Properties

Label 4730.2.a.bb.1.9
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 1.9
Root \(-1.80931\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.80931 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.80931 q^{6} +4.53794 q^{7} -1.00000 q^{8} +0.273608 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.80931 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.80931 q^{6} +4.53794 q^{7} -1.00000 q^{8} +0.273608 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.80931 q^{12} +1.28672 q^{13} -4.53794 q^{14} -1.80931 q^{15} +1.00000 q^{16} -2.49948 q^{17} -0.273608 q^{18} +4.30450 q^{19} -1.00000 q^{20} +8.21054 q^{21} +1.00000 q^{22} -0.713282 q^{23} -1.80931 q^{24} +1.00000 q^{25} -1.28672 q^{26} -4.93289 q^{27} +4.53794 q^{28} -4.09374 q^{29} +1.80931 q^{30} +6.87649 q^{31} -1.00000 q^{32} -1.80931 q^{33} +2.49948 q^{34} -4.53794 q^{35} +0.273608 q^{36} +2.58524 q^{37} -4.30450 q^{38} +2.32807 q^{39} +1.00000 q^{40} +2.61453 q^{41} -8.21054 q^{42} +1.00000 q^{43} -1.00000 q^{44} -0.273608 q^{45} +0.713282 q^{46} +7.75858 q^{47} +1.80931 q^{48} +13.5929 q^{49} -1.00000 q^{50} -4.52234 q^{51} +1.28672 q^{52} +7.15552 q^{53} +4.93289 q^{54} +1.00000 q^{55} -4.53794 q^{56} +7.78817 q^{57} +4.09374 q^{58} -2.05592 q^{59} -1.80931 q^{60} -7.20843 q^{61} -6.87649 q^{62} +1.24162 q^{63} +1.00000 q^{64} -1.28672 q^{65} +1.80931 q^{66} +4.88949 q^{67} -2.49948 q^{68} -1.29055 q^{69} +4.53794 q^{70} -10.4518 q^{71} -0.273608 q^{72} -4.33504 q^{73} -2.58524 q^{74} +1.80931 q^{75} +4.30450 q^{76} -4.53794 q^{77} -2.32807 q^{78} +14.1763 q^{79} -1.00000 q^{80} -9.74596 q^{81} -2.61453 q^{82} +14.5435 q^{83} +8.21054 q^{84} +2.49948 q^{85} -1.00000 q^{86} -7.40684 q^{87} +1.00000 q^{88} +3.85436 q^{89} +0.273608 q^{90} +5.83904 q^{91} -0.713282 q^{92} +12.4417 q^{93} -7.75858 q^{94} -4.30450 q^{95} -1.80931 q^{96} +10.0330 q^{97} -13.5929 q^{98} -0.273608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + O(q^{10}) \) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + 11q^{10} - 11q^{11} - q^{12} + 4q^{13} - 6q^{14} + q^{15} + 11q^{16} - 10q^{17} - 12q^{18} + 14q^{19} - 11q^{20} - 2q^{21} + 11q^{22} - 18q^{23} + q^{24} + 11q^{25} - 4q^{26} + 2q^{27} + 6q^{28} - 6q^{29} - q^{30} + 13q^{31} - 11q^{32} + q^{33} + 10q^{34} - 6q^{35} + 12q^{36} + q^{37} - 14q^{38} + 12q^{39} + 11q^{40} + 12q^{41} + 2q^{42} + 11q^{43} - 11q^{44} - 12q^{45} + 18q^{46} - 5q^{47} - q^{48} + 31q^{49} - 11q^{50} + q^{51} + 4q^{52} - 27q^{53} - 2q^{54} + 11q^{55} - 6q^{56} - 5q^{57} + 6q^{58} + 11q^{59} + q^{60} + 36q^{61} - 13q^{62} + 17q^{63} + 11q^{64} - 4q^{65} - q^{66} + 18q^{67} - 10q^{68} + 14q^{69} + 6q^{70} - 14q^{71} - 12q^{72} - 11q^{73} - q^{74} - q^{75} + 14q^{76} - 6q^{77} - 12q^{78} + 28q^{79} - 11q^{80} + 7q^{81} - 12q^{82} - 4q^{83} - 2q^{84} + 10q^{85} - 11q^{86} + 38q^{87} + 11q^{88} - 7q^{89} + 12q^{90} + 14q^{91} - 18q^{92} - 3q^{93} + 5q^{94} - 14q^{95} + q^{96} - q^{97} - 31q^{98} - 12q^{99} + O(q^{100}) \)

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
\(3\) 1.80931 1.04461 0.522303 0.852760i \(-0.325073\pi\)
0.522303 + 0.852760i \(0.325073\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.80931 −0.738648
\(7\) 4.53794 1.71518 0.857589 0.514335i \(-0.171961\pi\)
0.857589 + 0.514335i \(0.171961\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.273608 0.0912027
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) 1.80931 0.522303
\(13\) 1.28672 0.356871 0.178436 0.983952i \(-0.442896\pi\)
0.178436 + 0.983952i \(0.442896\pi\)
\(14\) −4.53794 −1.21281
\(15\) −1.80931 −0.467162
\(16\) 1.00000 0.250000
\(17\) −2.49948 −0.606213 −0.303106 0.952957i \(-0.598024\pi\)
−0.303106 + 0.952957i \(0.598024\pi\)
\(18\) −0.273608 −0.0644900
\(19\) 4.30450 0.987519 0.493760 0.869598i \(-0.335622\pi\)
0.493760 + 0.869598i \(0.335622\pi\)
\(20\) −1.00000 −0.223607
\(21\) 8.21054 1.79169
\(22\) 1.00000 0.213201
\(23\) −0.713282 −0.148730 −0.0743648 0.997231i \(-0.523693\pi\)
−0.0743648 + 0.997231i \(0.523693\pi\)
\(24\) −1.80931 −0.369324
\(25\) 1.00000 0.200000
\(26\) −1.28672 −0.252346
\(27\) −4.93289 −0.949336
\(28\) 4.53794 0.857589
\(29\) −4.09374 −0.760188 −0.380094 0.924948i \(-0.624108\pi\)
−0.380094 + 0.924948i \(0.624108\pi\)
\(30\) 1.80931 0.330334
\(31\) 6.87649 1.23505 0.617527 0.786550i \(-0.288135\pi\)
0.617527 + 0.786550i \(0.288135\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.80931 −0.314961
\(34\) 2.49948 0.428657
\(35\) −4.53794 −0.767051
\(36\) 0.273608 0.0456013
\(37\) 2.58524 0.425010 0.212505 0.977160i \(-0.431838\pi\)
0.212505 + 0.977160i \(0.431838\pi\)
\(38\) −4.30450 −0.698281
\(39\) 2.32807 0.372790
\(40\) 1.00000 0.158114
\(41\) 2.61453 0.408322 0.204161 0.978937i \(-0.434553\pi\)
0.204161 + 0.978937i \(0.434553\pi\)
\(42\) −8.21054 −1.26691
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) −0.273608 −0.0407871
\(46\) 0.713282 0.105168
\(47\) 7.75858 1.13171 0.565853 0.824506i \(-0.308547\pi\)
0.565853 + 0.824506i \(0.308547\pi\)
\(48\) 1.80931 0.261152
\(49\) 13.5929 1.94184
\(50\) −1.00000 −0.141421
\(51\) −4.52234 −0.633254
\(52\) 1.28672 0.178436
\(53\) 7.15552 0.982887 0.491443 0.870909i \(-0.336469\pi\)
0.491443 + 0.870909i \(0.336469\pi\)
\(54\) 4.93289 0.671282
\(55\) 1.00000 0.134840
\(56\) −4.53794 −0.606407
\(57\) 7.78817 1.03157
\(58\) 4.09374 0.537534
\(59\) −2.05592 −0.267658 −0.133829 0.991004i \(-0.542727\pi\)
−0.133829 + 0.991004i \(0.542727\pi\)
\(60\) −1.80931 −0.233581
\(61\) −7.20843 −0.922945 −0.461473 0.887154i \(-0.652679\pi\)
−0.461473 + 0.887154i \(0.652679\pi\)
\(62\) −6.87649 −0.873315
\(63\) 1.24162 0.156429
\(64\) 1.00000 0.125000
\(65\) −1.28672 −0.159598
\(66\) 1.80931 0.222711
\(67\) 4.88949 0.597346 0.298673 0.954356i \(-0.403456\pi\)
0.298673 + 0.954356i \(0.403456\pi\)
\(68\) −2.49948 −0.303106
\(69\) −1.29055 −0.155364
\(70\) 4.53794 0.542387
\(71\) −10.4518 −1.24040 −0.620202 0.784442i \(-0.712949\pi\)
−0.620202 + 0.784442i \(0.712949\pi\)
\(72\) −0.273608 −0.0322450
\(73\) −4.33504 −0.507378 −0.253689 0.967286i \(-0.581644\pi\)
−0.253689 + 0.967286i \(0.581644\pi\)
\(74\) −2.58524 −0.300527
\(75\) 1.80931 0.208921
\(76\) 4.30450 0.493760
\(77\) −4.53794 −0.517146
\(78\) −2.32807 −0.263602
\(79\) 14.1763 1.59496 0.797479 0.603347i \(-0.206166\pi\)
0.797479 + 0.603347i \(0.206166\pi\)
\(80\) −1.00000 −0.111803
\(81\) −9.74596 −1.08288
\(82\) −2.61453 −0.288727
\(83\) 14.5435 1.59635 0.798176 0.602424i \(-0.205798\pi\)
0.798176 + 0.602424i \(0.205798\pi\)
\(84\) 8.21054 0.895843
\(85\) 2.49948 0.271107
\(86\) −1.00000 −0.107833
\(87\) −7.40684 −0.794097
\(88\) 1.00000 0.106600
\(89\) 3.85436 0.408561 0.204280 0.978912i \(-0.434515\pi\)
0.204280 + 0.978912i \(0.434515\pi\)
\(90\) 0.273608 0.0288408
\(91\) 5.83904 0.612098
\(92\) −0.713282 −0.0743648
\(93\) 12.4417 1.29014
\(94\) −7.75858 −0.800236
\(95\) −4.30450 −0.441632
\(96\) −1.80931 −0.184662
\(97\) 10.0330 1.01870 0.509349 0.860560i \(-0.329886\pi\)
0.509349 + 0.860560i \(0.329886\pi\)
\(98\) −13.5929 −1.37309
\(99\) −0.273608 −0.0274986
\(100\) 1.00000 0.100000
\(101\) 17.9835 1.78942 0.894710 0.446647i \(-0.147382\pi\)
0.894710 + 0.446647i \(0.147382\pi\)
\(102\) 4.52234 0.447778
\(103\) 19.5618 1.92748 0.963740 0.266843i \(-0.0859806\pi\)
0.963740 + 0.266843i \(0.0859806\pi\)
\(104\) −1.28672 −0.126173
\(105\) −8.21054 −0.801267
\(106\) −7.15552 −0.695006
\(107\) −10.3310 −0.998735 −0.499367 0.866390i \(-0.666434\pi\)
−0.499367 + 0.866390i \(0.666434\pi\)
\(108\) −4.93289 −0.474668
\(109\) −15.6482 −1.49882 −0.749411 0.662105i \(-0.769663\pi\)
−0.749411 + 0.662105i \(0.769663\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 4.67750 0.443968
\(112\) 4.53794 0.428795
\(113\) 0.00194142 0.000182633 0 9.13167e−5 1.00000i \(-0.499971\pi\)
9.13167e−5 1.00000i \(0.499971\pi\)
\(114\) −7.78817 −0.729429
\(115\) 0.713282 0.0665139
\(116\) −4.09374 −0.380094
\(117\) 0.352056 0.0325476
\(118\) 2.05592 0.189263
\(119\) −11.3425 −1.03976
\(120\) 1.80931 0.165167
\(121\) 1.00000 0.0909091
\(122\) 7.20843 0.652621
\(123\) 4.73051 0.426535
\(124\) 6.87649 0.617527
\(125\) −1.00000 −0.0894427
\(126\) −1.24162 −0.110612
\(127\) 1.99032 0.176612 0.0883062 0.996093i \(-0.471855\pi\)
0.0883062 + 0.996093i \(0.471855\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.80931 0.159301
\(130\) 1.28672 0.112853
\(131\) −6.17996 −0.539945 −0.269973 0.962868i \(-0.587015\pi\)
−0.269973 + 0.962868i \(0.587015\pi\)
\(132\) −1.80931 −0.157480
\(133\) 19.5335 1.69377
\(134\) −4.88949 −0.422387
\(135\) 4.93289 0.424556
\(136\) 2.49948 0.214329
\(137\) −18.9373 −1.61792 −0.808961 0.587863i \(-0.799969\pi\)
−0.808961 + 0.587863i \(0.799969\pi\)
\(138\) 1.29055 0.109859
\(139\) −10.0357 −0.851220 −0.425610 0.904907i \(-0.639940\pi\)
−0.425610 + 0.904907i \(0.639940\pi\)
\(140\) −4.53794 −0.383526
\(141\) 14.0377 1.18219
\(142\) 10.4518 0.877098
\(143\) −1.28672 −0.107601
\(144\) 0.273608 0.0228007
\(145\) 4.09374 0.339966
\(146\) 4.33504 0.358771
\(147\) 24.5937 2.02846
\(148\) 2.58524 0.212505
\(149\) 14.0528 1.15125 0.575625 0.817714i \(-0.304759\pi\)
0.575625 + 0.817714i \(0.304759\pi\)
\(150\) −1.80931 −0.147730
\(151\) −11.3656 −0.924919 −0.462460 0.886640i \(-0.653033\pi\)
−0.462460 + 0.886640i \(0.653033\pi\)
\(152\) −4.30450 −0.349141
\(153\) −0.683878 −0.0552883
\(154\) 4.53794 0.365677
\(155\) −6.87649 −0.552333
\(156\) 2.32807 0.186395
\(157\) 16.9897 1.35593 0.677963 0.735096i \(-0.262863\pi\)
0.677963 + 0.735096i \(0.262863\pi\)
\(158\) −14.1763 −1.12781
\(159\) 12.9466 1.02673
\(160\) 1.00000 0.0790569
\(161\) −3.23683 −0.255098
\(162\) 9.74596 0.765715
\(163\) −18.7453 −1.46825 −0.734124 0.679015i \(-0.762407\pi\)
−0.734124 + 0.679015i \(0.762407\pi\)
\(164\) 2.61453 0.204161
\(165\) 1.80931 0.140855
\(166\) −14.5435 −1.12879
\(167\) 15.7842 1.22142 0.610711 0.791854i \(-0.290884\pi\)
0.610711 + 0.791854i \(0.290884\pi\)
\(168\) −8.21054 −0.633457
\(169\) −11.3444 −0.872643
\(170\) −2.49948 −0.191701
\(171\) 1.17774 0.0900644
\(172\) 1.00000 0.0762493
\(173\) 23.4793 1.78510 0.892548 0.450953i \(-0.148916\pi\)
0.892548 + 0.450953i \(0.148916\pi\)
\(174\) 7.40684 0.561511
\(175\) 4.53794 0.343036
\(176\) −1.00000 −0.0753778
\(177\) −3.71980 −0.279598
\(178\) −3.85436 −0.288896
\(179\) −0.0200101 −0.00149563 −0.000747813 1.00000i \(-0.500238\pi\)
−0.000747813 1.00000i \(0.500238\pi\)
\(180\) −0.273608 −0.0203935
\(181\) 15.0756 1.12056 0.560280 0.828303i \(-0.310693\pi\)
0.560280 + 0.828303i \(0.310693\pi\)
\(182\) −5.83904 −0.432819
\(183\) −13.0423 −0.964115
\(184\) 0.713282 0.0525839
\(185\) −2.58524 −0.190070
\(186\) −12.4417 −0.912270
\(187\) 2.49948 0.182780
\(188\) 7.75858 0.565853
\(189\) −22.3851 −1.62828
\(190\) 4.30450 0.312281
\(191\) −22.3644 −1.61823 −0.809114 0.587651i \(-0.800053\pi\)
−0.809114 + 0.587651i \(0.800053\pi\)
\(192\) 1.80931 0.130576
\(193\) −17.6534 −1.27072 −0.635361 0.772216i \(-0.719149\pi\)
−0.635361 + 0.772216i \(0.719149\pi\)
\(194\) −10.0330 −0.720328
\(195\) −2.32807 −0.166717
\(196\) 13.5929 0.970919
\(197\) −0.716160 −0.0510243 −0.0255122 0.999675i \(-0.508122\pi\)
−0.0255122 + 0.999675i \(0.508122\pi\)
\(198\) 0.273608 0.0194445
\(199\) −10.1363 −0.718547 −0.359273 0.933232i \(-0.616975\pi\)
−0.359273 + 0.933232i \(0.616975\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 8.84660 0.623991
\(202\) −17.9835 −1.26531
\(203\) −18.5771 −1.30386
\(204\) −4.52234 −0.316627
\(205\) −2.61453 −0.182607
\(206\) −19.5618 −1.36293
\(207\) −0.195160 −0.0135645
\(208\) 1.28672 0.0892178
\(209\) −4.30450 −0.297748
\(210\) 8.21054 0.566581
\(211\) 27.1396 1.86837 0.934184 0.356792i \(-0.116130\pi\)
0.934184 + 0.356792i \(0.116130\pi\)
\(212\) 7.15552 0.491443
\(213\) −18.9106 −1.29573
\(214\) 10.3310 0.706212
\(215\) −1.00000 −0.0681994
\(216\) 4.93289 0.335641
\(217\) 31.2051 2.11834
\(218\) 15.6482 1.05983
\(219\) −7.84344 −0.530011
\(220\) 1.00000 0.0674200
\(221\) −3.21613 −0.216340
\(222\) −4.67750 −0.313933
\(223\) −26.9918 −1.80750 −0.903752 0.428057i \(-0.859198\pi\)
−0.903752 + 0.428057i \(0.859198\pi\)
\(224\) −4.53794 −0.303204
\(225\) 0.273608 0.0182405
\(226\) −0.00194142 −0.000129141 0
\(227\) 16.1933 1.07479 0.537395 0.843331i \(-0.319408\pi\)
0.537395 + 0.843331i \(0.319408\pi\)
\(228\) 7.78817 0.515784
\(229\) −3.67036 −0.242544 −0.121272 0.992619i \(-0.538697\pi\)
−0.121272 + 0.992619i \(0.538697\pi\)
\(230\) −0.713282 −0.0470324
\(231\) −8.21054 −0.540214
\(232\) 4.09374 0.268767
\(233\) 2.89466 0.189636 0.0948179 0.995495i \(-0.469773\pi\)
0.0948179 + 0.995495i \(0.469773\pi\)
\(234\) −0.352056 −0.0230146
\(235\) −7.75858 −0.506114
\(236\) −2.05592 −0.133829
\(237\) 25.6493 1.66610
\(238\) 11.3425 0.735224
\(239\) −24.6223 −1.59269 −0.796343 0.604845i \(-0.793235\pi\)
−0.796343 + 0.604845i \(0.793235\pi\)
\(240\) −1.80931 −0.116791
\(241\) 13.6048 0.876365 0.438182 0.898886i \(-0.355622\pi\)
0.438182 + 0.898886i \(0.355622\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −2.83481 −0.181853
\(244\) −7.20843 −0.461473
\(245\) −13.5929 −0.868416
\(246\) −4.73051 −0.301606
\(247\) 5.53867 0.352417
\(248\) −6.87649 −0.436657
\(249\) 26.3136 1.66756
\(250\) 1.00000 0.0632456
\(251\) 26.1525 1.65073 0.825366 0.564599i \(-0.190969\pi\)
0.825366 + 0.564599i \(0.190969\pi\)
\(252\) 1.24162 0.0782145
\(253\) 0.713282 0.0448437
\(254\) −1.99032 −0.124884
\(255\) 4.52234 0.283200
\(256\) 1.00000 0.0625000
\(257\) −22.3009 −1.39109 −0.695547 0.718481i \(-0.744838\pi\)
−0.695547 + 0.718481i \(0.744838\pi\)
\(258\) −1.80931 −0.112643
\(259\) 11.7316 0.728968
\(260\) −1.28672 −0.0797989
\(261\) −1.12008 −0.0693312
\(262\) 6.17996 0.381799
\(263\) 8.00847 0.493824 0.246912 0.969038i \(-0.420584\pi\)
0.246912 + 0.969038i \(0.420584\pi\)
\(264\) 1.80931 0.111355
\(265\) −7.15552 −0.439560
\(266\) −19.5335 −1.19768
\(267\) 6.97373 0.426785
\(268\) 4.88949 0.298673
\(269\) 28.5272 1.73933 0.869666 0.493640i \(-0.164334\pi\)
0.869666 + 0.493640i \(0.164334\pi\)
\(270\) −4.93289 −0.300206
\(271\) −10.0036 −0.607678 −0.303839 0.952723i \(-0.598268\pi\)
−0.303839 + 0.952723i \(0.598268\pi\)
\(272\) −2.49948 −0.151553
\(273\) 10.5646 0.639402
\(274\) 18.9373 1.14404
\(275\) −1.00000 −0.0603023
\(276\) −1.29055 −0.0776820
\(277\) 22.9013 1.37600 0.688002 0.725709i \(-0.258488\pi\)
0.688002 + 0.725709i \(0.258488\pi\)
\(278\) 10.0357 0.601903
\(279\) 1.88146 0.112640
\(280\) 4.53794 0.271194
\(281\) 29.4235 1.75526 0.877630 0.479339i \(-0.159124\pi\)
0.877630 + 0.479339i \(0.159124\pi\)
\(282\) −14.0377 −0.835932
\(283\) 9.51051 0.565341 0.282671 0.959217i \(-0.408780\pi\)
0.282671 + 0.959217i \(0.408780\pi\)
\(284\) −10.4518 −0.620202
\(285\) −7.78817 −0.461332
\(286\) 1.28672 0.0760852
\(287\) 11.8646 0.700345
\(288\) −0.273608 −0.0161225
\(289\) −10.7526 −0.632506
\(290\) −4.09374 −0.240392
\(291\) 18.1528 1.06414
\(292\) −4.33504 −0.253689
\(293\) 3.18399 0.186011 0.0930054 0.995666i \(-0.470353\pi\)
0.0930054 + 0.995666i \(0.470353\pi\)
\(294\) −24.5937 −1.43433
\(295\) 2.05592 0.119700
\(296\) −2.58524 −0.150264
\(297\) 4.93289 0.286235
\(298\) −14.0528 −0.814056
\(299\) −0.917793 −0.0530773
\(300\) 1.80931 0.104461
\(301\) 4.53794 0.261562
\(302\) 11.3656 0.654017
\(303\) 32.5377 1.86924
\(304\) 4.30450 0.246880
\(305\) 7.20843 0.412754
\(306\) 0.683878 0.0390947
\(307\) −26.7734 −1.52804 −0.764019 0.645194i \(-0.776777\pi\)
−0.764019 + 0.645194i \(0.776777\pi\)
\(308\) −4.53794 −0.258573
\(309\) 35.3934 2.01346
\(310\) 6.87649 0.390558
\(311\) −24.5195 −1.39037 −0.695187 0.718829i \(-0.744678\pi\)
−0.695187 + 0.718829i \(0.744678\pi\)
\(312\) −2.32807 −0.131801
\(313\) 25.0633 1.41666 0.708332 0.705879i \(-0.249448\pi\)
0.708332 + 0.705879i \(0.249448\pi\)
\(314\) −16.9897 −0.958784
\(315\) −1.24162 −0.0699571
\(316\) 14.1763 0.797479
\(317\) −29.6933 −1.66774 −0.833870 0.551960i \(-0.813880\pi\)
−0.833870 + 0.551960i \(0.813880\pi\)
\(318\) −12.9466 −0.726008
\(319\) 4.09374 0.229205
\(320\) −1.00000 −0.0559017
\(321\) −18.6920 −1.04328
\(322\) 3.23683 0.180381
\(323\) −10.7590 −0.598647
\(324\) −9.74596 −0.541442
\(325\) 1.28672 0.0713743
\(326\) 18.7453 1.03821
\(327\) −28.3124 −1.56568
\(328\) −2.61453 −0.144364
\(329\) 35.2079 1.94108
\(330\) −1.80931 −0.0995993
\(331\) 27.3999 1.50604 0.753018 0.658000i \(-0.228597\pi\)
0.753018 + 0.658000i \(0.228597\pi\)
\(332\) 14.5435 0.798176
\(333\) 0.707341 0.0387621
\(334\) −15.7842 −0.863675
\(335\) −4.88949 −0.267141
\(336\) 8.21054 0.447922
\(337\) −14.1951 −0.773258 −0.386629 0.922235i \(-0.626361\pi\)
−0.386629 + 0.922235i \(0.626361\pi\)
\(338\) 11.3444 0.617052
\(339\) 0.00351263 0.000190780 0
\(340\) 2.49948 0.135553
\(341\) −6.87649 −0.372383
\(342\) −1.17774 −0.0636852
\(343\) 29.9180 1.61542
\(344\) −1.00000 −0.0539164
\(345\) 1.29055 0.0694809
\(346\) −23.4793 −1.26225
\(347\) −14.9223 −0.801069 −0.400534 0.916282i \(-0.631176\pi\)
−0.400534 + 0.916282i \(0.631176\pi\)
\(348\) −7.40684 −0.397048
\(349\) −31.3875 −1.68013 −0.840067 0.542483i \(-0.817484\pi\)
−0.840067 + 0.542483i \(0.817484\pi\)
\(350\) −4.53794 −0.242563
\(351\) −6.34724 −0.338791
\(352\) 1.00000 0.0533002
\(353\) 11.3874 0.606090 0.303045 0.952976i \(-0.401997\pi\)
0.303045 + 0.952976i \(0.401997\pi\)
\(354\) 3.71980 0.197705
\(355\) 10.4518 0.554725
\(356\) 3.85436 0.204280
\(357\) −20.5221 −1.08614
\(358\) 0.0200101 0.00105757
\(359\) 10.9849 0.579759 0.289880 0.957063i \(-0.406385\pi\)
0.289880 + 0.957063i \(0.406385\pi\)
\(360\) 0.273608 0.0144204
\(361\) −0.471312 −0.0248059
\(362\) −15.0756 −0.792356
\(363\) 1.80931 0.0949642
\(364\) 5.83904 0.306049
\(365\) 4.33504 0.226907
\(366\) 13.0423 0.681732
\(367\) −29.5964 −1.54492 −0.772459 0.635065i \(-0.780973\pi\)
−0.772459 + 0.635065i \(0.780973\pi\)
\(368\) −0.713282 −0.0371824
\(369\) 0.715358 0.0372400
\(370\) 2.58524 0.134400
\(371\) 32.4713 1.68583
\(372\) 12.4417 0.645072
\(373\) −24.7257 −1.28025 −0.640125 0.768271i \(-0.721117\pi\)
−0.640125 + 0.768271i \(0.721117\pi\)
\(374\) −2.49948 −0.129245
\(375\) −1.80931 −0.0934324
\(376\) −7.75858 −0.400118
\(377\) −5.26748 −0.271289
\(378\) 22.3851 1.15137
\(379\) −8.11573 −0.416877 −0.208439 0.978035i \(-0.566838\pi\)
−0.208439 + 0.978035i \(0.566838\pi\)
\(380\) −4.30450 −0.220816
\(381\) 3.60111 0.184490
\(382\) 22.3644 1.14426
\(383\) −18.4543 −0.942972 −0.471486 0.881874i \(-0.656282\pi\)
−0.471486 + 0.881874i \(0.656282\pi\)
\(384\) −1.80931 −0.0923310
\(385\) 4.53794 0.231275
\(386\) 17.6534 0.898536
\(387\) 0.273608 0.0139083
\(388\) 10.0330 0.509349
\(389\) 13.2506 0.671830 0.335915 0.941892i \(-0.390954\pi\)
0.335915 + 0.941892i \(0.390954\pi\)
\(390\) 2.32807 0.117887
\(391\) 1.78283 0.0901618
\(392\) −13.5929 −0.686543
\(393\) −11.1815 −0.564031
\(394\) 0.716160 0.0360796
\(395\) −14.1763 −0.713287
\(396\) −0.273608 −0.0137493
\(397\) −1.89992 −0.0953542 −0.0476771 0.998863i \(-0.515182\pi\)
−0.0476771 + 0.998863i \(0.515182\pi\)
\(398\) 10.1363 0.508089
\(399\) 35.3422 1.76932
\(400\) 1.00000 0.0500000
\(401\) 29.6511 1.48070 0.740352 0.672219i \(-0.234659\pi\)
0.740352 + 0.672219i \(0.234659\pi\)
\(402\) −8.84660 −0.441229
\(403\) 8.84810 0.440755
\(404\) 17.9835 0.894710
\(405\) 9.74596 0.484281
\(406\) 18.5771 0.921967
\(407\) −2.58524 −0.128145
\(408\) 4.52234 0.223889
\(409\) −22.3016 −1.10275 −0.551373 0.834259i \(-0.685896\pi\)
−0.551373 + 0.834259i \(0.685896\pi\)
\(410\) 2.61453 0.129123
\(411\) −34.2634 −1.69009
\(412\) 19.5618 0.963740
\(413\) −9.32964 −0.459082
\(414\) 0.195160 0.00959158
\(415\) −14.5435 −0.713910
\(416\) −1.28672 −0.0630865
\(417\) −18.1578 −0.889190
\(418\) 4.30450 0.210540
\(419\) −6.62038 −0.323427 −0.161713 0.986838i \(-0.551702\pi\)
−0.161713 + 0.986838i \(0.551702\pi\)
\(420\) −8.21054 −0.400633
\(421\) 15.4538 0.753175 0.376587 0.926381i \(-0.377098\pi\)
0.376587 + 0.926381i \(0.377098\pi\)
\(422\) −27.1396 −1.32114
\(423\) 2.12281 0.103215
\(424\) −7.15552 −0.347503
\(425\) −2.49948 −0.121243
\(426\) 18.9106 0.916222
\(427\) −32.7114 −1.58302
\(428\) −10.3310 −0.499367
\(429\) −2.32807 −0.112400
\(430\) 1.00000 0.0482243
\(431\) −2.64134 −0.127229 −0.0636145 0.997975i \(-0.520263\pi\)
−0.0636145 + 0.997975i \(0.520263\pi\)
\(432\) −4.93289 −0.237334
\(433\) −16.1858 −0.777839 −0.388919 0.921272i \(-0.627152\pi\)
−0.388919 + 0.921272i \(0.627152\pi\)
\(434\) −31.2051 −1.49789
\(435\) 7.40684 0.355131
\(436\) −15.6482 −0.749411
\(437\) −3.07032 −0.146873
\(438\) 7.84344 0.374774
\(439\) 35.5178 1.69517 0.847586 0.530658i \(-0.178055\pi\)
0.847586 + 0.530658i \(0.178055\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 3.71912 0.177101
\(442\) 3.21613 0.152975
\(443\) −39.7320 −1.88772 −0.943862 0.330339i \(-0.892837\pi\)
−0.943862 + 0.330339i \(0.892837\pi\)
\(444\) 4.67750 0.221984
\(445\) −3.85436 −0.182714
\(446\) 26.9918 1.27810
\(447\) 25.4259 1.20260
\(448\) 4.53794 0.214397
\(449\) 4.55922 0.215163 0.107581 0.994196i \(-0.465689\pi\)
0.107581 + 0.994196i \(0.465689\pi\)
\(450\) −0.273608 −0.0128980
\(451\) −2.61453 −0.123114
\(452\) 0.00194142 9.13167e−5 0
\(453\) −20.5639 −0.966177
\(454\) −16.1933 −0.759991
\(455\) −5.83904 −0.273739
\(456\) −7.78817 −0.364715
\(457\) 14.5725 0.681673 0.340837 0.940123i \(-0.389290\pi\)
0.340837 + 0.940123i \(0.389290\pi\)
\(458\) 3.67036 0.171505
\(459\) 12.3297 0.575499
\(460\) 0.713282 0.0332570
\(461\) 37.2850 1.73653 0.868267 0.496097i \(-0.165234\pi\)
0.868267 + 0.496097i \(0.165234\pi\)
\(462\) 8.21054 0.381989
\(463\) 13.2646 0.616457 0.308229 0.951312i \(-0.400264\pi\)
0.308229 + 0.951312i \(0.400264\pi\)
\(464\) −4.09374 −0.190047
\(465\) −12.4417 −0.576970
\(466\) −2.89466 −0.134093
\(467\) −18.9504 −0.876922 −0.438461 0.898750i \(-0.644476\pi\)
−0.438461 + 0.898750i \(0.644476\pi\)
\(468\) 0.352056 0.0162738
\(469\) 22.1882 1.02455
\(470\) 7.75858 0.357877
\(471\) 30.7397 1.41641
\(472\) 2.05592 0.0946315
\(473\) −1.00000 −0.0459800
\(474\) −25.6493 −1.17811
\(475\) 4.30450 0.197504
\(476\) −11.3425 −0.519882
\(477\) 1.95781 0.0896419
\(478\) 24.6223 1.12620
\(479\) 0.0755036 0.00344985 0.00172492 0.999999i \(-0.499451\pi\)
0.00172492 + 0.999999i \(0.499451\pi\)
\(480\) 1.80931 0.0825834
\(481\) 3.32647 0.151674
\(482\) −13.6048 −0.619683
\(483\) −5.85643 −0.266477
\(484\) 1.00000 0.0454545
\(485\) −10.0330 −0.455575
\(486\) 2.83481 0.128589
\(487\) 16.1032 0.729706 0.364853 0.931065i \(-0.381119\pi\)
0.364853 + 0.931065i \(0.381119\pi\)
\(488\) 7.20843 0.326310
\(489\) −33.9162 −1.53374
\(490\) 13.5929 0.614063
\(491\) −2.33686 −0.105461 −0.0527304 0.998609i \(-0.516792\pi\)
−0.0527304 + 0.998609i \(0.516792\pi\)
\(492\) 4.73051 0.213268
\(493\) 10.2322 0.460836
\(494\) −5.53867 −0.249197
\(495\) 0.273608 0.0122978
\(496\) 6.87649 0.308763
\(497\) −47.4297 −2.12751
\(498\) −26.3136 −1.17914
\(499\) −14.5428 −0.651023 −0.325512 0.945538i \(-0.605537\pi\)
−0.325512 + 0.945538i \(0.605537\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 28.5586 1.27590
\(502\) −26.1525 −1.16724
\(503\) 34.3695 1.53246 0.766229 0.642567i \(-0.222131\pi\)
0.766229 + 0.642567i \(0.222131\pi\)
\(504\) −1.24162 −0.0553060
\(505\) −17.9835 −0.800253
\(506\) −0.713282 −0.0317093
\(507\) −20.5255 −0.911568
\(508\) 1.99032 0.0883062
\(509\) 17.8363 0.790580 0.395290 0.918556i \(-0.370644\pi\)
0.395290 + 0.918556i \(0.370644\pi\)
\(510\) −4.52234 −0.200252
\(511\) −19.6721 −0.870245
\(512\) −1.00000 −0.0441942
\(513\) −21.2336 −0.937487
\(514\) 22.3009 0.983652
\(515\) −19.5618 −0.861995
\(516\) 1.80931 0.0796505
\(517\) −7.75858 −0.341222
\(518\) −11.7316 −0.515458
\(519\) 42.4813 1.86472
\(520\) 1.28672 0.0564263
\(521\) −3.88070 −0.170016 −0.0850082 0.996380i \(-0.527092\pi\)
−0.0850082 + 0.996380i \(0.527092\pi\)
\(522\) 1.12008 0.0490245
\(523\) 2.12930 0.0931078 0.0465539 0.998916i \(-0.485176\pi\)
0.0465539 + 0.998916i \(0.485176\pi\)
\(524\) −6.17996 −0.269973
\(525\) 8.21054 0.358337
\(526\) −8.00847 −0.349186
\(527\) −17.1876 −0.748705
\(528\) −1.80931 −0.0787402
\(529\) −22.4912 −0.977880
\(530\) 7.15552 0.310816
\(531\) −0.562517 −0.0244112
\(532\) 19.5335 0.846886
\(533\) 3.36417 0.145718
\(534\) −6.97373 −0.301783
\(535\) 10.3310 0.446648
\(536\) −4.88949 −0.211194
\(537\) −0.0362045 −0.00156234
\(538\) −28.5272 −1.22989
\(539\) −13.5929 −0.585486
\(540\) 4.93289 0.212278
\(541\) −7.50761 −0.322777 −0.161389 0.986891i \(-0.551597\pi\)
−0.161389 + 0.986891i \(0.551597\pi\)
\(542\) 10.0036 0.429693
\(543\) 27.2764 1.17054
\(544\) 2.49948 0.107164
\(545\) 15.6482 0.670293
\(546\) −10.5646 −0.452125
\(547\) −29.8435 −1.27601 −0.638007 0.770030i \(-0.720241\pi\)
−0.638007 + 0.770030i \(0.720241\pi\)
\(548\) −18.9373 −0.808961
\(549\) −1.97229 −0.0841751
\(550\) 1.00000 0.0426401
\(551\) −17.6215 −0.750700
\(552\) 1.29055 0.0549294
\(553\) 64.3311 2.73564
\(554\) −22.9013 −0.972981
\(555\) −4.67750 −0.198549
\(556\) −10.0357 −0.425610
\(557\) 5.53462 0.234509 0.117255 0.993102i \(-0.462591\pi\)
0.117255 + 0.993102i \(0.462591\pi\)
\(558\) −1.88146 −0.0796487
\(559\) 1.28672 0.0544224
\(560\) −4.53794 −0.191763
\(561\) 4.52234 0.190933
\(562\) −29.4235 −1.24116
\(563\) 23.7525 1.00105 0.500524 0.865723i \(-0.333141\pi\)
0.500524 + 0.865723i \(0.333141\pi\)
\(564\) 14.0377 0.591093
\(565\) −0.00194142 −8.16762e−5 0
\(566\) −9.51051 −0.399757
\(567\) −44.2266 −1.85734
\(568\) 10.4518 0.438549
\(569\) −7.35422 −0.308305 −0.154152 0.988047i \(-0.549265\pi\)
−0.154152 + 0.988047i \(0.549265\pi\)
\(570\) 7.78817 0.326211
\(571\) 4.55128 0.190465 0.0952326 0.995455i \(-0.469641\pi\)
0.0952326 + 0.995455i \(0.469641\pi\)
\(572\) −1.28672 −0.0538004
\(573\) −40.4641 −1.69041
\(574\) −11.8646 −0.495218
\(575\) −0.713282 −0.0297459
\(576\) 0.273608 0.0114003
\(577\) −31.6243 −1.31654 −0.658269 0.752783i \(-0.728711\pi\)
−0.658269 + 0.752783i \(0.728711\pi\)
\(578\) 10.7526 0.447249
\(579\) −31.9405 −1.32740
\(580\) 4.09374 0.169983
\(581\) 65.9973 2.73803
\(582\) −18.1528 −0.752459
\(583\) −7.15552 −0.296352
\(584\) 4.33504 0.179385
\(585\) −0.352056 −0.0145557
\(586\) −3.18399 −0.131529
\(587\) −7.14164 −0.294767 −0.147383 0.989079i \(-0.547085\pi\)
−0.147383 + 0.989079i \(0.547085\pi\)
\(588\) 24.5937 1.01423
\(589\) 29.5998 1.21964
\(590\) −2.05592 −0.0846410
\(591\) −1.29576 −0.0533003
\(592\) 2.58524 0.106253
\(593\) 29.2853 1.20260 0.601302 0.799022i \(-0.294649\pi\)
0.601302 + 0.799022i \(0.294649\pi\)
\(594\) −4.93289 −0.202399
\(595\) 11.3425 0.464996
\(596\) 14.0528 0.575625
\(597\) −18.3398 −0.750598
\(598\) 0.917793 0.0375313
\(599\) −4.16821 −0.170308 −0.0851542 0.996368i \(-0.527138\pi\)
−0.0851542 + 0.996368i \(0.527138\pi\)
\(600\) −1.80931 −0.0738648
\(601\) 40.9185 1.66910 0.834550 0.550932i \(-0.185728\pi\)
0.834550 + 0.550932i \(0.185728\pi\)
\(602\) −4.53794 −0.184952
\(603\) 1.33780 0.0544796
\(604\) −11.3656 −0.462460
\(605\) −1.00000 −0.0406558
\(606\) −32.5377 −1.32175
\(607\) 33.1708 1.34636 0.673181 0.739478i \(-0.264928\pi\)
0.673181 + 0.739478i \(0.264928\pi\)
\(608\) −4.30450 −0.174570
\(609\) −33.6118 −1.36202
\(610\) −7.20843 −0.291861
\(611\) 9.98310 0.403873
\(612\) −0.683878 −0.0276441
\(613\) 2.87391 0.116076 0.0580382 0.998314i \(-0.481515\pi\)
0.0580382 + 0.998314i \(0.481515\pi\)
\(614\) 26.7734 1.08049
\(615\) −4.73051 −0.190752
\(616\) 4.53794 0.182839
\(617\) 4.33161 0.174384 0.0871920 0.996192i \(-0.472211\pi\)
0.0871920 + 0.996192i \(0.472211\pi\)
\(618\) −35.3934 −1.42373
\(619\) −4.96649 −0.199620 −0.0998100 0.995007i \(-0.531823\pi\)
−0.0998100 + 0.995007i \(0.531823\pi\)
\(620\) −6.87649 −0.276166
\(621\) 3.51854 0.141194
\(622\) 24.5195 0.983142
\(623\) 17.4908 0.700755
\(624\) 2.32807 0.0931975
\(625\) 1.00000 0.0400000
\(626\) −25.0633 −1.00173
\(627\) −7.78817 −0.311030
\(628\) 16.9897 0.677963
\(629\) −6.46174 −0.257647
\(630\) 1.24162 0.0494672
\(631\) −25.7883 −1.02662 −0.513309 0.858204i \(-0.671580\pi\)
−0.513309 + 0.858204i \(0.671580\pi\)
\(632\) −14.1763 −0.563903
\(633\) 49.1040 1.95171
\(634\) 29.6933 1.17927
\(635\) −1.99032 −0.0789835
\(636\) 12.9466 0.513365
\(637\) 17.4902 0.692986
\(638\) −4.09374 −0.162073
\(639\) −2.85970 −0.113128
\(640\) 1.00000 0.0395285
\(641\) −0.739713 −0.0292169 −0.0146085 0.999893i \(-0.504650\pi\)
−0.0146085 + 0.999893i \(0.504650\pi\)
\(642\) 18.6920 0.737714
\(643\) 9.59710 0.378473 0.189236 0.981932i \(-0.439399\pi\)
0.189236 + 0.981932i \(0.439399\pi\)
\(644\) −3.23683 −0.127549
\(645\) −1.80931 −0.0712416
\(646\) 10.7590 0.423307
\(647\) −32.0119 −1.25852 −0.629258 0.777196i \(-0.716641\pi\)
−0.629258 + 0.777196i \(0.716641\pi\)
\(648\) 9.74596 0.382858
\(649\) 2.05592 0.0807020
\(650\) −1.28672 −0.0504692
\(651\) 56.4597 2.21283
\(652\) −18.7453 −0.734124
\(653\) −33.5007 −1.31098 −0.655491 0.755203i \(-0.727538\pi\)
−0.655491 + 0.755203i \(0.727538\pi\)
\(654\) 28.3124 1.10710
\(655\) 6.17996 0.241471
\(656\) 2.61453 0.102080
\(657\) −1.18610 −0.0462743
\(658\) −35.2079 −1.37255
\(659\) 12.1853 0.474672 0.237336 0.971428i \(-0.423726\pi\)
0.237336 + 0.971428i \(0.423726\pi\)
\(660\) 1.80931 0.0704274
\(661\) 16.2883 0.633541 0.316770 0.948502i \(-0.397401\pi\)
0.316770 + 0.948502i \(0.397401\pi\)
\(662\) −27.3999 −1.06493
\(663\) −5.81897 −0.225990
\(664\) −14.5435 −0.564396
\(665\) −19.5335 −0.757478
\(666\) −0.707341 −0.0274089
\(667\) 2.91999 0.113062
\(668\) 15.7842 0.610711
\(669\) −48.8365 −1.88813
\(670\) 4.88949 0.188897
\(671\) 7.20843 0.278278
\(672\) −8.21054 −0.316728
\(673\) −1.53360 −0.0591159 −0.0295580 0.999563i \(-0.509410\pi\)
−0.0295580 + 0.999563i \(0.509410\pi\)
\(674\) 14.1951 0.546776
\(675\) −4.93289 −0.189867
\(676\) −11.3444 −0.436321
\(677\) 21.6667 0.832718 0.416359 0.909200i \(-0.363306\pi\)
0.416359 + 0.909200i \(0.363306\pi\)
\(678\) −0.00351263 −0.000134902 0
\(679\) 45.5291 1.74725
\(680\) −2.49948 −0.0958507
\(681\) 29.2988 1.12273
\(682\) 6.87649 0.263314
\(683\) 48.0157 1.83727 0.918636 0.395106i \(-0.129292\pi\)
0.918636 + 0.395106i \(0.129292\pi\)
\(684\) 1.17774 0.0450322
\(685\) 18.9373 0.723556
\(686\) −29.9180 −1.14227
\(687\) −6.64083 −0.253363
\(688\) 1.00000 0.0381246
\(689\) 9.20714 0.350764
\(690\) −1.29055 −0.0491304
\(691\) −20.4041 −0.776209 −0.388105 0.921615i \(-0.626870\pi\)
−0.388105 + 0.921615i \(0.626870\pi\)
\(692\) 23.4793 0.892548
\(693\) −1.24162 −0.0471651
\(694\) 14.9223 0.566441
\(695\) 10.0357 0.380677
\(696\) 7.40684 0.280756
\(697\) −6.53498 −0.247530
\(698\) 31.3875 1.18803
\(699\) 5.23735 0.198095
\(700\) 4.53794 0.171518
\(701\) 8.71773 0.329264 0.164632 0.986355i \(-0.447356\pi\)
0.164632 + 0.986355i \(0.447356\pi\)
\(702\) 6.34724 0.239561
\(703\) 11.1281 0.419706
\(704\) −1.00000 −0.0376889
\(705\) −14.0377 −0.528690
\(706\) −11.3874 −0.428571
\(707\) 81.6078 3.06918
\(708\) −3.71980 −0.139799
\(709\) −3.71148 −0.139388 −0.0696938 0.997568i \(-0.522202\pi\)
−0.0696938 + 0.997568i \(0.522202\pi\)
\(710\) −10.4518 −0.392250
\(711\) 3.87875 0.145464
\(712\) −3.85436 −0.144448
\(713\) −4.90488 −0.183689
\(714\) 20.5221 0.768019
\(715\) 1.28672 0.0481205
\(716\) −0.0200101 −0.000747813 0
\(717\) −44.5495 −1.66373
\(718\) −10.9849 −0.409952
\(719\) −12.7644 −0.476033 −0.238016 0.971261i \(-0.576497\pi\)
−0.238016 + 0.971261i \(0.576497\pi\)
\(720\) −0.273608 −0.0101968
\(721\) 88.7701 3.30597
\(722\) 0.471312 0.0175404
\(723\) 24.6154 0.915456
\(724\) 15.0756 0.560280
\(725\) −4.09374 −0.152038
\(726\) −1.80931 −0.0671498
\(727\) −22.8600 −0.847831 −0.423916 0.905702i \(-0.639345\pi\)
−0.423916 + 0.905702i \(0.639345\pi\)
\(728\) −5.83904 −0.216409
\(729\) 24.1088 0.892920
\(730\) −4.33504 −0.160447
\(731\) −2.49948 −0.0924466
\(732\) −13.0423 −0.482057
\(733\) 28.4960 1.05253 0.526263 0.850322i \(-0.323593\pi\)
0.526263 + 0.850322i \(0.323593\pi\)
\(734\) 29.5964 1.09242
\(735\) −24.5937 −0.907153
\(736\) 0.713282 0.0262919
\(737\) −4.88949 −0.180107
\(738\) −0.715358 −0.0263327
\(739\) 5.62330 0.206857 0.103428 0.994637i \(-0.467019\pi\)
0.103428 + 0.994637i \(0.467019\pi\)
\(740\) −2.58524 −0.0950351
\(741\) 10.0212 0.368137
\(742\) −32.4713 −1.19206
\(743\) −24.5104 −0.899198 −0.449599 0.893230i \(-0.648433\pi\)
−0.449599 + 0.893230i \(0.648433\pi\)
\(744\) −12.4417 −0.456135
\(745\) −14.0528 −0.514854
\(746\) 24.7257 0.905273
\(747\) 3.97921 0.145592
\(748\) 2.49948 0.0913900
\(749\) −46.8814 −1.71301
\(750\) 1.80931 0.0660667
\(751\) 15.1572 0.553092 0.276546 0.961001i \(-0.410810\pi\)
0.276546 + 0.961001i \(0.410810\pi\)
\(752\) 7.75858 0.282926
\(753\) 47.3180 1.72436
\(754\) 5.26748 0.191830
\(755\) 11.3656 0.413636
\(756\) −22.3851 −0.814140
\(757\) 29.0010 1.05406 0.527029 0.849847i \(-0.323306\pi\)
0.527029 + 0.849847i \(0.323306\pi\)
\(758\) 8.11573 0.294777
\(759\) 1.29055 0.0468440
\(760\) 4.30450 0.156140
\(761\) 12.2831 0.445260 0.222630 0.974903i \(-0.428536\pi\)
0.222630 + 0.974903i \(0.428536\pi\)
\(762\) −3.60111 −0.130454
\(763\) −71.0103 −2.57075
\(764\) −22.3644 −0.809114
\(765\) 0.683878 0.0247257
\(766\) 18.4543 0.666782
\(767\) −2.64539 −0.0955196
\(768\) 1.80931 0.0652879
\(769\) 44.5197 1.60542 0.802711 0.596368i \(-0.203390\pi\)
0.802711 + 0.596368i \(0.203390\pi\)
\(770\) −4.53794 −0.163536
\(771\) −40.3493 −1.45315
\(772\) −17.6534 −0.635361
\(773\) −9.80872 −0.352795 −0.176398 0.984319i \(-0.556444\pi\)
−0.176398 + 0.984319i \(0.556444\pi\)
\(774\) −0.273608 −0.00983464
\(775\) 6.87649 0.247011
\(776\) −10.0330 −0.360164
\(777\) 21.2262 0.761485
\(778\) −13.2506 −0.475056
\(779\) 11.2543 0.403225
\(780\) −2.32807 −0.0833584
\(781\) 10.4518 0.373996
\(782\) −1.78283 −0.0637540
\(783\) 20.1940 0.721673
\(784\) 13.5929 0.485459
\(785\) −16.9897 −0.606388
\(786\) 11.1815 0.398830
\(787\) −43.1246 −1.53723 −0.768614 0.639713i \(-0.779053\pi\)
−0.768614 + 0.639713i \(0.779053\pi\)
\(788\) −0.716160 −0.0255122
\(789\) 14.4898 0.515851
\(790\) 14.1763 0.504370
\(791\) 0.00881004 0.000313249 0
\(792\) 0.273608 0.00972224
\(793\) −9.27522 −0.329373
\(794\) 1.89992 0.0674256
\(795\) −12.9466 −0.459168
\(796\) −10.1363 −0.359273
\(797\) −16.2719 −0.576379 −0.288189 0.957573i \(-0.593053\pi\)
−0.288189 + 0.957573i \(0.593053\pi\)
\(798\) −35.3422 −1.25110
\(799\) −19.3924 −0.686054
\(800\) −1.00000 −0.0353553
\(801\) 1.05458 0.0372619
\(802\) −29.6511 −1.04702
\(803\) 4.33504 0.152980
\(804\) 8.84660 0.311996
\(805\) 3.23683 0.114083
\(806\) −8.84810 −0.311661
\(807\) 51.6146 1.81692
\(808\) −17.9835 −0.632656
\(809\) −27.0641 −0.951523 −0.475761 0.879574i \(-0.657827\pi\)
−0.475761 + 0.879574i \(0.657827\pi\)
\(810\) −9.74596 −0.342438
\(811\) −10.1074 −0.354919 −0.177460 0.984128i \(-0.556788\pi\)
−0.177460 + 0.984128i \(0.556788\pi\)
\(812\) −18.5771 −0.651929
\(813\) −18.0997 −0.634784
\(814\) 2.58524 0.0906124
\(815\) 18.7453 0.656621
\(816\) −4.52234 −0.158313
\(817\) 4.30450 0.150595
\(818\) 22.3016 0.779759
\(819\) 1.59761 0.0558250
\(820\) −2.61453 −0.0913035
\(821\) −8.85984 −0.309211 −0.154605 0.987976i \(-0.549411\pi\)
−0.154605 + 0.987976i \(0.549411\pi\)
\(822\) 34.2634 1.19507
\(823\) −31.6527 −1.10334 −0.551671 0.834062i \(-0.686010\pi\)
−0.551671 + 0.834062i \(0.686010\pi\)
\(824\) −19.5618 −0.681467
\(825\) −1.80931 −0.0629921
\(826\) 9.32964 0.324620
\(827\) −23.8599 −0.829689 −0.414845 0.909892i \(-0.636164\pi\)
−0.414845 + 0.909892i \(0.636164\pi\)
\(828\) −0.195160 −0.00678227
\(829\) −12.2759 −0.426360 −0.213180 0.977013i \(-0.568382\pi\)
−0.213180 + 0.977013i \(0.568382\pi\)
\(830\) 14.5435 0.504811
\(831\) 41.4355 1.43738
\(832\) 1.28672 0.0446089
\(833\) −33.9751 −1.17717
\(834\) 18.1578 0.628752
\(835\) −15.7842 −0.546236
\(836\) −4.30450 −0.148874
\(837\) −33.9210 −1.17248
\(838\) 6.62038 0.228697
\(839\) 12.4611 0.430206 0.215103 0.976591i \(-0.430991\pi\)
0.215103 + 0.976591i \(0.430991\pi\)
\(840\) 8.21054 0.283291
\(841\) −12.2413 −0.422115
\(842\) −15.4538 −0.532575
\(843\) 53.2363 1.83356
\(844\) 27.1396 0.934184
\(845\) 11.3444 0.390258
\(846\) −2.12281 −0.0729837
\(847\) 4.53794 0.155925
\(848\) 7.15552 0.245722
\(849\) 17.2075 0.590559
\(850\) 2.49948 0.0857315
\(851\) −1.84400 −0.0632116
\(852\) −18.9106 −0.647867
\(853\) −11.4093 −0.390646 −0.195323 0.980739i \(-0.562575\pi\)
−0.195323 + 0.980739i \(0.562575\pi\)
\(854\) 32.7114 1.11936
\(855\) −1.17774 −0.0402780
\(856\) 10.3310 0.353106
\(857\) −25.7559 −0.879804 −0.439902 0.898046i \(-0.644987\pi\)
−0.439902 + 0.898046i \(0.644987\pi\)
\(858\) 2.32807 0.0794791
\(859\) −37.9418 −1.29456 −0.647279 0.762253i \(-0.724093\pi\)
−0.647279 + 0.762253i \(0.724093\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 21.4667 0.731584
\(862\) 2.64134 0.0899645
\(863\) 0.963151 0.0327860 0.0163930 0.999866i \(-0.494782\pi\)
0.0163930 + 0.999866i \(0.494782\pi\)
\(864\) 4.93289 0.167820
\(865\) −23.4793 −0.798319
\(866\) 16.1858 0.550015
\(867\) −19.4548 −0.660720
\(868\) 31.2051 1.05917
\(869\) −14.1763 −0.480898
\(870\) −7.40684 −0.251116
\(871\) 6.29139 0.213176
\(872\) 15.6482 0.529913
\(873\) 2.74511 0.0929080
\(874\) 3.07032 0.103855
\(875\) −4.53794 −0.153410
\(876\) −7.84344 −0.265005
\(877\) −51.4027 −1.73575 −0.867873 0.496787i \(-0.834513\pi\)
−0.867873 + 0.496787i \(0.834513\pi\)
\(878\) −35.5178 −1.19867
\(879\) 5.76083 0.194308
\(880\) 1.00000 0.0337100
\(881\) −6.17209 −0.207943 −0.103971 0.994580i \(-0.533155\pi\)
−0.103971 + 0.994580i \(0.533155\pi\)
\(882\) −3.71912 −0.125229
\(883\) 33.3931 1.12377 0.561884 0.827216i \(-0.310077\pi\)
0.561884 + 0.827216i \(0.310077\pi\)
\(884\) −3.21613 −0.108170
\(885\) 3.71980 0.125040
\(886\) 39.7320 1.33482
\(887\) −29.4796 −0.989829 −0.494915 0.868942i \(-0.664801\pi\)
−0.494915 + 0.868942i \(0.664801\pi\)
\(888\) −4.67750 −0.156966
\(889\) 9.03195 0.302922
\(890\) 3.85436 0.129198
\(891\) 9.74596 0.326502
\(892\) −26.9918 −0.903752
\(893\) 33.3968 1.11758
\(894\) −25.4259 −0.850368
\(895\) 0.0200101 0.000668865 0
\(896\) −4.53794 −0.151602
\(897\) −1.66057 −0.0554449
\(898\) −4.55922 −0.152143
\(899\) −28.1505 −0.938872
\(900\) 0.273608 0.00912027
\(901\) −17.8851 −0.595839
\(902\) 2.61453 0.0870545
\(903\) 8.21054 0.273230
\(904\) −0.00194142 −6.45707e−5 0
\(905\) −15.0756 −0.501130
\(906\) 20.5639 0.683190
\(907\) 2.62122 0.0870360 0.0435180 0.999053i \(-0.486143\pi\)
0.0435180 + 0.999053i \(0.486143\pi\)
\(908\) 16.1933 0.537395
\(909\) 4.92042 0.163200
\(910\) 5.83904 0.193562
\(911\) −5.21219 −0.172688 −0.0863438 0.996265i \(-0.527518\pi\)
−0.0863438 + 0.996265i \(0.527518\pi\)
\(912\) 7.78817 0.257892
\(913\) −14.5435 −0.481318
\(914\) −14.5725 −0.482016
\(915\) 13.0423 0.431165
\(916\) −3.67036 −0.121272
\(917\) −28.0443 −0.926103
\(918\) −12.3297 −0.406940
\(919\) −0.383739 −0.0126584 −0.00632918 0.999980i \(-0.502015\pi\)
−0.00632918 + 0.999980i \(0.502015\pi\)
\(920\) −0.713282 −0.0235162
\(921\) −48.4414 −1.59620
\(922\) −37.2850 −1.22792
\(923\) −13.4486 −0.442664
\(924\) −8.21054 −0.270107
\(925\) 2.58524 0.0850020
\(926\) −13.2646 −0.435901
\(927\) 5.35226 0.175791
\(928\) 4.09374 0.134383
\(929\) −21.7734 −0.714361 −0.357181 0.934035i \(-0.616262\pi\)
−0.357181 + 0.934035i \(0.616262\pi\)
\(930\) 12.4417 0.407980
\(931\) 58.5104 1.91760
\(932\) 2.89466 0.0948179
\(933\) −44.3634 −1.45239
\(934\) 18.9504 0.620077
\(935\) −2.49948 −0.0817417
\(936\) −0.352056 −0.0115073
\(937\) −21.3384 −0.697096 −0.348548 0.937291i \(-0.613325\pi\)
−0.348548 + 0.937291i \(0.613325\pi\)
\(938\) −22.1882 −0.724470
\(939\) 45.3474 1.47986
\(940\) −7.75858 −0.253057
\(941\) −33.1664 −1.08119 −0.540596 0.841282i \(-0.681801\pi\)
−0.540596 + 0.841282i \(0.681801\pi\)
\(942\) −30.7397 −1.00155
\(943\) −1.86490 −0.0607295
\(944\) −2.05592 −0.0669146
\(945\) 22.3851 0.728189
\(946\) 1.00000 0.0325128
\(947\) −2.99219 −0.0972331 −0.0486166 0.998818i \(-0.515481\pi\)
−0.0486166 + 0.998818i \(0.515481\pi\)
\(948\) 25.6493 0.833052
\(949\) −5.57798 −0.181069
\(950\) −4.30450 −0.139656
\(951\) −53.7244 −1.74213
\(952\) 11.3425 0.367612
\(953\) −30.6329 −0.992296 −0.496148 0.868238i \(-0.665253\pi\)
−0.496148 + 0.868238i \(0.665253\pi\)
\(954\) −1.95781 −0.0633864
\(955\) 22.3644 0.723694
\(956\) −24.6223 −0.796343
\(957\) 7.40684 0.239429
\(958\) −0.0755036 −0.00243941
\(959\) −85.9362 −2.77502
\(960\) −1.80931 −0.0583953
\(961\) 16.2861 0.525357
\(962\) −3.32647 −0.107250
\(963\) −2.82664 −0.0910873
\(964\) 13.6048 0.438182
\(965\) 17.6534 0.568284
\(966\) 5.85643 0.188428
\(967\) −4.71248 −0.151543 −0.0757716 0.997125i \(-0.524142\pi\)
−0.0757716 + 0.997125i \(0.524142\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −19.4664 −0.625350
\(970\) 10.0330 0.322140
\(971\) 13.9972 0.449193 0.224597 0.974452i \(-0.427894\pi\)
0.224597 + 0.974452i \(0.427894\pi\)
\(972\) −2.83481 −0.0909264
\(973\) −45.5415 −1.45999
\(974\) −16.1032 −0.515980
\(975\) 2.32807 0.0745580
\(976\) −7.20843 −0.230736
\(977\) −36.0644 −1.15380 −0.576902 0.816814i \(-0.695738\pi\)
−0.576902 + 0.816814i \(0.695738\pi\)
\(978\) 33.9162 1.08452
\(979\) −3.85436 −0.123186
\(980\) −13.5929 −0.434208
\(981\) −4.28146 −0.136697
\(982\) 2.33686 0.0745721
\(983\) −25.3547 −0.808689 −0.404345 0.914607i \(-0.632500\pi\)
−0.404345 + 0.914607i \(0.632500\pi\)
\(984\) −4.73051 −0.150803
\(985\) 0.716160 0.0228188
\(986\) −10.2322 −0.325860
\(987\) 63.7021 2.02766
\(988\) 5.53867 0.176209
\(989\) −0.713282 −0.0226811
\(990\) −0.273608 −0.00869584
\(991\) 7.09576 0.225404 0.112702 0.993629i \(-0.464049\pi\)
0.112702 + 0.993629i \(0.464049\pi\)
\(992\) −6.87649 −0.218329
\(993\) 49.5750 1.57322
\(994\) 47.4297 1.50438
\(995\) 10.1363 0.321344
\(996\) 26.3136 0.833780
\(997\) −31.3283 −0.992176 −0.496088 0.868272i \(-0.665231\pi\)
−0.496088 + 0.868272i \(0.665231\pi\)
\(998\) 14.5428 0.460343
\(999\) −12.7527 −0.403477
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.1.9 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bb.1.9 11 1.1 even 1 trivial