Properties

Label 4730.2.a.bb.1.11
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 1.11
Root \(-3.34767\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +3.34767 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.34767 q^{6} +2.01478 q^{7} -1.00000 q^{8} +8.20687 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +3.34767 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.34767 q^{6} +2.01478 q^{7} -1.00000 q^{8} +8.20687 q^{9} +1.00000 q^{10} -1.00000 q^{11} +3.34767 q^{12} +1.48948 q^{13} -2.01478 q^{14} -3.34767 q^{15} +1.00000 q^{16} -4.62109 q^{17} -8.20687 q^{18} +4.61164 q^{19} -1.00000 q^{20} +6.74481 q^{21} +1.00000 q^{22} -0.510515 q^{23} -3.34767 q^{24} +1.00000 q^{25} -1.48948 q^{26} +17.4309 q^{27} +2.01478 q^{28} +6.69280 q^{29} +3.34767 q^{30} -3.21861 q^{31} -1.00000 q^{32} -3.34767 q^{33} +4.62109 q^{34} -2.01478 q^{35} +8.20687 q^{36} -2.87600 q^{37} -4.61164 q^{38} +4.98630 q^{39} +1.00000 q^{40} +5.97483 q^{41} -6.74481 q^{42} +1.00000 q^{43} -1.00000 q^{44} -8.20687 q^{45} +0.510515 q^{46} +0.687284 q^{47} +3.34767 q^{48} -2.94066 q^{49} -1.00000 q^{50} -15.4699 q^{51} +1.48948 q^{52} -9.90378 q^{53} -17.4309 q^{54} +1.00000 q^{55} -2.01478 q^{56} +15.4382 q^{57} -6.69280 q^{58} +6.00237 q^{59} -3.34767 q^{60} +10.5041 q^{61} +3.21861 q^{62} +16.5350 q^{63} +1.00000 q^{64} -1.48948 q^{65} +3.34767 q^{66} +9.21417 q^{67} -4.62109 q^{68} -1.70903 q^{69} +2.01478 q^{70} -1.91041 q^{71} -8.20687 q^{72} +13.5257 q^{73} +2.87600 q^{74} +3.34767 q^{75} +4.61164 q^{76} -2.01478 q^{77} -4.98630 q^{78} +4.69668 q^{79} -1.00000 q^{80} +33.7321 q^{81} -5.97483 q^{82} -13.3863 q^{83} +6.74481 q^{84} +4.62109 q^{85} -1.00000 q^{86} +22.4053 q^{87} +1.00000 q^{88} +8.93667 q^{89} +8.20687 q^{90} +3.00098 q^{91} -0.510515 q^{92} -10.7748 q^{93} -0.687284 q^{94} -4.61164 q^{95} -3.34767 q^{96} -18.5182 q^{97} +2.94066 q^{98} -8.20687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + O(q^{10}) \) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + 11q^{10} - 11q^{11} - q^{12} + 4q^{13} - 6q^{14} + q^{15} + 11q^{16} - 10q^{17} - 12q^{18} + 14q^{19} - 11q^{20} - 2q^{21} + 11q^{22} - 18q^{23} + q^{24} + 11q^{25} - 4q^{26} + 2q^{27} + 6q^{28} - 6q^{29} - q^{30} + 13q^{31} - 11q^{32} + q^{33} + 10q^{34} - 6q^{35} + 12q^{36} + q^{37} - 14q^{38} + 12q^{39} + 11q^{40} + 12q^{41} + 2q^{42} + 11q^{43} - 11q^{44} - 12q^{45} + 18q^{46} - 5q^{47} - q^{48} + 31q^{49} - 11q^{50} + q^{51} + 4q^{52} - 27q^{53} - 2q^{54} + 11q^{55} - 6q^{56} - 5q^{57} + 6q^{58} + 11q^{59} + q^{60} + 36q^{61} - 13q^{62} + 17q^{63} + 11q^{64} - 4q^{65} - q^{66} + 18q^{67} - 10q^{68} + 14q^{69} + 6q^{70} - 14q^{71} - 12q^{72} - 11q^{73} - q^{74} - q^{75} + 14q^{76} - 6q^{77} - 12q^{78} + 28q^{79} - 11q^{80} + 7q^{81} - 12q^{82} - 4q^{83} - 2q^{84} + 10q^{85} - 11q^{86} + 38q^{87} + 11q^{88} - 7q^{89} + 12q^{90} + 14q^{91} - 18q^{92} - 3q^{93} + 5q^{94} - 14q^{95} + q^{96} - q^{97} - 31q^{98} - 12q^{99} + O(q^{100}) \)

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
\(3\) 3.34767 1.93278 0.966388 0.257087i \(-0.0827628\pi\)
0.966388 + 0.257087i \(0.0827628\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −3.34767 −1.36668
\(7\) 2.01478 0.761515 0.380758 0.924675i \(-0.375663\pi\)
0.380758 + 0.924675i \(0.375663\pi\)
\(8\) −1.00000 −0.353553
\(9\) 8.20687 2.73562
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) 3.34767 0.966388
\(13\) 1.48948 0.413109 0.206554 0.978435i \(-0.433775\pi\)
0.206554 + 0.978435i \(0.433775\pi\)
\(14\) −2.01478 −0.538472
\(15\) −3.34767 −0.864364
\(16\) 1.00000 0.250000
\(17\) −4.62109 −1.12078 −0.560390 0.828229i \(-0.689349\pi\)
−0.560390 + 0.828229i \(0.689349\pi\)
\(18\) −8.20687 −1.93438
\(19\) 4.61164 1.05798 0.528991 0.848627i \(-0.322571\pi\)
0.528991 + 0.848627i \(0.322571\pi\)
\(20\) −1.00000 −0.223607
\(21\) 6.74481 1.47184
\(22\) 1.00000 0.213201
\(23\) −0.510515 −0.106450 −0.0532249 0.998583i \(-0.516950\pi\)
−0.0532249 + 0.998583i \(0.516950\pi\)
\(24\) −3.34767 −0.683340
\(25\) 1.00000 0.200000
\(26\) −1.48948 −0.292112
\(27\) 17.4309 3.35457
\(28\) 2.01478 0.380758
\(29\) 6.69280 1.24282 0.621411 0.783485i \(-0.286560\pi\)
0.621411 + 0.783485i \(0.286560\pi\)
\(30\) 3.34767 0.611198
\(31\) −3.21861 −0.578080 −0.289040 0.957317i \(-0.593336\pi\)
−0.289040 + 0.957317i \(0.593336\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.34767 −0.582754
\(34\) 4.62109 0.792511
\(35\) −2.01478 −0.340560
\(36\) 8.20687 1.36781
\(37\) −2.87600 −0.472812 −0.236406 0.971654i \(-0.575969\pi\)
−0.236406 + 0.971654i \(0.575969\pi\)
\(38\) −4.61164 −0.748106
\(39\) 4.98630 0.798447
\(40\) 1.00000 0.158114
\(41\) 5.97483 0.933112 0.466556 0.884492i \(-0.345495\pi\)
0.466556 + 0.884492i \(0.345495\pi\)
\(42\) −6.74481 −1.04075
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) −8.20687 −1.22341
\(46\) 0.510515 0.0752714
\(47\) 0.687284 0.100251 0.0501253 0.998743i \(-0.484038\pi\)
0.0501253 + 0.998743i \(0.484038\pi\)
\(48\) 3.34767 0.483194
\(49\) −2.94066 −0.420095
\(50\) −1.00000 −0.141421
\(51\) −15.4699 −2.16622
\(52\) 1.48948 0.206554
\(53\) −9.90378 −1.36039 −0.680194 0.733032i \(-0.738105\pi\)
−0.680194 + 0.733032i \(0.738105\pi\)
\(54\) −17.4309 −2.37204
\(55\) 1.00000 0.134840
\(56\) −2.01478 −0.269236
\(57\) 15.4382 2.04484
\(58\) −6.69280 −0.878808
\(59\) 6.00237 0.781442 0.390721 0.920509i \(-0.372226\pi\)
0.390721 + 0.920509i \(0.372226\pi\)
\(60\) −3.34767 −0.432182
\(61\) 10.5041 1.34491 0.672457 0.740136i \(-0.265239\pi\)
0.672457 + 0.740136i \(0.265239\pi\)
\(62\) 3.21861 0.408764
\(63\) 16.5350 2.08322
\(64\) 1.00000 0.125000
\(65\) −1.48948 −0.184748
\(66\) 3.34767 0.412069
\(67\) 9.21417 1.12569 0.562845 0.826562i \(-0.309707\pi\)
0.562845 + 0.826562i \(0.309707\pi\)
\(68\) −4.62109 −0.560390
\(69\) −1.70903 −0.205744
\(70\) 2.01478 0.240812
\(71\) −1.91041 −0.226724 −0.113362 0.993554i \(-0.536162\pi\)
−0.113362 + 0.993554i \(0.536162\pi\)
\(72\) −8.20687 −0.967189
\(73\) 13.5257 1.58307 0.791534 0.611125i \(-0.209283\pi\)
0.791534 + 0.611125i \(0.209283\pi\)
\(74\) 2.87600 0.334328
\(75\) 3.34767 0.386555
\(76\) 4.61164 0.528991
\(77\) −2.01478 −0.229605
\(78\) −4.98630 −0.564587
\(79\) 4.69668 0.528418 0.264209 0.964465i \(-0.414889\pi\)
0.264209 + 0.964465i \(0.414889\pi\)
\(80\) −1.00000 −0.111803
\(81\) 33.7321 3.74802
\(82\) −5.97483 −0.659810
\(83\) −13.3863 −1.46934 −0.734669 0.678426i \(-0.762662\pi\)
−0.734669 + 0.678426i \(0.762662\pi\)
\(84\) 6.74481 0.735919
\(85\) 4.62109 0.501228
\(86\) −1.00000 −0.107833
\(87\) 22.4053 2.40210
\(88\) 1.00000 0.106600
\(89\) 8.93667 0.947285 0.473642 0.880717i \(-0.342939\pi\)
0.473642 + 0.880717i \(0.342939\pi\)
\(90\) 8.20687 0.865080
\(91\) 3.00098 0.314589
\(92\) −0.510515 −0.0532249
\(93\) −10.7748 −1.11730
\(94\) −0.687284 −0.0708879
\(95\) −4.61164 −0.473144
\(96\) −3.34767 −0.341670
\(97\) −18.5182 −1.88024 −0.940121 0.340841i \(-0.889288\pi\)
−0.940121 + 0.340841i \(0.889288\pi\)
\(98\) 2.94066 0.297052
\(99\) −8.20687 −0.824822
\(100\) 1.00000 0.100000
\(101\) −1.14767 −0.114198 −0.0570988 0.998369i \(-0.518185\pi\)
−0.0570988 + 0.998369i \(0.518185\pi\)
\(102\) 15.4699 1.53175
\(103\) −13.7309 −1.35294 −0.676472 0.736468i \(-0.736492\pi\)
−0.676472 + 0.736468i \(0.736492\pi\)
\(104\) −1.48948 −0.146056
\(105\) −6.74481 −0.658226
\(106\) 9.90378 0.961940
\(107\) 14.5724 1.40877 0.704384 0.709819i \(-0.251223\pi\)
0.704384 + 0.709819i \(0.251223\pi\)
\(108\) 17.4309 1.67729
\(109\) 8.75054 0.838149 0.419075 0.907952i \(-0.362355\pi\)
0.419075 + 0.907952i \(0.362355\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −9.62790 −0.913839
\(112\) 2.01478 0.190379
\(113\) −6.03707 −0.567920 −0.283960 0.958836i \(-0.591648\pi\)
−0.283960 + 0.958836i \(0.591648\pi\)
\(114\) −15.4382 −1.44592
\(115\) 0.510515 0.0476058
\(116\) 6.69280 0.621411
\(117\) 12.2240 1.13011
\(118\) −6.00237 −0.552563
\(119\) −9.31048 −0.853490
\(120\) 3.34767 0.305599
\(121\) 1.00000 0.0909091
\(122\) −10.5041 −0.950998
\(123\) 20.0017 1.80350
\(124\) −3.21861 −0.289040
\(125\) −1.00000 −0.0894427
\(126\) −16.5350 −1.47306
\(127\) −3.20196 −0.284128 −0.142064 0.989858i \(-0.545374\pi\)
−0.142064 + 0.989858i \(0.545374\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.34767 0.294746
\(130\) 1.48948 0.130636
\(131\) −13.6496 −1.19258 −0.596288 0.802771i \(-0.703358\pi\)
−0.596288 + 0.802771i \(0.703358\pi\)
\(132\) −3.34767 −0.291377
\(133\) 9.29143 0.805669
\(134\) −9.21417 −0.795983
\(135\) −17.4309 −1.50021
\(136\) 4.62109 0.396255
\(137\) 1.47015 0.125604 0.0628018 0.998026i \(-0.479996\pi\)
0.0628018 + 0.998026i \(0.479996\pi\)
\(138\) 1.70903 0.145483
\(139\) 2.94406 0.249712 0.124856 0.992175i \(-0.460153\pi\)
0.124856 + 0.992175i \(0.460153\pi\)
\(140\) −2.01478 −0.170280
\(141\) 2.30080 0.193762
\(142\) 1.91041 0.160318
\(143\) −1.48948 −0.124557
\(144\) 8.20687 0.683906
\(145\) −6.69280 −0.555807
\(146\) −13.5257 −1.11940
\(147\) −9.84436 −0.811949
\(148\) −2.87600 −0.236406
\(149\) −17.8364 −1.46122 −0.730608 0.682797i \(-0.760763\pi\)
−0.730608 + 0.682797i \(0.760763\pi\)
\(150\) −3.34767 −0.273336
\(151\) 5.52170 0.449349 0.224675 0.974434i \(-0.427868\pi\)
0.224675 + 0.974434i \(0.427868\pi\)
\(152\) −4.61164 −0.374053
\(153\) −37.9247 −3.06603
\(154\) 2.01478 0.162356
\(155\) 3.21861 0.258525
\(156\) 4.98630 0.399223
\(157\) 8.76485 0.699511 0.349756 0.936841i \(-0.386265\pi\)
0.349756 + 0.936841i \(0.386265\pi\)
\(158\) −4.69668 −0.373648
\(159\) −33.1546 −2.62933
\(160\) 1.00000 0.0790569
\(161\) −1.02858 −0.0810631
\(162\) −33.7321 −2.65025
\(163\) 9.07445 0.710765 0.355383 0.934721i \(-0.384351\pi\)
0.355383 + 0.934721i \(0.384351\pi\)
\(164\) 5.97483 0.466556
\(165\) 3.34767 0.260616
\(166\) 13.3863 1.03898
\(167\) 25.2448 1.95350 0.976750 0.214382i \(-0.0687736\pi\)
0.976750 + 0.214382i \(0.0687736\pi\)
\(168\) −6.74481 −0.520373
\(169\) −10.7814 −0.829341
\(170\) −4.62109 −0.354421
\(171\) 37.8471 2.89424
\(172\) 1.00000 0.0762493
\(173\) −11.2676 −0.856663 −0.428332 0.903622i \(-0.640898\pi\)
−0.428332 + 0.903622i \(0.640898\pi\)
\(174\) −22.4053 −1.69854
\(175\) 2.01478 0.152303
\(176\) −1.00000 −0.0753778
\(177\) 20.0939 1.51035
\(178\) −8.93667 −0.669831
\(179\) −5.95539 −0.445127 −0.222564 0.974918i \(-0.571442\pi\)
−0.222564 + 0.974918i \(0.571442\pi\)
\(180\) −8.20687 −0.611704
\(181\) −2.55950 −0.190246 −0.0951229 0.995466i \(-0.530324\pi\)
−0.0951229 + 0.995466i \(0.530324\pi\)
\(182\) −3.00098 −0.222448
\(183\) 35.1643 2.59942
\(184\) 0.510515 0.0376357
\(185\) 2.87600 0.211448
\(186\) 10.7748 0.790050
\(187\) 4.62109 0.337928
\(188\) 0.687284 0.0501253
\(189\) 35.1194 2.55456
\(190\) 4.61164 0.334563
\(191\) −2.93960 −0.212702 −0.106351 0.994329i \(-0.533917\pi\)
−0.106351 + 0.994329i \(0.533917\pi\)
\(192\) 3.34767 0.241597
\(193\) 14.0810 1.01357 0.506786 0.862072i \(-0.330833\pi\)
0.506786 + 0.862072i \(0.330833\pi\)
\(194\) 18.5182 1.32953
\(195\) −4.98630 −0.357076
\(196\) −2.94066 −0.210047
\(197\) −8.24038 −0.587103 −0.293551 0.955943i \(-0.594837\pi\)
−0.293551 + 0.955943i \(0.594837\pi\)
\(198\) 8.20687 0.583237
\(199\) 15.1524 1.07412 0.537061 0.843543i \(-0.319534\pi\)
0.537061 + 0.843543i \(0.319534\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 30.8460 2.17571
\(202\) 1.14767 0.0807499
\(203\) 13.4845 0.946428
\(204\) −15.4699 −1.08311
\(205\) −5.97483 −0.417300
\(206\) 13.7309 0.956677
\(207\) −4.18973 −0.291207
\(208\) 1.48948 0.103277
\(209\) −4.61164 −0.318994
\(210\) 6.74481 0.465436
\(211\) 13.1232 0.903437 0.451718 0.892161i \(-0.350811\pi\)
0.451718 + 0.892161i \(0.350811\pi\)
\(212\) −9.90378 −0.680194
\(213\) −6.39542 −0.438207
\(214\) −14.5724 −0.996150
\(215\) −1.00000 −0.0681994
\(216\) −17.4309 −1.18602
\(217\) −6.48479 −0.440217
\(218\) −8.75054 −0.592661
\(219\) 45.2797 3.05972
\(220\) 1.00000 0.0674200
\(221\) −6.88304 −0.463004
\(222\) 9.62790 0.646182
\(223\) 0.783875 0.0524922 0.0262461 0.999656i \(-0.491645\pi\)
0.0262461 + 0.999656i \(0.491645\pi\)
\(224\) −2.01478 −0.134618
\(225\) 8.20687 0.547125
\(226\) 6.03707 0.401580
\(227\) −19.4564 −1.29137 −0.645685 0.763604i \(-0.723428\pi\)
−0.645685 + 0.763604i \(0.723428\pi\)
\(228\) 15.4382 1.02242
\(229\) −11.2079 −0.740636 −0.370318 0.928905i \(-0.620751\pi\)
−0.370318 + 0.928905i \(0.620751\pi\)
\(230\) −0.510515 −0.0336624
\(231\) −6.74481 −0.443776
\(232\) −6.69280 −0.439404
\(233\) −2.07385 −0.135862 −0.0679312 0.997690i \(-0.521640\pi\)
−0.0679312 + 0.997690i \(0.521640\pi\)
\(234\) −12.2240 −0.799109
\(235\) −0.687284 −0.0448335
\(236\) 6.00237 0.390721
\(237\) 15.7229 1.02131
\(238\) 9.31048 0.603509
\(239\) −12.0463 −0.779213 −0.389607 0.920981i \(-0.627389\pi\)
−0.389607 + 0.920981i \(0.627389\pi\)
\(240\) −3.34767 −0.216091
\(241\) 7.59111 0.488986 0.244493 0.969651i \(-0.421378\pi\)
0.244493 + 0.969651i \(0.421378\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 60.6313 3.88950
\(244\) 10.5041 0.672457
\(245\) 2.94066 0.187872
\(246\) −20.0017 −1.27526
\(247\) 6.86896 0.437062
\(248\) 3.21861 0.204382
\(249\) −44.8129 −2.83990
\(250\) 1.00000 0.0632456
\(251\) −14.3646 −0.906685 −0.453342 0.891336i \(-0.649769\pi\)
−0.453342 + 0.891336i \(0.649769\pi\)
\(252\) 16.5350 1.04161
\(253\) 0.510515 0.0320958
\(254\) 3.20196 0.200909
\(255\) 15.4699 0.968761
\(256\) 1.00000 0.0625000
\(257\) 16.9270 1.05588 0.527939 0.849282i \(-0.322965\pi\)
0.527939 + 0.849282i \(0.322965\pi\)
\(258\) −3.34767 −0.208417
\(259\) −5.79451 −0.360053
\(260\) −1.48948 −0.0923739
\(261\) 54.9270 3.39989
\(262\) 13.6496 0.843278
\(263\) 6.51799 0.401917 0.200958 0.979600i \(-0.435594\pi\)
0.200958 + 0.979600i \(0.435594\pi\)
\(264\) 3.34767 0.206035
\(265\) 9.90378 0.608384
\(266\) −9.29143 −0.569694
\(267\) 29.9170 1.83089
\(268\) 9.21417 0.562845
\(269\) −24.4660 −1.49172 −0.745860 0.666103i \(-0.767961\pi\)
−0.745860 + 0.666103i \(0.767961\pi\)
\(270\) 17.4309 1.06081
\(271\) −22.0693 −1.34061 −0.670307 0.742084i \(-0.733837\pi\)
−0.670307 + 0.742084i \(0.733837\pi\)
\(272\) −4.62109 −0.280195
\(273\) 10.0463 0.608029
\(274\) −1.47015 −0.0888152
\(275\) −1.00000 −0.0603023
\(276\) −1.70903 −0.102872
\(277\) 23.2674 1.39800 0.699002 0.715120i \(-0.253628\pi\)
0.699002 + 0.715120i \(0.253628\pi\)
\(278\) −2.94406 −0.176573
\(279\) −26.4147 −1.58141
\(280\) 2.01478 0.120406
\(281\) 14.5212 0.866264 0.433132 0.901330i \(-0.357408\pi\)
0.433132 + 0.901330i \(0.357408\pi\)
\(282\) −2.30080 −0.137011
\(283\) −32.3625 −1.92375 −0.961874 0.273492i \(-0.911821\pi\)
−0.961874 + 0.273492i \(0.911821\pi\)
\(284\) −1.91041 −0.113362
\(285\) −15.4382 −0.914481
\(286\) 1.48948 0.0880751
\(287\) 12.0380 0.710579
\(288\) −8.20687 −0.483595
\(289\) 4.35448 0.256146
\(290\) 6.69280 0.393015
\(291\) −61.9929 −3.63409
\(292\) 13.5257 0.791534
\(293\) 0.869375 0.0507894 0.0253947 0.999678i \(-0.491916\pi\)
0.0253947 + 0.999678i \(0.491916\pi\)
\(294\) 9.84436 0.574135
\(295\) −6.00237 −0.349472
\(296\) 2.87600 0.167164
\(297\) −17.4309 −1.01144
\(298\) 17.8364 1.03324
\(299\) −0.760405 −0.0439753
\(300\) 3.34767 0.193278
\(301\) 2.01478 0.116130
\(302\) −5.52170 −0.317738
\(303\) −3.84202 −0.220719
\(304\) 4.61164 0.264496
\(305\) −10.5041 −0.601464
\(306\) 37.9247 2.16801
\(307\) 12.5435 0.715896 0.357948 0.933742i \(-0.383477\pi\)
0.357948 + 0.933742i \(0.383477\pi\)
\(308\) −2.01478 −0.114803
\(309\) −45.9664 −2.61494
\(310\) −3.21861 −0.182805
\(311\) 10.8906 0.617547 0.308773 0.951136i \(-0.400082\pi\)
0.308773 + 0.951136i \(0.400082\pi\)
\(312\) −4.98630 −0.282294
\(313\) −4.86148 −0.274787 −0.137394 0.990517i \(-0.543872\pi\)
−0.137394 + 0.990517i \(0.543872\pi\)
\(314\) −8.76485 −0.494629
\(315\) −16.5350 −0.931644
\(316\) 4.69668 0.264209
\(317\) −15.3998 −0.864941 −0.432470 0.901648i \(-0.642358\pi\)
−0.432470 + 0.901648i \(0.642358\pi\)
\(318\) 33.1546 1.85922
\(319\) −6.69280 −0.374725
\(320\) −1.00000 −0.0559017
\(321\) 48.7836 2.72284
\(322\) 1.02858 0.0573203
\(323\) −21.3108 −1.18576
\(324\) 33.7321 1.87401
\(325\) 1.48948 0.0826218
\(326\) −9.07445 −0.502587
\(327\) 29.2939 1.61996
\(328\) −5.97483 −0.329905
\(329\) 1.38473 0.0763424
\(330\) −3.34767 −0.184283
\(331\) 25.3548 1.39363 0.696813 0.717253i \(-0.254601\pi\)
0.696813 + 0.717253i \(0.254601\pi\)
\(332\) −13.3863 −0.734669
\(333\) −23.6030 −1.29344
\(334\) −25.2448 −1.38133
\(335\) −9.21417 −0.503424
\(336\) 6.74481 0.367960
\(337\) −18.6303 −1.01486 −0.507429 0.861694i \(-0.669404\pi\)
−0.507429 + 0.861694i \(0.669404\pi\)
\(338\) 10.7814 0.586433
\(339\) −20.2101 −1.09766
\(340\) 4.62109 0.250614
\(341\) 3.21861 0.174298
\(342\) −37.8471 −2.04654
\(343\) −20.0282 −1.08142
\(344\) −1.00000 −0.0539164
\(345\) 1.70903 0.0920113
\(346\) 11.2676 0.605752
\(347\) −21.0407 −1.12953 −0.564763 0.825253i \(-0.691032\pi\)
−0.564763 + 0.825253i \(0.691032\pi\)
\(348\) 22.4053 1.20105
\(349\) 22.2309 1.18999 0.594997 0.803728i \(-0.297153\pi\)
0.594997 + 0.803728i \(0.297153\pi\)
\(350\) −2.01478 −0.107694
\(351\) 25.9630 1.38580
\(352\) 1.00000 0.0533002
\(353\) 31.5180 1.67753 0.838767 0.544491i \(-0.183277\pi\)
0.838767 + 0.544491i \(0.183277\pi\)
\(354\) −20.0939 −1.06798
\(355\) 1.91041 0.101394
\(356\) 8.93667 0.473642
\(357\) −31.1684 −1.64961
\(358\) 5.95539 0.314752
\(359\) −17.5193 −0.924636 −0.462318 0.886714i \(-0.652982\pi\)
−0.462318 + 0.886714i \(0.652982\pi\)
\(360\) 8.20687 0.432540
\(361\) 2.26720 0.119326
\(362\) 2.55950 0.134524
\(363\) 3.34767 0.175707
\(364\) 3.00098 0.157294
\(365\) −13.5257 −0.707970
\(366\) −35.1643 −1.83807
\(367\) −34.2260 −1.78658 −0.893292 0.449477i \(-0.851610\pi\)
−0.893292 + 0.449477i \(0.851610\pi\)
\(368\) −0.510515 −0.0266124
\(369\) 49.0347 2.55264
\(370\) −2.87600 −0.149516
\(371\) −19.9539 −1.03596
\(372\) −10.7748 −0.558650
\(373\) 0.0440564 0.00228115 0.00114058 0.999999i \(-0.499637\pi\)
0.00114058 + 0.999999i \(0.499637\pi\)
\(374\) −4.62109 −0.238951
\(375\) −3.34767 −0.172873
\(376\) −0.687284 −0.0354440
\(377\) 9.96883 0.513421
\(378\) −35.1194 −1.80635
\(379\) 27.8952 1.43288 0.716441 0.697648i \(-0.245770\pi\)
0.716441 + 0.697648i \(0.245770\pi\)
\(380\) −4.61164 −0.236572
\(381\) −10.7191 −0.549155
\(382\) 2.93960 0.150403
\(383\) 31.4666 1.60787 0.803933 0.594719i \(-0.202737\pi\)
0.803933 + 0.594719i \(0.202737\pi\)
\(384\) −3.34767 −0.170835
\(385\) 2.01478 0.102683
\(386\) −14.0810 −0.716704
\(387\) 8.20687 0.417179
\(388\) −18.5182 −0.940121
\(389\) −21.3938 −1.08471 −0.542355 0.840150i \(-0.682467\pi\)
−0.542355 + 0.840150i \(0.682467\pi\)
\(390\) 4.98630 0.252491
\(391\) 2.35914 0.119307
\(392\) 2.94066 0.148526
\(393\) −45.6945 −2.30498
\(394\) 8.24038 0.415144
\(395\) −4.69668 −0.236316
\(396\) −8.20687 −0.412411
\(397\) −25.2152 −1.26551 −0.632757 0.774350i \(-0.718077\pi\)
−0.632757 + 0.774350i \(0.718077\pi\)
\(398\) −15.1524 −0.759520
\(399\) 31.1046 1.55718
\(400\) 1.00000 0.0500000
\(401\) 18.5312 0.925404 0.462702 0.886514i \(-0.346880\pi\)
0.462702 + 0.886514i \(0.346880\pi\)
\(402\) −30.8460 −1.53846
\(403\) −4.79407 −0.238810
\(404\) −1.14767 −0.0570988
\(405\) −33.7321 −1.67616
\(406\) −13.4845 −0.669225
\(407\) 2.87600 0.142558
\(408\) 15.4699 0.765873
\(409\) 3.18044 0.157263 0.0786314 0.996904i \(-0.474945\pi\)
0.0786314 + 0.996904i \(0.474945\pi\)
\(410\) 5.97483 0.295076
\(411\) 4.92158 0.242764
\(412\) −13.7309 −0.676472
\(413\) 12.0935 0.595080
\(414\) 4.18973 0.205914
\(415\) 13.3863 0.657108
\(416\) −1.48948 −0.0730280
\(417\) 9.85575 0.482638
\(418\) 4.61164 0.225563
\(419\) −13.4896 −0.659010 −0.329505 0.944154i \(-0.606882\pi\)
−0.329505 + 0.944154i \(0.606882\pi\)
\(420\) −6.74481 −0.329113
\(421\) −24.0053 −1.16995 −0.584973 0.811053i \(-0.698895\pi\)
−0.584973 + 0.811053i \(0.698895\pi\)
\(422\) −13.1232 −0.638826
\(423\) 5.64045 0.274248
\(424\) 9.90378 0.480970
\(425\) −4.62109 −0.224156
\(426\) 6.39542 0.309859
\(427\) 21.1635 1.02417
\(428\) 14.5724 0.704384
\(429\) −4.98630 −0.240741
\(430\) 1.00000 0.0482243
\(431\) −19.5818 −0.943224 −0.471612 0.881806i \(-0.656328\pi\)
−0.471612 + 0.881806i \(0.656328\pi\)
\(432\) 17.4309 0.838643
\(433\) 1.78736 0.0858952 0.0429476 0.999077i \(-0.486325\pi\)
0.0429476 + 0.999077i \(0.486325\pi\)
\(434\) 6.48479 0.311280
\(435\) −22.4053 −1.07425
\(436\) 8.75054 0.419075
\(437\) −2.35431 −0.112622
\(438\) −45.2797 −2.16355
\(439\) 17.1291 0.817529 0.408764 0.912640i \(-0.365960\pi\)
0.408764 + 0.912640i \(0.365960\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −24.1337 −1.14922
\(442\) 6.88304 0.327393
\(443\) −26.0378 −1.23709 −0.618547 0.785748i \(-0.712278\pi\)
−0.618547 + 0.785748i \(0.712278\pi\)
\(444\) −9.62790 −0.456920
\(445\) −8.93667 −0.423639
\(446\) −0.783875 −0.0371176
\(447\) −59.7103 −2.82420
\(448\) 2.01478 0.0951894
\(449\) 3.31664 0.156522 0.0782610 0.996933i \(-0.475063\pi\)
0.0782610 + 0.996933i \(0.475063\pi\)
\(450\) −8.20687 −0.386876
\(451\) −5.97483 −0.281344
\(452\) −6.03707 −0.283960
\(453\) 18.4848 0.868492
\(454\) 19.4564 0.913136
\(455\) −3.00098 −0.140688
\(456\) −15.4382 −0.722961
\(457\) 25.1803 1.17789 0.588943 0.808174i \(-0.299544\pi\)
0.588943 + 0.808174i \(0.299544\pi\)
\(458\) 11.2079 0.523709
\(459\) −80.5497 −3.75974
\(460\) 0.510515 0.0238029
\(461\) −4.59424 −0.213975 −0.106988 0.994260i \(-0.534121\pi\)
−0.106988 + 0.994260i \(0.534121\pi\)
\(462\) 6.74481 0.313797
\(463\) 7.26300 0.337540 0.168770 0.985655i \(-0.446020\pi\)
0.168770 + 0.985655i \(0.446020\pi\)
\(464\) 6.69280 0.310706
\(465\) 10.7748 0.499671
\(466\) 2.07385 0.0960692
\(467\) −24.4668 −1.13219 −0.566094 0.824340i \(-0.691546\pi\)
−0.566094 + 0.824340i \(0.691546\pi\)
\(468\) 12.2240 0.565055
\(469\) 18.5645 0.857230
\(470\) 0.687284 0.0317021
\(471\) 29.3418 1.35200
\(472\) −6.00237 −0.276282
\(473\) −1.00000 −0.0459800
\(474\) −15.7229 −0.722177
\(475\) 4.61164 0.211596
\(476\) −9.31048 −0.426745
\(477\) −81.2791 −3.72151
\(478\) 12.0463 0.550987
\(479\) −7.23813 −0.330718 −0.165359 0.986233i \(-0.552878\pi\)
−0.165359 + 0.986233i \(0.552878\pi\)
\(480\) 3.34767 0.152799
\(481\) −4.28376 −0.195323
\(482\) −7.59111 −0.345766
\(483\) −3.44333 −0.156677
\(484\) 1.00000 0.0454545
\(485\) 18.5182 0.840870
\(486\) −60.6313 −2.75029
\(487\) −21.9913 −0.996520 −0.498260 0.867028i \(-0.666028\pi\)
−0.498260 + 0.867028i \(0.666028\pi\)
\(488\) −10.5041 −0.475499
\(489\) 30.3782 1.37375
\(490\) −2.94066 −0.132846
\(491\) −10.1902 −0.459876 −0.229938 0.973205i \(-0.573852\pi\)
−0.229938 + 0.973205i \(0.573852\pi\)
\(492\) 20.0017 0.901748
\(493\) −30.9280 −1.39293
\(494\) −6.86896 −0.309049
\(495\) 8.20687 0.368871
\(496\) −3.21861 −0.144520
\(497\) −3.84906 −0.172654
\(498\) 44.8129 2.00811
\(499\) −7.45725 −0.333832 −0.166916 0.985971i \(-0.553381\pi\)
−0.166916 + 0.985971i \(0.553381\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 84.5111 3.77568
\(502\) 14.3646 0.641123
\(503\) 3.98676 0.177761 0.0888804 0.996042i \(-0.471671\pi\)
0.0888804 + 0.996042i \(0.471671\pi\)
\(504\) −16.5350 −0.736529
\(505\) 1.14767 0.0510707
\(506\) −0.510515 −0.0226952
\(507\) −36.0927 −1.60293
\(508\) −3.20196 −0.142064
\(509\) 6.04174 0.267795 0.133898 0.990995i \(-0.457251\pi\)
0.133898 + 0.990995i \(0.457251\pi\)
\(510\) −15.4699 −0.685017
\(511\) 27.2514 1.20553
\(512\) −1.00000 −0.0441942
\(513\) 80.3849 3.54908
\(514\) −16.9270 −0.746619
\(515\) 13.7309 0.605055
\(516\) 3.34767 0.147373
\(517\) −0.687284 −0.0302267
\(518\) 5.79451 0.254596
\(519\) −37.7203 −1.65574
\(520\) 1.48948 0.0653182
\(521\) 6.66591 0.292039 0.146019 0.989282i \(-0.453354\pi\)
0.146019 + 0.989282i \(0.453354\pi\)
\(522\) −54.9270 −2.40409
\(523\) −17.3931 −0.760547 −0.380273 0.924874i \(-0.624170\pi\)
−0.380273 + 0.924874i \(0.624170\pi\)
\(524\) −13.6496 −0.596288
\(525\) 6.74481 0.294368
\(526\) −6.51799 −0.284198
\(527\) 14.8735 0.647900
\(528\) −3.34767 −0.145688
\(529\) −22.7394 −0.988668
\(530\) −9.90378 −0.430193
\(531\) 49.2607 2.13773
\(532\) 9.29143 0.402835
\(533\) 8.89942 0.385477
\(534\) −29.9170 −1.29463
\(535\) −14.5724 −0.630021
\(536\) −9.21417 −0.397992
\(537\) −19.9367 −0.860331
\(538\) 24.4660 1.05480
\(539\) 2.94066 0.126663
\(540\) −17.4309 −0.750105
\(541\) −37.9162 −1.63014 −0.815071 0.579360i \(-0.803302\pi\)
−0.815071 + 0.579360i \(0.803302\pi\)
\(542\) 22.0693 0.947957
\(543\) −8.56834 −0.367703
\(544\) 4.62109 0.198128
\(545\) −8.75054 −0.374832
\(546\) −10.0463 −0.429942
\(547\) −14.9070 −0.637379 −0.318689 0.947859i \(-0.603243\pi\)
−0.318689 + 0.947859i \(0.603243\pi\)
\(548\) 1.47015 0.0628018
\(549\) 86.2060 3.67918
\(550\) 1.00000 0.0426401
\(551\) 30.8648 1.31488
\(552\) 1.70903 0.0727413
\(553\) 9.46277 0.402398
\(554\) −23.2674 −0.988538
\(555\) 9.62790 0.408681
\(556\) 2.94406 0.124856
\(557\) 19.1986 0.813471 0.406735 0.913546i \(-0.366667\pi\)
0.406735 + 0.913546i \(0.366667\pi\)
\(558\) 26.4147 1.11823
\(559\) 1.48948 0.0629985
\(560\) −2.01478 −0.0851400
\(561\) 15.4699 0.653139
\(562\) −14.5212 −0.612541
\(563\) 34.0338 1.43435 0.717177 0.696891i \(-0.245434\pi\)
0.717177 + 0.696891i \(0.245434\pi\)
\(564\) 2.30080 0.0968811
\(565\) 6.03707 0.253981
\(566\) 32.3625 1.36030
\(567\) 67.9628 2.85417
\(568\) 1.91041 0.0801591
\(569\) 20.0492 0.840506 0.420253 0.907407i \(-0.361941\pi\)
0.420253 + 0.907407i \(0.361941\pi\)
\(570\) 15.4382 0.646636
\(571\) −0.789587 −0.0330432 −0.0165216 0.999864i \(-0.505259\pi\)
−0.0165216 + 0.999864i \(0.505259\pi\)
\(572\) −1.48948 −0.0622785
\(573\) −9.84082 −0.411106
\(574\) −12.0380 −0.502455
\(575\) −0.510515 −0.0212900
\(576\) 8.20687 0.341953
\(577\) −10.7861 −0.449032 −0.224516 0.974470i \(-0.572080\pi\)
−0.224516 + 0.974470i \(0.572080\pi\)
\(578\) −4.35448 −0.181123
\(579\) 47.1385 1.95901
\(580\) −6.69280 −0.277903
\(581\) −26.9705 −1.11892
\(582\) 61.9929 2.56969
\(583\) 9.90378 0.410173
\(584\) −13.5257 −0.559699
\(585\) −12.2240 −0.505401
\(586\) −0.869375 −0.0359135
\(587\) 11.5310 0.475935 0.237968 0.971273i \(-0.423519\pi\)
0.237968 + 0.971273i \(0.423519\pi\)
\(588\) −9.84436 −0.405975
\(589\) −14.8431 −0.611598
\(590\) 6.00237 0.247114
\(591\) −27.5860 −1.13474
\(592\) −2.87600 −0.118203
\(593\) −16.6202 −0.682509 −0.341255 0.939971i \(-0.610852\pi\)
−0.341255 + 0.939971i \(0.610852\pi\)
\(594\) 17.4309 0.715197
\(595\) 9.31048 0.381692
\(596\) −17.8364 −0.730608
\(597\) 50.7251 2.07604
\(598\) 0.760405 0.0310953
\(599\) 35.5350 1.45192 0.725960 0.687737i \(-0.241396\pi\)
0.725960 + 0.687737i \(0.241396\pi\)
\(600\) −3.34767 −0.136668
\(601\) 28.4318 1.15976 0.579878 0.814704i \(-0.303100\pi\)
0.579878 + 0.814704i \(0.303100\pi\)
\(602\) −2.01478 −0.0821163
\(603\) 75.6195 3.07947
\(604\) 5.52170 0.224675
\(605\) −1.00000 −0.0406558
\(606\) 3.84202 0.156072
\(607\) −17.1793 −0.697285 −0.348643 0.937256i \(-0.613357\pi\)
−0.348643 + 0.937256i \(0.613357\pi\)
\(608\) −4.61164 −0.187027
\(609\) 45.1417 1.82923
\(610\) 10.5041 0.425299
\(611\) 1.02370 0.0414144
\(612\) −37.9247 −1.53302
\(613\) −5.87621 −0.237338 −0.118669 0.992934i \(-0.537863\pi\)
−0.118669 + 0.992934i \(0.537863\pi\)
\(614\) −12.5435 −0.506215
\(615\) −20.0017 −0.806548
\(616\) 2.01478 0.0811778
\(617\) 2.74950 0.110691 0.0553454 0.998467i \(-0.482374\pi\)
0.0553454 + 0.998467i \(0.482374\pi\)
\(618\) 45.9664 1.84904
\(619\) −35.5230 −1.42779 −0.713895 0.700253i \(-0.753070\pi\)
−0.713895 + 0.700253i \(0.753070\pi\)
\(620\) 3.21861 0.129263
\(621\) −8.89873 −0.357094
\(622\) −10.8906 −0.436672
\(623\) 18.0054 0.721372
\(624\) 4.98630 0.199612
\(625\) 1.00000 0.0400000
\(626\) 4.86148 0.194304
\(627\) −15.4382 −0.616543
\(628\) 8.76485 0.349756
\(629\) 13.2903 0.529918
\(630\) 16.5350 0.658772
\(631\) −35.9310 −1.43039 −0.715196 0.698924i \(-0.753663\pi\)
−0.715196 + 0.698924i \(0.753663\pi\)
\(632\) −4.69668 −0.186824
\(633\) 43.9320 1.74614
\(634\) 15.3998 0.611605
\(635\) 3.20196 0.127066
\(636\) −33.1546 −1.31466
\(637\) −4.38007 −0.173545
\(638\) 6.69280 0.264971
\(639\) −15.6785 −0.620232
\(640\) 1.00000 0.0395285
\(641\) 7.43849 0.293803 0.146901 0.989151i \(-0.453070\pi\)
0.146901 + 0.989151i \(0.453070\pi\)
\(642\) −48.7836 −1.92534
\(643\) −32.2934 −1.27353 −0.636764 0.771059i \(-0.719727\pi\)
−0.636764 + 0.771059i \(0.719727\pi\)
\(644\) −1.02858 −0.0405315
\(645\) −3.34767 −0.131814
\(646\) 21.3108 0.838462
\(647\) −14.1027 −0.554436 −0.277218 0.960807i \(-0.589412\pi\)
−0.277218 + 0.960807i \(0.589412\pi\)
\(648\) −33.7321 −1.32512
\(649\) −6.00237 −0.235614
\(650\) −1.48948 −0.0584224
\(651\) −21.7089 −0.850840
\(652\) 9.07445 0.355383
\(653\) 34.5633 1.35257 0.676283 0.736642i \(-0.263590\pi\)
0.676283 + 0.736642i \(0.263590\pi\)
\(654\) −29.2939 −1.14548
\(655\) 13.6496 0.533336
\(656\) 5.97483 0.233278
\(657\) 111.004 4.33068
\(658\) −1.38473 −0.0539822
\(659\) −47.7324 −1.85939 −0.929695 0.368331i \(-0.879929\pi\)
−0.929695 + 0.368331i \(0.879929\pi\)
\(660\) 3.34767 0.130308
\(661\) −40.0085 −1.55615 −0.778075 0.628171i \(-0.783804\pi\)
−0.778075 + 0.628171i \(0.783804\pi\)
\(662\) −25.3548 −0.985442
\(663\) −23.0421 −0.894883
\(664\) 13.3863 0.519489
\(665\) −9.29143 −0.360306
\(666\) 23.6030 0.914597
\(667\) −3.41678 −0.132298
\(668\) 25.2448 0.976750
\(669\) 2.62415 0.101456
\(670\) 9.21417 0.355975
\(671\) −10.5041 −0.405507
\(672\) −6.74481 −0.260187
\(673\) 34.2935 1.32192 0.660959 0.750422i \(-0.270150\pi\)
0.660959 + 0.750422i \(0.270150\pi\)
\(674\) 18.6303 0.717613
\(675\) 17.4309 0.670915
\(676\) −10.7814 −0.414671
\(677\) −47.6651 −1.83192 −0.915958 0.401273i \(-0.868568\pi\)
−0.915958 + 0.401273i \(0.868568\pi\)
\(678\) 20.2101 0.776164
\(679\) −37.3102 −1.43183
\(680\) −4.62109 −0.177211
\(681\) −65.1337 −2.49593
\(682\) −3.21861 −0.123247
\(683\) 47.1483 1.80408 0.902040 0.431653i \(-0.142069\pi\)
0.902040 + 0.431653i \(0.142069\pi\)
\(684\) 37.8471 1.44712
\(685\) −1.47015 −0.0561717
\(686\) 20.0282 0.764682
\(687\) −37.5202 −1.43148
\(688\) 1.00000 0.0381246
\(689\) −14.7515 −0.561989
\(690\) −1.70903 −0.0650618
\(691\) 48.6227 1.84969 0.924847 0.380339i \(-0.124193\pi\)
0.924847 + 0.380339i \(0.124193\pi\)
\(692\) −11.2676 −0.428332
\(693\) −16.5350 −0.628114
\(694\) 21.0407 0.798696
\(695\) −2.94406 −0.111675
\(696\) −22.4053 −0.849270
\(697\) −27.6102 −1.04581
\(698\) −22.2309 −0.841453
\(699\) −6.94255 −0.262592
\(700\) 2.01478 0.0761515
\(701\) 6.33047 0.239099 0.119549 0.992828i \(-0.461855\pi\)
0.119549 + 0.992828i \(0.461855\pi\)
\(702\) −25.9630 −0.979911
\(703\) −13.2631 −0.500226
\(704\) −1.00000 −0.0376889
\(705\) −2.30080 −0.0866531
\(706\) −31.5180 −1.18619
\(707\) −2.31231 −0.0869632
\(708\) 20.0939 0.755177
\(709\) 31.5740 1.18578 0.592892 0.805282i \(-0.297986\pi\)
0.592892 + 0.805282i \(0.297986\pi\)
\(710\) −1.91041 −0.0716965
\(711\) 38.5450 1.44555
\(712\) −8.93667 −0.334916
\(713\) 1.64315 0.0615365
\(714\) 31.1684 1.16645
\(715\) 1.48948 0.0557036
\(716\) −5.95539 −0.222564
\(717\) −40.3272 −1.50605
\(718\) 17.5193 0.653816
\(719\) −21.1222 −0.787725 −0.393863 0.919169i \(-0.628861\pi\)
−0.393863 + 0.919169i \(0.628861\pi\)
\(720\) −8.20687 −0.305852
\(721\) −27.6647 −1.03029
\(722\) −2.26720 −0.0843763
\(723\) 25.4125 0.945101
\(724\) −2.55950 −0.0951229
\(725\) 6.69280 0.248564
\(726\) −3.34767 −0.124244
\(727\) 10.2646 0.380693 0.190347 0.981717i \(-0.439039\pi\)
0.190347 + 0.981717i \(0.439039\pi\)
\(728\) −3.00098 −0.111224
\(729\) 101.777 3.76952
\(730\) 13.5257 0.500610
\(731\) −4.62109 −0.170917
\(732\) 35.1643 1.29971
\(733\) 20.0782 0.741604 0.370802 0.928712i \(-0.379083\pi\)
0.370802 + 0.928712i \(0.379083\pi\)
\(734\) 34.2260 1.26331
\(735\) 9.84436 0.363115
\(736\) 0.510515 0.0188178
\(737\) −9.21417 −0.339408
\(738\) −49.0347 −1.80499
\(739\) −47.6831 −1.75405 −0.877026 0.480442i \(-0.840476\pi\)
−0.877026 + 0.480442i \(0.840476\pi\)
\(740\) 2.87600 0.105724
\(741\) 22.9950 0.844742
\(742\) 19.9539 0.732532
\(743\) 19.6593 0.721228 0.360614 0.932715i \(-0.382567\pi\)
0.360614 + 0.932715i \(0.382567\pi\)
\(744\) 10.7748 0.395025
\(745\) 17.8364 0.653475
\(746\) −0.0440564 −0.00161302
\(747\) −109.860 −4.01956
\(748\) 4.62109 0.168964
\(749\) 29.3602 1.07280
\(750\) 3.34767 0.122240
\(751\) −5.69776 −0.207914 −0.103957 0.994582i \(-0.533150\pi\)
−0.103957 + 0.994582i \(0.533150\pi\)
\(752\) 0.687284 0.0250627
\(753\) −48.0879 −1.75242
\(754\) −9.96883 −0.363043
\(755\) −5.52170 −0.200955
\(756\) 35.1194 1.27728
\(757\) 12.1647 0.442133 0.221067 0.975259i \(-0.429046\pi\)
0.221067 + 0.975259i \(0.429046\pi\)
\(758\) −27.8952 −1.01320
\(759\) 1.70903 0.0620340
\(760\) 4.61164 0.167282
\(761\) 27.3010 0.989660 0.494830 0.868990i \(-0.335230\pi\)
0.494830 + 0.868990i \(0.335230\pi\)
\(762\) 10.7191 0.388311
\(763\) 17.6304 0.638263
\(764\) −2.93960 −0.106351
\(765\) 37.9247 1.37117
\(766\) −31.4666 −1.13693
\(767\) 8.94044 0.322821
\(768\) 3.34767 0.120799
\(769\) 46.3280 1.67063 0.835315 0.549772i \(-0.185285\pi\)
0.835315 + 0.549772i \(0.185285\pi\)
\(770\) −2.01478 −0.0726076
\(771\) 56.6660 2.04078
\(772\) 14.0810 0.506786
\(773\) 47.4161 1.70544 0.852720 0.522368i \(-0.174951\pi\)
0.852720 + 0.522368i \(0.174951\pi\)
\(774\) −8.20687 −0.294990
\(775\) −3.21861 −0.115616
\(776\) 18.5182 0.664766
\(777\) −19.3981 −0.695902
\(778\) 21.3938 0.767005
\(779\) 27.5537 0.987215
\(780\) −4.98630 −0.178538
\(781\) 1.91041 0.0683599
\(782\) −2.35914 −0.0843626
\(783\) 116.661 4.16914
\(784\) −2.94066 −0.105024
\(785\) −8.76485 −0.312831
\(786\) 45.6945 1.62987
\(787\) 27.1334 0.967203 0.483602 0.875288i \(-0.339328\pi\)
0.483602 + 0.875288i \(0.339328\pi\)
\(788\) −8.24038 −0.293551
\(789\) 21.8201 0.776815
\(790\) 4.69668 0.167100
\(791\) −12.1634 −0.432479
\(792\) 8.20687 0.291619
\(793\) 15.6457 0.555596
\(794\) 25.2152 0.894854
\(795\) 33.1546 1.17587
\(796\) 15.1524 0.537061
\(797\) −46.5107 −1.64749 −0.823747 0.566958i \(-0.808120\pi\)
−0.823747 + 0.566958i \(0.808120\pi\)
\(798\) −31.1046 −1.10109
\(799\) −3.17600 −0.112359
\(800\) −1.00000 −0.0353553
\(801\) 73.3421 2.59141
\(802\) −18.5312 −0.654359
\(803\) −13.5257 −0.477313
\(804\) 30.8460 1.08785
\(805\) 1.02858 0.0362525
\(806\) 4.79407 0.168864
\(807\) −81.9041 −2.88316
\(808\) 1.14767 0.0403750
\(809\) 40.1382 1.41118 0.705592 0.708619i \(-0.250681\pi\)
0.705592 + 0.708619i \(0.250681\pi\)
\(810\) 33.7321 1.18523
\(811\) 30.8189 1.08220 0.541099 0.840959i \(-0.318008\pi\)
0.541099 + 0.840959i \(0.318008\pi\)
\(812\) 13.4845 0.473214
\(813\) −73.8806 −2.59111
\(814\) −2.87600 −0.100804
\(815\) −9.07445 −0.317864
\(816\) −15.4699 −0.541554
\(817\) 4.61164 0.161341
\(818\) −3.18044 −0.111202
\(819\) 24.6287 0.860596
\(820\) −5.97483 −0.208650
\(821\) 5.55019 0.193703 0.0968515 0.995299i \(-0.469123\pi\)
0.0968515 + 0.995299i \(0.469123\pi\)
\(822\) −4.92158 −0.171660
\(823\) −3.10128 −0.108104 −0.0540518 0.998538i \(-0.517214\pi\)
−0.0540518 + 0.998538i \(0.517214\pi\)
\(824\) 13.7309 0.478338
\(825\) −3.34767 −0.116551
\(826\) −12.0935 −0.420785
\(827\) −45.8463 −1.59423 −0.797116 0.603827i \(-0.793642\pi\)
−0.797116 + 0.603827i \(0.793642\pi\)
\(828\) −4.18973 −0.145603
\(829\) 29.8724 1.03751 0.518756 0.854922i \(-0.326395\pi\)
0.518756 + 0.854922i \(0.326395\pi\)
\(830\) −13.3863 −0.464645
\(831\) 77.8915 2.70203
\(832\) 1.48948 0.0516386
\(833\) 13.5891 0.470834
\(834\) −9.85575 −0.341277
\(835\) −25.2448 −0.873632
\(836\) −4.61164 −0.159497
\(837\) −56.1032 −1.93921
\(838\) 13.4896 0.465991
\(839\) −6.98368 −0.241103 −0.120552 0.992707i \(-0.538466\pi\)
−0.120552 + 0.992707i \(0.538466\pi\)
\(840\) 6.74481 0.232718
\(841\) 15.7936 0.544607
\(842\) 24.0053 0.827276
\(843\) 48.6123 1.67430
\(844\) 13.1232 0.451718
\(845\) 10.7814 0.370893
\(846\) −5.64045 −0.193923
\(847\) 2.01478 0.0692286
\(848\) −9.90378 −0.340097
\(849\) −108.339 −3.71818
\(850\) 4.62109 0.158502
\(851\) 1.46824 0.0503307
\(852\) −6.39542 −0.219104
\(853\) −32.6637 −1.11838 −0.559192 0.829038i \(-0.688889\pi\)
−0.559192 + 0.829038i \(0.688889\pi\)
\(854\) −21.1635 −0.724200
\(855\) −37.8471 −1.29434
\(856\) −14.5724 −0.498075
\(857\) −18.2452 −0.623244 −0.311622 0.950206i \(-0.600872\pi\)
−0.311622 + 0.950206i \(0.600872\pi\)
\(858\) 4.98630 0.170229
\(859\) 0.415306 0.0141701 0.00708503 0.999975i \(-0.497745\pi\)
0.00708503 + 0.999975i \(0.497745\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 40.2991 1.37339
\(862\) 19.5818 0.666960
\(863\) −52.6700 −1.79291 −0.896454 0.443137i \(-0.853866\pi\)
−0.896454 + 0.443137i \(0.853866\pi\)
\(864\) −17.4309 −0.593010
\(865\) 11.2676 0.383111
\(866\) −1.78736 −0.0607371
\(867\) 14.5774 0.495073
\(868\) −6.48479 −0.220108
\(869\) −4.69668 −0.159324
\(870\) 22.4053 0.759610
\(871\) 13.7244 0.465033
\(872\) −8.75054 −0.296331
\(873\) −151.977 −5.14363
\(874\) 2.35431 0.0796357
\(875\) −2.01478 −0.0681120
\(876\) 45.2797 1.52986
\(877\) −14.7608 −0.498438 −0.249219 0.968447i \(-0.580174\pi\)
−0.249219 + 0.968447i \(0.580174\pi\)
\(878\) −17.1291 −0.578080
\(879\) 2.91038 0.0981646
\(880\) 1.00000 0.0337100
\(881\) 18.5642 0.625443 0.312722 0.949845i \(-0.398759\pi\)
0.312722 + 0.949845i \(0.398759\pi\)
\(882\) 24.1337 0.812622
\(883\) −20.3161 −0.683692 −0.341846 0.939756i \(-0.611052\pi\)
−0.341846 + 0.939756i \(0.611052\pi\)
\(884\) −6.88304 −0.231502
\(885\) −20.0939 −0.675451
\(886\) 26.0378 0.874757
\(887\) −20.9300 −0.702760 −0.351380 0.936233i \(-0.614288\pi\)
−0.351380 + 0.936233i \(0.614288\pi\)
\(888\) 9.62790 0.323091
\(889\) −6.45123 −0.216367
\(890\) 8.93667 0.299558
\(891\) −33.7321 −1.13007
\(892\) 0.783875 0.0262461
\(893\) 3.16950 0.106063
\(894\) 59.7103 1.99701
\(895\) 5.95539 0.199067
\(896\) −2.01478 −0.0673091
\(897\) −2.54558 −0.0849945
\(898\) −3.31664 −0.110678
\(899\) −21.5415 −0.718450
\(900\) 8.20687 0.273562
\(901\) 45.7663 1.52470
\(902\) 5.97483 0.198940
\(903\) 6.74481 0.224453
\(904\) 6.03707 0.200790
\(905\) 2.55950 0.0850805
\(906\) −18.4848 −0.614116
\(907\) −15.7810 −0.524000 −0.262000 0.965068i \(-0.584382\pi\)
−0.262000 + 0.965068i \(0.584382\pi\)
\(908\) −19.4564 −0.645685
\(909\) −9.41880 −0.312402
\(910\) 3.00098 0.0994816
\(911\) 5.97895 0.198092 0.0990458 0.995083i \(-0.468421\pi\)
0.0990458 + 0.995083i \(0.468421\pi\)
\(912\) 15.4382 0.511211
\(913\) 13.3863 0.443022
\(914\) −25.1803 −0.832892
\(915\) −35.1643 −1.16250
\(916\) −11.2079 −0.370318
\(917\) −27.5010 −0.908164
\(918\) 80.5497 2.65853
\(919\) −1.80493 −0.0595392 −0.0297696 0.999557i \(-0.509477\pi\)
−0.0297696 + 0.999557i \(0.509477\pi\)
\(920\) −0.510515 −0.0168312
\(921\) 41.9915 1.38367
\(922\) 4.59424 0.151303
\(923\) −2.84553 −0.0936618
\(924\) −6.74481 −0.221888
\(925\) −2.87600 −0.0945624
\(926\) −7.26300 −0.238677
\(927\) −112.688 −3.70115
\(928\) −6.69280 −0.219702
\(929\) −53.2285 −1.74637 −0.873184 0.487390i \(-0.837949\pi\)
−0.873184 + 0.487390i \(0.837949\pi\)
\(930\) −10.7748 −0.353321
\(931\) −13.5613 −0.444453
\(932\) −2.07385 −0.0679312
\(933\) 36.4580 1.19358
\(934\) 24.4668 0.800578
\(935\) −4.62109 −0.151126
\(936\) −12.2240 −0.399554
\(937\) 29.5350 0.964865 0.482433 0.875933i \(-0.339753\pi\)
0.482433 + 0.875933i \(0.339753\pi\)
\(938\) −18.5645 −0.606153
\(939\) −16.2746 −0.531102
\(940\) −0.687284 −0.0224167
\(941\) 14.6068 0.476168 0.238084 0.971245i \(-0.423481\pi\)
0.238084 + 0.971245i \(0.423481\pi\)
\(942\) −29.3418 −0.956007
\(943\) −3.05024 −0.0993295
\(944\) 6.00237 0.195361
\(945\) −35.1194 −1.14243
\(946\) 1.00000 0.0325128
\(947\) −38.7219 −1.25829 −0.629146 0.777287i \(-0.716595\pi\)
−0.629146 + 0.777287i \(0.716595\pi\)
\(948\) 15.7229 0.510657
\(949\) 20.1464 0.653980
\(950\) −4.61164 −0.149621
\(951\) −51.5535 −1.67174
\(952\) 9.31048 0.301754
\(953\) −42.3834 −1.37293 −0.686466 0.727162i \(-0.740839\pi\)
−0.686466 + 0.727162i \(0.740839\pi\)
\(954\) 81.2791 2.63151
\(955\) 2.93960 0.0951234
\(956\) −12.0463 −0.389607
\(957\) −22.4053 −0.724260
\(958\) 7.23813 0.233853
\(959\) 2.96203 0.0956491
\(960\) −3.34767 −0.108045
\(961\) −20.6405 −0.665824
\(962\) 4.28376 0.138114
\(963\) 119.594 3.85386
\(964\) 7.59111 0.244493
\(965\) −14.0810 −0.453283
\(966\) 3.44333 0.110787
\(967\) 13.1072 0.421500 0.210750 0.977540i \(-0.432409\pi\)
0.210750 + 0.977540i \(0.432409\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −71.3414 −2.29182
\(970\) −18.5182 −0.594585
\(971\) 43.1723 1.38546 0.692732 0.721195i \(-0.256407\pi\)
0.692732 + 0.721195i \(0.256407\pi\)
\(972\) 60.6313 1.94475
\(973\) 5.93164 0.190160
\(974\) 21.9913 0.704646
\(975\) 4.98630 0.159689
\(976\) 10.5041 0.336229
\(977\) −0.939950 −0.0300717 −0.0150358 0.999887i \(-0.504786\pi\)
−0.0150358 + 0.999887i \(0.504786\pi\)
\(978\) −30.3782 −0.971388
\(979\) −8.93667 −0.285617
\(980\) 2.94066 0.0939361
\(981\) 71.8145 2.29286
\(982\) 10.1902 0.325182
\(983\) −34.7224 −1.10747 −0.553736 0.832692i \(-0.686798\pi\)
−0.553736 + 0.832692i \(0.686798\pi\)
\(984\) −20.0017 −0.637632
\(985\) 8.24038 0.262560
\(986\) 30.9280 0.984950
\(987\) 4.63560 0.147553
\(988\) 6.86896 0.218531
\(989\) −0.510515 −0.0162334
\(990\) −8.20687 −0.260832
\(991\) −24.8675 −0.789943 −0.394971 0.918693i \(-0.629245\pi\)
−0.394971 + 0.918693i \(0.629245\pi\)
\(992\) 3.21861 0.102191
\(993\) 84.8794 2.69357
\(994\) 3.84906 0.122085
\(995\) −15.1524 −0.480362
\(996\) −44.8129 −1.41995
\(997\) 7.44447 0.235769 0.117884 0.993027i \(-0.462389\pi\)
0.117884 + 0.993027i \(0.462389\pi\)
\(998\) 7.45725 0.236055
\(999\) −50.1312 −1.58608
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.1.11 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bb.1.11 11 1.1 even 1 trivial