0253 2.79080
\(362\) −23.1945 −1.21908
\(363\) −2.87555 −0.150927
\(364\) 2.93344 0.153754
\(365\) 16.2362 0.849839
\(366\) −20.3465 −1.06353
\(367\) 24.1696 1.26164 0.630820 0.775929i \(-0.282718\pi\)
0.630820 + 0.775929i \(0.282718\pi\)
\(368\) −6.59700 −0.343892
\(369\) 31.4867 1.63913
\(370\) 8.68495 0.451509
\(371\) 1.06434 0.0552579
\(372\) 7.44416 0.385962
\(373\) 31.4941 1.63070 0.815352 0.578966i \(-0.196543\pi\)
0.815352 + 0.578966i \(0.196543\pi\)
\(374\) 2.19981 0.113749
\(375\) 2.87555 0.148493
\(376\) 7.43235 0.383294
\(377\) 33.7719 1.73934
\(378\) −4.16314 −0.214129
\(379\) 20.1041 1.03268 0.516340 0.856384i \(-0.327294\pi\)
0.516340 + 0.856384i \(0.327294\pi\)
\(380\) −8.48677 −0.435362
\(381\) −41.1844 −2.10994
\(382\) −1.40312 −0.0717899
\(383\) 5.85924 0.299393 0.149696 0.988732i \(-0.452170\pi\)
0.149696 + 0.988732i \(0.452170\pi\)
\(384\) 2.87555 0.146742
\(385\) −0.638121 −0.0325217
\(386\) 12.2988 0.625993
\(387\) 5.26880 0.267828
\(388\) 6.87292 0.348920
\(389\) 23.6324 1.19821 0.599104 0.800671i \(-0.295524\pi\)
0.599104 + 0.800671i \(0.295524\pi\)
\(390\) 13.2189 0.669365
\(391\) −14.5121 −0.733909
\(392\) 6.59280 0.332987
\(393\) 58.4446 2.94814
\(394\) −11.3866 −0.573648
\(395\) −6.29306 −0.316638
\(396\) −5.26880 −0.264767
\(397\) −0.614338 −0.0308328 −0.0154164 0.999881i \(-0.504907\pi\)
−0.0154164 + 0.999881i \(0.504907\pi\)
\(398\) 0.348978 0.0174927
\(399\) 15.5728 0.779616
\(400\) 1.00000 0.0500000
\(401\) −14.0403 −0.701137 −0.350569 0.936537i \(-0.614012\pi\)
−0.350569 + 0.936537i \(0.614012\pi\)
\(402\) 8.84375 0.441086
\(403\) 11.9006 0.592811
\(404\) −3.48201 −0.173237
\(405\) −2.95388 −0.146779
\(406\) −4.68797 −0.232660
\(407\) −8.68495 −0.430497
\(408\) 6.32566 0.313167
\(409\) 15.3070 0.756885 0.378442 0.925625i \(-0.376460\pi\)
0.378442 + 0.925625i \(0.376460\pi\)
\(410\) 5.97606 0.295137
\(411\) 5.27471 0.260182
\(412\) −2.39572 −0.118028
\(413\) −5.79467 −0.285137
\(414\) 34.7583 1.70828
\(415\) 2.36375 0.116032
\(416\) 4.59700 0.225386
\(417\) −54.6618 −2.67680
\(418\) 8.48677 0.415102
\(419\) 8.77181 0.428531 0.214266 0.976775i \(-0.431264\pi\)
0.214266 + 0.976775i \(0.431264\pi\)
\(420\) −1.83495 −0.0895364
\(421\) −25.5129 −1.24342 −0.621711 0.783247i \(-0.713562\pi\)
−0.621711 + 0.783247i \(0.713562\pi\)
\(422\) −16.2045 −0.788822
\(423\) −39.1596 −1.90400
\(424\) 1.66793 0.0810019
\(425\) 2.19981 0.106706
\(426\) −7.46952 −0.361899
\(427\) 4.51514 0.218503
\(428\) −2.44388 −0.118130
\(429\) −13.2189 −0.638215
\(430\) 1.00000 0.0482243
\(431\) 26.6342 1.28292 0.641462 0.767155i \(-0.278328\pi\)
0.641462 + 0.767155i \(0.278328\pi\)
\(432\) −6.52406 −0.313889
\(433\) 23.1169 1.11093 0.555464 0.831541i \(-0.312541\pi\)
0.555464 + 0.831541i \(0.312541\pi\)
\(434\) −1.65195 −0.0792963
\(435\) −21.1253 −1.01288
\(436\) −17.0063 −0.814453
\(437\) −55.9872 −2.67823
\(438\) −46.6879 −2.23084
\(439\) −6.45373 −0.308020 −0.154010 0.988069i \(-0.549219\pi\)
−0.154010 + 0.988069i \(0.549219\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −34.7362 −1.65410
\(442\) 10.1125 0.481003
\(443\) 20.2055 0.959990 0.479995 0.877271i \(-0.340638\pi\)
0.479995 + 0.877271i \(0.340638\pi\)
\(444\) −24.9740 −1.18522
\(445\) −3.41566 −0.161918
\(446\) 7.27004 0.344247
\(447\) 16.2364 0.767955
\(448\) −0.638121 −0.0301484
\(449\) −8.99123 −0.424322 −0.212161 0.977235i \(-0.568050\pi\)
−0.212161 + 0.977235i \(0.568050\pi\)
\(450\) −5.26880 −0.248374
\(451\) −5.97606 −0.281402
\(452\) −19.3050 −0.908031
\(453\) 36.5427 1.71693
\(454\) 22.9239 1.07587
\(455\) −2.93344 −0.137522
\(456\) 24.4042 1.14283
\(457\) −4.97783 −0.232853 −0.116427 0.993199i \(-0.537144\pi\)
−0.116427 + 0.993199i \(0.537144\pi\)
\(458\) 17.3301 0.809781
\(459\) −14.3517 −0.669879
\(460\) 6.59700 0.307587
\(461\) −4.25819 −0.198324 −0.0991619 0.995071i \(-0.531616\pi\)
−0.0991619 + 0.995071i \(0.531616\pi\)
\(462\) 1.83495 0.0853697
\(463\) −1.78970 −0.0831742 −0.0415871 0.999135i \(-0.513241\pi\)
−0.0415871 + 0.999135i \(0.513241\pi\)
\(464\) −7.34651 −0.341053
\(465\) −7.44416 −0.345215
\(466\) −16.5045 −0.764555
\(467\) 4.04228 0.187055 0.0935273 0.995617i \(-0.470186\pi\)
0.0935273 + 0.995617i \(0.470186\pi\)
\(468\) −24.2207 −1.11960
\(469\) −1.96254 −0.0906216
\(470\) −7.43235 −0.342829
\(471\) 23.8949 1.10102
\(472\) −9.08082 −0.417979
\(473\) −1.00000 −0.0459800
\(474\) 18.0960 0.831177
\(475\) 8.48677 0.389400
\(476\) −1.40374 −0.0643404
\(477\) −8.78801 −0.402375
\(478\) −19.8684 −0.908761
\(479\) −0.426479 −0.0194863 −0.00974315 0.999953i \(-0.503101\pi\)
−0.00974315 + 0.999953i \(0.503101\pi\)
\(480\) −2.87555 −0.131250
\(481\) −39.9247 −1.82041
\(482\) 26.6728 1.21491
\(483\) −12.1052 −0.550804
\(484\) 1.00000 0.0454545
\(485\) −6.87292 −0.312083
\(486\) −11.0782 −0.502515
\(487\) −11.7826 −0.533919 −0.266960 0.963708i \(-0.586019\pi\)
−0.266960 + 0.963708i \(0.586019\pi\)
\(488\) 7.07567 0.320301
\(489\) −3.93578 −0.177982
\(490\) −6.59280 −0.297832
\(491\) 20.4651 0.923576 0.461788 0.886990i \(-0.347208\pi\)
0.461788 + 0.886990i \(0.347208\pi\)
\(492\) −17.1845 −0.774736
\(493\) −16.1609 −0.727850
\(494\) 39.0137 1.75531
\(495\) 5.26880 0.236815
\(496\) −2.58878 −0.116239
\(497\) 1.65758 0.0743526
\(498\) −6.79709 −0.304585
\(499\) 31.3220 1.40217 0.701083 0.713079i \(-0.252700\pi\)
0.701083 + 0.713079i \(0.252700\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 0.776140 0.0346754
\(502\) −4.27840 −0.190954
\(503\) −37.4072 −1.66790 −0.833952 0.551837i \(-0.813927\pi\)
−0.833952 + 0.551837i \(0.813927\pi\)
\(504\) 3.36213 0.149761
\(505\) 3.48201 0.154948
\(506\) −6.59700 −0.293272
\(507\) −23.3851 −1.03857
\(508\) 14.3223 0.635447
\(509\) −8.27957 −0.366986 −0.183493 0.983021i \(-0.558740\pi\)
−0.183493 + 0.983021i \(0.558740\pi\)
\(510\) −6.32566 −0.280105
\(511\) 10.3606 0.458328
\(512\) −1.00000 −0.0441942
\(513\) −55.3682 −2.44457
\(514\) −14.5985 −0.643911
\(515\) 2.39572 0.105568
\(516\) −2.87555 −0.126589
\(517\) 7.43235 0.326874
\(518\) 5.54205 0.243504
\(519\) −1.85890 −0.0815965
\(520\) −4.59700 −0.201592
\(521\) −30.4036 −1.33201 −0.666003 0.745949i \(-0.731996\pi\)
−0.666003 + 0.745949i \(0.731996\pi\)
\(522\) 38.7073 1.69417
\(523\) 13.3889 0.585457 0.292728 0.956196i \(-0.405437\pi\)
0.292728 + 0.956196i \(0.405437\pi\)
\(524\) −20.3247 −0.887887
\(525\) 1.83495 0.0800838
\(526\) −0.0322302 −0.00140530
\(527\) −5.69481 −0.248070
\(528\) 2.87555 0.125142
\(529\) 20.5204 0.892190
\(530\) −1.66793 −0.0724503
\(531\) 47.8451 2.07630
\(532\) −5.41559 −0.234796
\(533\) −27.4719 −1.18994
\(534\) 9.82191 0.425035
\(535\) 2.44388 0.105658
\(536\) −3.07549 −0.132841
\(537\) 26.8556 1.15890
\(538\) 0.394595 0.0170122
\(539\) 6.59280 0.283972
\(540\) 6.52406 0.280751
\(541\) 41.4011 1.77997 0.889987 0.455986i \(-0.150713\pi\)
0.889987 + 0.455986i \(0.150713\pi\)
\(542\) −28.5263 −1.22531
\(543\) −66.6970 −2.86224
\(544\) −2.19981 −0.0943159
\(545\) 17.0063 0.728469
\(546\) 8.43526 0.360996
\(547\) 20.5225 0.877477 0.438738 0.898615i \(-0.355425\pi\)
0.438738 + 0.898615i \(0.355425\pi\)
\(548\) −1.83433 −0.0783586
\(549\) −37.2803 −1.59109
\(550\) 1.00000 0.0426401
\(551\) −62.3482 −2.65612
\(552\) −18.9700 −0.807417
\(553\) −4.01573 −0.170766
\(554\) −30.2610 −1.28567
\(555\) 24.9740 1.06009
\(556\) 19.0091 0.806167
\(557\) 4.70330 0.199285 0.0996425 0.995023i \(-0.468230\pi\)
0.0996425 + 0.995023i \(0.468230\pi\)
\(558\) 13.6398 0.577417
\(559\) −4.59700 −0.194432
\(560\) 0.638121 0.0269655
\(561\) 6.32566 0.267069
\(562\) −15.4840 −0.653151
\(563\) 41.0955 1.73197 0.865984 0.500072i \(-0.166693\pi\)
0.865984 + 0.500072i \(0.166693\pi\)
\(564\) 21.3721 0.899928
\(565\) 19.3050 0.812168
\(566\) 10.0140 0.420920
\(567\) −1.88493 −0.0791597
\(568\) 2.59759 0.108993
\(569\) −22.3293 −0.936091 −0.468046 0.883704i \(-0.655042\pi\)
−0.468046 + 0.883704i \(0.655042\pi\)
\(570\) −24.4042 −1.02218
\(571\) 44.2211 1.85060 0.925298 0.379240i \(-0.123814\pi\)
0.925298 + 0.379240i \(0.123814\pi\)
\(572\) 4.59700 0.192210
\(573\) −4.03475 −0.168554
\(574\) 3.81345 0.159170
\(575\) −6.59700 −0.275114
\(576\) 5.26880 0.219533
\(577\) 21.3812 0.890112 0.445056 0.895503i \(-0.353184\pi\)
0.445056 + 0.895503i \(0.353184\pi\)
\(578\) 12.1609 0.505825
\(579\) 35.3659 1.46975
\(580\) 7.34651 0.305047
\(581\) 1.50836 0.0625773
\(582\) 19.7635 0.819222
\(583\) 1.66793 0.0690787
\(584\) 16.2362 0.671857
\(585\) 24.2207 1.00140
\(586\) −10.6641 −0.440529
\(587\) −32.8265 −1.35489 −0.677447 0.735571i \(-0.736914\pi\)
−0.677447 + 0.735571i \(0.736914\pi\)
\(588\) 18.9579 0.781813
\(589\) −21.9703 −0.905272
\(590\) 9.08082 0.373852
\(591\) −32.7427 −1.34686
\(592\) 8.68495 0.356949
\(593\) −12.7659 −0.524233 −0.262116 0.965036i \(-0.584420\pi\)
−0.262116 + 0.965036i \(0.584420\pi\)
\(594\) −6.52406 −0.267686
\(595\) 1.40374 0.0575478
\(596\) −5.64636 −0.231284
\(597\) 1.00350 0.0410707
\(598\) −30.3264 −1.24014
\(599\) 18.3086 0.748069 0.374035 0.927415i \(-0.377974\pi\)
0.374035 + 0.927415i \(0.377974\pi\)
\(600\) 2.87555 0.117394
\(601\) −31.3338 −1.27813 −0.639066 0.769152i \(-0.720679\pi\)
−0.639066 + 0.769152i \(0.720679\pi\)
\(602\) 0.638121 0.0260079
\(603\) 16.2042 0.659885
\(604\) −12.7081 −0.517084
\(605\) −1.00000 −0.0406558
\(606\) −10.0127 −0.406739
\(607\) −25.5715 −1.03791 −0.518957 0.854800i \(-0.673680\pi\)
−0.518957 + 0.854800i \(0.673680\pi\)
\(608\) −8.48677 −0.344184
\(609\) −13.4805 −0.546257
\(610\) −7.07567 −0.286486
\(611\) 34.1665 1.38223
\(612\) 11.5903 0.468512
\(613\) −15.0173 −0.606542 −0.303271 0.952904i \(-0.598079\pi\)
−0.303271 + 0.952904i \(0.598079\pi\)
\(614\) −15.1916 −0.613082
\(615\) 17.1845 0.692945
\(616\) −0.638121 −0.0257106
\(617\) −34.3038 −1.38102 −0.690510 0.723323i \(-0.742614\pi\)
−0.690510 + 0.723323i \(0.742614\pi\)
\(618\) −6.88901 −0.277116
\(619\) 15.2296 0.612131 0.306065 0.952010i \(-0.400987\pi\)
0.306065 + 0.952010i \(0.400987\pi\)
\(620\) 2.58878 0.103968
\(621\) 43.0392 1.72710
\(622\) 21.3131 0.854577
\(623\) −2.17960 −0.0873240
\(624\) 13.2189 0.529180
\(625\) 1.00000 0.0400000
\(626\) −3.96895 −0.158631
\(627\) 24.4042 0.974608
\(628\) −8.30966 −0.331592
\(629\) 19.1052 0.761775
\(630\) −3.36213 −0.133951
\(631\) −4.96641 −0.197710 −0.0988548 0.995102i \(-0.531518\pi\)
−0.0988548 + 0.995102i \(0.531518\pi\)
\(632\) −6.29306 −0.250324
\(633\) −46.5968 −1.85206
\(634\) −1.66920 −0.0662922
\(635\) −14.3223 −0.568361
\(636\) 4.79623 0.190183
\(637\) 30.3071 1.20081
\(638\) −7.34651 −0.290851
\(639\) −13.6862 −0.541418
\(640\) 1.00000 0.0395285
\(641\) −37.0352 −1.46280 −0.731400 0.681948i \(-0.761133\pi\)
−0.731400 + 0.681948i \(0.761133\pi\)
\(642\) −7.02752 −0.277354
\(643\) 11.1674 0.440400 0.220200 0.975455i \(-0.429329\pi\)
0.220200 + 0.975455i \(0.429329\pi\)
\(644\) 4.20968 0.165885
\(645\) 2.87555 0.113225
\(646\) −18.6692 −0.734532
\(647\) −22.4095 −0.881007 −0.440503 0.897751i \(-0.645200\pi\)
−0.440503 + 0.897751i \(0.645200\pi\)
\(648\) −2.95388 −0.116039
\(649\) −9.08082 −0.356454
\(650\) 4.59700 0.180309
\(651\) −4.75028 −0.186178
\(652\) 1.36870 0.0536025
\(653\) 6.15856 0.241003 0.120502 0.992713i \(-0.461550\pi\)
0.120502 + 0.992713i \(0.461550\pi\)
\(654\) −48.9025 −1.91224
\(655\) 20.3247 0.794150
\(656\) 5.97606 0.233326
\(657\) −85.5451 −3.33743
\(658\) −4.74274 −0.184891
\(659\) −34.8201 −1.35640 −0.678199 0.734879i \(-0.737239\pi\)
−0.678199 + 0.734879i \(0.737239\pi\)
\(660\) −2.87555 −0.111931
\(661\) 2.11984 0.0824521 0.0412260 0.999150i \(-0.486874\pi\)
0.0412260 + 0.999150i \(0.486874\pi\)
\(662\) −28.2235 −1.09694
\(663\) 29.0790 1.12934
\(664\) 2.36375 0.0917313
\(665\) 5.41559 0.210007
\(666\) −45.7593 −1.77314
\(667\) 48.4649 1.87657
\(668\) −0.269910 −0.0104431
\(669\) 20.9054 0.808249
\(670\) 3.07549 0.118817
\(671\) 7.07567 0.273153
\(672\) −1.83495 −0.0707848
\(673\) 8.62867 0.332611 0.166305 0.986074i \(-0.446816\pi\)
0.166305 + 0.986074i \(0.446816\pi\)
\(674\) 19.2662 0.742108
\(675\) −6.52406 −0.251111
\(676\) 8.13238 0.312784
\(677\) −27.1640 −1.04400 −0.521999 0.852946i \(-0.674814\pi\)
−0.521999 + 0.852946i \(0.674814\pi\)
\(678\) −55.5126 −2.13195
\(679\) −4.38576 −0.168310
\(680\) 2.19981 0.0843587
\(681\) 65.9188 2.52602
\(682\) −2.58878 −0.0991294
\(683\) 5.82198 0.222772 0.111386 0.993777i \(-0.464471\pi\)
0.111386 + 0.993777i \(0.464471\pi\)
\(684\) 44.7151 1.70973
\(685\) 1.83433 0.0700861
\(686\) −8.67385 −0.331169
\(687\) 49.8335 1.90127
\(688\) 1.00000 0.0381246
\(689\) 7.66748 0.292108
\(690\) 18.9700 0.722176
\(691\) 27.9562 1.06350 0.531752 0.846900i \(-0.321534\pi\)
0.531752 + 0.846900i \(0.321534\pi\)
\(692\) 0.646448 0.0245743
\(693\) 3.36213 0.127717
\(694\) −28.1125 −1.06714
\(695\) −19.0091 −0.721058
\(696\) −21.1253 −0.800752
\(697\) 13.1462 0.497947
\(698\) 18.4755 0.699309
\(699\) −47.4595 −1.79508
\(700\) −0.638121 −0.0241187
\(701\) −11.7301 −0.443040 −0.221520 0.975156i \(-0.571102\pi\)
−0.221520 + 0.975156i \(0.571102\pi\)
\(702\) −29.9911 −1.13194
\(703\) 73.7072 2.77992
\(704\) −1.00000 −0.0376889
\(705\) −21.3721 −0.804920
\(706\) −35.2433 −1.32640
\(707\) 2.22195 0.0835649
\(708\) −26.1124 −0.981364
\(709\) 17.2242 0.646867 0.323434 0.946251i \(-0.395163\pi\)
0.323434 + 0.946251i \(0.395163\pi\)
\(710\) −2.59759 −0.0974860
\(711\) 33.1569 1.24348
\(712\) −3.41566 −0.128007
\(713\) 17.0781 0.639582
\(714\) −4.03654 −0.151064
\(715\) −4.59700 −0.171918
\(716\) −9.33927 −0.349025
\(717\) −57.1327 −2.13366
\(718\) 7.85867 0.293283
\(719\) 48.5029 1.80885 0.904426 0.426630i \(-0.140299\pi\)
0.904426 + 0.426630i \(0.140299\pi\)
\(720\) −5.26880 −0.196357
\(721\) 1.52876 0.0569339
\(722\) −53.0253 −1.97340
\(723\) 76.6990 2.85247
\(724\) 23.1945 0.862017
\(725\) −7.34651 −0.272843
\(726\) 2.87555 0.106722
\(727\) −27.2863 −1.01199 −0.505997 0.862535i \(-0.668875\pi\)
−0.505997 + 0.862535i \(0.668875\pi\)
\(728\) −2.93344 −0.108721
\(729\) −40.7175 −1.50805
\(730\) −16.2362 −0.600927
\(731\) 2.19981 0.0813628
\(732\) 20.3465 0.752027
\(733\) −25.3697 −0.937052 −0.468526 0.883450i \(-0.655215\pi\)
−0.468526 + 0.883450i \(0.655215\pi\)
\(734\) −24.1696 −0.892115
\(735\) −18.9579 −0.699274
\(736\) 6.59700 0.243169
\(737\) −3.07549 −0.113287
\(738\) −31.4867 −1.15904
\(739\) 30.1802 1.11019 0.555097 0.831785i \(-0.312681\pi\)
0.555097 + 0.831785i \(0.312681\pi\)
\(740\) −8.68495 −0.319265
\(741\) 112.186 4.12125
\(742\) −1.06434 −0.0390733
\(743\) −7.83477 −0.287430 −0.143715 0.989619i \(-0.545905\pi\)
−0.143715 + 0.989619i \(0.545905\pi\)
\(744\) −7.44416 −0.272916
\(745\) 5.64636 0.206867
\(746\) −31.4941 −1.15308
\(747\) −12.4541 −0.455673
\(748\) −2.19981 −0.0804329
\(749\) 1.55949 0.0569827
\(750\) −2.87555 −0.105000
\(751\) 19.6346 0.716477 0.358239 0.933630i \(-0.383377\pi\)
0.358239 + 0.933630i \(0.383377\pi\)
\(752\) −7.43235 −0.271030
\(753\) −12.3028 −0.448338
\(754\) −33.7719 −1.22990
\(755\) 12.7081 0.462494
\(756\) 4.16314 0.151412
\(757\) −5.29850 −0.192577 −0.0962886 0.995353i \(-0.530697\pi\)
−0.0962886 + 0.995353i \(0.530697\pi\)
\(758\) −20.1041 −0.730215
\(759\) −18.9700 −0.688568
\(760\) 8.48677 0.307848
\(761\) 11.2280 0.407013 0.203507 0.979074i \(-0.434766\pi\)
0.203507 + 0.979074i \(0.434766\pi\)
\(762\) 41.1844 1.49195
\(763\) 10.8521 0.392871
\(764\) 1.40312 0.0507631
\(765\) −11.5903 −0.419050
\(766\) −5.85924 −0.211703
\(767\) −41.7445 −1.50731
\(768\) −2.87555 −0.103763
\(769\) −29.2911 −1.05626 −0.528132 0.849162i \(-0.677107\pi\)
−0.528132 + 0.849162i \(0.677107\pi\)
\(770\) 0.638121 0.0229963
\(771\) −41.9787 −1.51183
\(772\) −12.2988 −0.442644
\(773\) −29.7669 −1.07064 −0.535321 0.844649i \(-0.679809\pi\)
−0.535321 + 0.844649i \(0.679809\pi\)
\(774\) −5.26880 −0.189383
\(775\) −2.58878 −0.0929916
\(776\) −6.87292 −0.246724
\(777\) 15.9365 0.571717
\(778\) −23.6324 −0.847261
\(779\) 50.7175 1.81714
\(780\) −13.2189 −0.473313
\(781\) 2.59759 0.0929492
\(782\) 14.5121 0.518952
\(783\) 47.9291 1.71285
\(784\) −6.59280 −0.235457
\(785\) 8.30966 0.296585
\(786\) −58.4446 −2.08465
\(787\) 4.95817 0.176740 0.0883698 0.996088i \(-0.471834\pi\)
0.0883698 + 0.996088i \(0.471834\pi\)
\(788\) 11.3866 0.405630
\(789\) −0.0926797 −0.00329948
\(790\) 6.29306 0.223897
\(791\) 12.3189 0.438011
\(792\) 5.26880 0.187219
\(793\) 32.5268 1.15506
\(794\) 0.614338 0.0218020
\(795\) −4.79623 −0.170105
\(796\) −0.348978 −0.0123692
\(797\) 16.1850 0.573303 0.286652 0.958035i \(-0.407458\pi\)
0.286652 + 0.958035i \(0.407458\pi\)
\(798\) −15.5728 −0.551271
\(799\) −16.3497 −0.578412
\(800\) −1.00000 −0.0353553
\(801\) 17.9964 0.635873
\(802\) 14.0403 0.495779
\(803\) 16.2362 0.572962
\(804\) −8.84375 −0.311895
\(805\) −4.20968 −0.148372
\(806\) −11.9006 −0.419181
\(807\) 1.13468 0.0399426
\(808\) 3.48201 0.122497
\(809\) 45.7892 1.60986 0.804931 0.593369i \(-0.202202\pi\)
0.804931 + 0.593369i \(0.202202\pi\)
\(810\) 2.95388 0.103789
\(811\) −27.5186 −0.966307 −0.483154 0.875536i \(-0.660509\pi\)
−0.483154 + 0.875536i \(0.660509\pi\)
\(812\) 4.68797 0.164515
\(813\) −82.0288 −2.87687
\(814\) 8.68495 0.304407
\(815\) −1.36870 −0.0479436
\(816\) −6.32566 −0.221442
\(817\) 8.48677 0.296915
\(818\) −15.3070 −0.535198
\(819\) 15.4557 0.540067
\(820\) −5.97606 −0.208693
\(821\) −16.0882 −0.561483 −0.280742 0.959783i \(-0.590580\pi\)
−0.280742 + 0.959783i \(0.590580\pi\)
\(822\) −5.27471 −0.183977
\(823\) 22.2062 0.774059 0.387029 0.922067i \(-0.373501\pi\)
0.387029 + 0.922067i \(0.373501\pi\)
\(824\) 2.39572 0.0834587
\(825\) 2.87555 0.100114
\(826\) 5.79467 0.201622
\(827\) −40.2921 −1.40109 −0.700546 0.713607i \(-0.747060\pi\)
−0.700546 + 0.713607i \(0.747060\pi\)
\(828\) −34.7583 −1.20793
\(829\) 0.540032 0.0187561 0.00937805 0.999956i \(-0.497015\pi\)
0.00937805 + 0.999956i \(0.497015\pi\)
\(830\) −2.36375 −0.0820469
\(831\) −87.0172 −3.01859
\(832\) −4.59700 −0.159372
\(833\) −14.5029 −0.502495
\(834\) 54.6618 1.89278
\(835\) 0.269910 0.00934062
\(836\) −8.48677 −0.293521
\(837\) 16.8893 0.583781
\(838\) −8.77181 −0.303017
\(839\) −49.6637 −1.71458 −0.857290 0.514833i \(-0.827854\pi\)
−0.857290 + 0.514833i \(0.827854\pi\)
\(840\) 1.83495 0.0633118
\(841\) 24.9713 0.861078
\(842\) 25.5129 0.879232
\(843\) −44.5249 −1.53352
\(844\) 16.2045 0.557781
\(845\) −8.13238 −0.279762
\(846\) 39.1596 1.34633
\(847\) −0.638121 −0.0219261
\(848\) −1.66793 −0.0572770
\(849\) 28.7958 0.988270
\(850\) −2.19981 −0.0754527
\(851\) −57.2946 −1.96403
\(852\) 7.46952 0.255901
\(853\) −30.6175 −1.04832 −0.524162 0.851619i \(-0.675621\pi\)
−0.524162 + 0.851619i \(0.675621\pi\)
\(854\) −4.51514 −0.154505
\(855\) −44.7151 −1.52922
\(856\) 2.44388 0.0835302
\(857\) −15.4649 −0.528271 −0.264136 0.964486i \(-0.585087\pi\)
−0.264136 + 0.964486i \(0.585087\pi\)
\(858\) 13.2189 0.451286
\(859\) 37.7982 1.28966 0.644830 0.764326i \(-0.276928\pi\)
0.644830 + 0.764326i \(0.276928\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 10.9658 0.373713
\(862\) −26.6342 −0.907164
\(863\) 18.7929 0.639716 0.319858 0.947465i \(-0.396365\pi\)
0.319858 + 0.947465i \(0.396365\pi\)
\(864\) 6.52406 0.221953
\(865\) −0.646448 −0.0219799
\(866\) −23.1169 −0.785545
\(867\) 34.9692 1.18762
\(868\) 1.65195 0.0560709
\(869\) −6.29306 −0.213477
\(870\) 21.1253 0.716214
\(871\) −14.1380 −0.479049
\(872\) 17.0063 0.575905
\(873\) 36.2121 1.22559
\(874\) 55.9872 1.89380
\(875\) 0.638121 0.0215724
\(876\) 46.6879 1.57744
\(877\) 29.4637 0.994918 0.497459 0.867487i \(-0.334266\pi\)
0.497459 + 0.867487i \(0.334266\pi\)
\(878\) 6.45373 0.217803
\(879\) −30.6651 −1.03431
\(880\) 1.00000 0.0337100
\(881\) −26.4214 −0.890160 −0.445080 0.895491i \(-0.646825\pi\)
−0.445080 + 0.895491i \(0.646825\pi\)
\(882\) 34.7362 1.16963
\(883\) 48.0012 1.61537 0.807684 0.589615i \(-0.200721\pi\)
0.807684 + 0.589615i \(0.200721\pi\)
\(884\) −10.1125 −0.340120
\(885\) 26.1124 0.877758
\(886\) −20.2055 −0.678816
\(887\) 34.6035 1.16187 0.580937 0.813949i \(-0.302686\pi\)
0.580937 + 0.813949i \(0.302686\pi\)
\(888\) 24.9740 0.838074
\(889\) −9.13933 −0.306523
\(890\) 3.41566 0.114493
\(891\) −2.95388 −0.0989586
\(892\) −7.27004 −0.243419
\(893\) −63.0766 −2.11078
\(894\) −16.2364 −0.543026
\(895\) 9.33927 0.312177
\(896\) 0.638121 0.0213181
\(897\) −87.2051 −2.91169
\(898\) 8.99123 0.300041
\(899\) 19.0185 0.634302
\(900\) 5.26880 0.175627
\(901\) −3.66913 −0.122236
\(902\) 5.97606 0.198981
\(903\) 1.83495 0.0610633
\(904\) 19.3050 0.642075
\(905\) −23.1945 −0.771012
\(906\) −36.5427 −1.21405
\(907\) −45.9937 −1.52719 −0.763597 0.645693i \(-0.776569\pi\)
−0.763597 + 0.645693i \(0.776569\pi\)
\(908\) −22.9239 −0.760756
\(909\) −18.3460 −0.608500
\(910\) 2.93344 0.0972426
\(911\) 20.1996 0.669242 0.334621 0.942353i \(-0.391392\pi\)
0.334621 + 0.942353i \(0.391392\pi\)
\(912\) −24.4042 −0.808102
\(913\) 2.36375 0.0782287
\(914\) 4.97783 0.164652
\(915\) −20.3465 −0.672633
\(916\) −17.3301 −0.572602
\(917\) 12.9696 0.428294
\(918\) 14.3517 0.473676
\(919\) 8.01951 0.264539 0.132270 0.991214i \(-0.457774\pi\)
0.132270 + 0.991214i \(0.457774\pi\)
\(920\) −6.59700 −0.217497
\(921\) −43.6842 −1.43944
\(922\) 4.25819 0.140236
\(923\) 11.9411 0.393047
\(924\) −1.83495 −0.0603655
\(925\) 8.68495 0.285560
\(926\) 1.78970 0.0588131
\(927\) −12.6226 −0.414579
\(928\) 7.34651 0.241161
\(929\) −3.02292 −0.0991789 −0.0495894 0.998770i \(-0.515791\pi\)
−0.0495894 + 0.998770i \(0.515791\pi\)
\(930\) 7.44416 0.244104
\(931\) −55.9516 −1.83374
\(932\) 16.5045 0.540622
\(933\) 61.2869 2.00644
\(934\) −4.04228 −0.132268
\(935\) 2.19981 0.0719413
\(936\) 24.2207 0.791677
\(937\) −9.41462 −0.307562 −0.153781 0.988105i \(-0.549145\pi\)
−0.153781 + 0.988105i \(0.549145\pi\)
\(938\) 1.96254 0.0640791
\(939\) −11.4129 −0.372447
\(940\) 7.43235 0.242417
\(941\) 49.3505 1.60878 0.804390 0.594101i \(-0.202492\pi\)
0.804390 + 0.594101i \(0.202492\pi\)
\(942\) −23.8949 −0.778537
\(943\) −39.4241 −1.28382
\(944\) 9.08082 0.295556
\(945\) −4.16314 −0.135427
\(946\) 1.00000 0.0325128
\(947\) −22.6328 −0.735466 −0.367733 0.929931i \(-0.619866\pi\)
−0.367733 + 0.929931i \(0.619866\pi\)
\(948\) −18.0960 −0.587731
\(949\) 74.6376 2.42284
\(950\) −8.48677 −0.275347
\(951\) −4.79986 −0.155646
\(952\) 1.40374 0.0454956
\(953\) 28.2361 0.914656 0.457328 0.889298i \(-0.348807\pi\)
0.457328 + 0.889298i \(0.348807\pi\)
\(954\) 8.78801 0.284522
\(955\) −1.40312 −0.0454039
\(956\) 19.8684 0.642591
\(957\) −21.1253 −0.682884
\(958\) 0.426479 0.0137789
\(959\) 1.17052 0.0377982
\(960\) 2.87555 0.0928081
\(961\) −24.2982 −0.783814
\(962\) 39.9247 1.28722
\(963\) −12.8763 −0.414934
\(964\) −26.6728 −0.859072
\(965\) 12.2988 0.395912
\(966\) 12.1052 0.389477
\(967\) −12.8001 −0.411625 −0.205812 0.978591i \(-0.565984\pi\)
−0.205812 + 0.978591i \(0.565984\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −53.6844 −1.72459
\(970\) 6.87292 0.220676
\(971\) 41.1070 1.31919 0.659593 0.751623i \(-0.270729\pi\)
0.659593 + 0.751623i \(0.270729\pi\)
\(972\) 11.0782 0.355332
\(973\) −12.1301 −0.388874
\(974\) 11.7826 0.377538
\(975\) 13.2189 0.423344
\(976\) −7.07567 −0.226487
\(977\) 25.6163 0.819538 0.409769 0.912189i \(-0.365609\pi\)
0.409769 + 0.912189i \(0.365609\pi\)
\(978\) 3.93578 0.125852
\(979\) −3.41566 −0.109165
\(980\) 6.59280 0.210599
\(981\) −89.6027 −2.86080
\(982\) −20.4651 −0.653067
\(983\) −18.1604 −0.579227 −0.289614 0.957144i \(-0.593527\pi\)
−0.289614 + 0.957144i \(0.593527\pi\)
\(984\) 17.1845 0.547821
\(985\) −11.3866 −0.362807
\(986\) 16.1609 0.514668
\(987\) −13.6380 −0.434102
\(988\) −39.0137 −1.24119
\(989\) −6.59700 −0.209772
\(990\) −5.26880 −0.167454
\(991\) −37.9311 −1.20492 −0.602461 0.798148i \(-0.705813\pi\)
−0.602461 + 0.798148i \(0.705813\pi\)
\(992\) 2.58878 0.0821937
\(993\) −81.1582 −2.57548
\(994\) −1.65758 −0.0525752
\(995\) 0.348978 0.0110633
\(996\) 6.79709 0.215374
\(997\) 14.8104 0.469051 0.234526 0.972110i \(-0.424646\pi\)
0.234526 + 0.972110i \(0.424646\pi\)
\(998\) −31.3220 −0.991482
\(999\) −56.6612 −1.79268
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 4730.2.a.bb.1.1 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bb.1.1 11 1.1 even 1 trivial