Properties

Label 4730.2.a.bf.1.6
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 13
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: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.743787\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.743787 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.743787 q^{6} +2.37023 q^{7} +1.00000 q^{8} -2.44678 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.743787 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.743787 q^{6} +2.37023 q^{7} +1.00000 q^{8} -2.44678 q^{9} -1.00000 q^{10} +1.00000 q^{11} -0.743787 q^{12} -6.39183 q^{13} +2.37023 q^{14} +0.743787 q^{15} +1.00000 q^{16} +4.07984 q^{17} -2.44678 q^{18} +0.435288 q^{19} -1.00000 q^{20} -1.76294 q^{21} +1.00000 q^{22} +6.26363 q^{23} -0.743787 q^{24} +1.00000 q^{25} -6.39183 q^{26} +4.05125 q^{27} +2.37023 q^{28} -1.79475 q^{29} +0.743787 q^{30} -8.03034 q^{31} +1.00000 q^{32} -0.743787 q^{33} +4.07984 q^{34} -2.37023 q^{35} -2.44678 q^{36} +2.46727 q^{37} +0.435288 q^{38} +4.75416 q^{39} -1.00000 q^{40} +3.46869 q^{41} -1.76294 q^{42} +1.00000 q^{43} +1.00000 q^{44} +2.44678 q^{45} +6.26363 q^{46} +13.4587 q^{47} -0.743787 q^{48} -1.38202 q^{49} +1.00000 q^{50} -3.03453 q^{51} -6.39183 q^{52} -3.17735 q^{53} +4.05125 q^{54} -1.00000 q^{55} +2.37023 q^{56} -0.323761 q^{57} -1.79475 q^{58} +3.31965 q^{59} +0.743787 q^{60} -7.47912 q^{61} -8.03034 q^{62} -5.79943 q^{63} +1.00000 q^{64} +6.39183 q^{65} -0.743787 q^{66} +10.3564 q^{67} +4.07984 q^{68} -4.65881 q^{69} -2.37023 q^{70} +15.7728 q^{71} -2.44678 q^{72} -11.7977 q^{73} +2.46727 q^{74} -0.743787 q^{75} +0.435288 q^{76} +2.37023 q^{77} +4.75416 q^{78} +10.9519 q^{79} -1.00000 q^{80} +4.32708 q^{81} +3.46869 q^{82} +15.5992 q^{83} -1.76294 q^{84} -4.07984 q^{85} +1.00000 q^{86} +1.33491 q^{87} +1.00000 q^{88} +3.81948 q^{89} +2.44678 q^{90} -15.1501 q^{91} +6.26363 q^{92} +5.97287 q^{93} +13.4587 q^{94} -0.435288 q^{95} -0.743787 q^{96} +10.5689 q^{97} -1.38202 q^{98} -2.44678 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13q + 13q^{2} + 13q^{4} - 13q^{5} + 7q^{7} + 13q^{8} + 25q^{9} + O(q^{10}) \) \( 13q + 13q^{2} + 13q^{4} - 13q^{5} + 7q^{7} + 13q^{8} + 25q^{9} - 13q^{10} + 13q^{11} + 11q^{13} + 7q^{14} + 13q^{16} - 2q^{17} + 25q^{18} + 7q^{19} - 13q^{20} + 12q^{21} + 13q^{22} + 12q^{23} + 13q^{25} + 11q^{26} - 15q^{27} + 7q^{28} + 14q^{29} + 20q^{31} + 13q^{32} - 2q^{34} - 7q^{35} + 25q^{36} + 17q^{37} + 7q^{38} - 4q^{39} - 13q^{40} + 9q^{41} + 12q^{42} + 13q^{43} + 13q^{44} - 25q^{45} + 12q^{46} - 9q^{47} + 30q^{49} + 13q^{50} - 3q^{51} + 11q^{52} + 22q^{53} - 15q^{54} - 13q^{55} + 7q^{56} + 17q^{57} + 14q^{58} + 19q^{59} + 2q^{61} + 20q^{62} + 12q^{63} + 13q^{64} - 11q^{65} + 9q^{67} - 2q^{68} - 6q^{69} - 7q^{70} + 6q^{71} + 25q^{72} + 7q^{73} + 17q^{74} + 7q^{76} + 7q^{77} - 4q^{78} + 50q^{79} - 13q^{80} + 85q^{81} + 9q^{82} + q^{83} + 12q^{84} + 2q^{85} + 13q^{86} - 21q^{87} + 13q^{88} + 5q^{89} - 25q^{90} + 5q^{91} + 12q^{92} + 3q^{93} - 9q^{94} - 7q^{95} + 20q^{97} + 30q^{98} + 25q^{99} + O(q^{100}) \)

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
\(3\) −0.743787 −0.429426 −0.214713 0.976677i \(-0.568882\pi\)
−0.214713 + 0.976677i \(0.568882\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −0.743787 −0.303650
\(7\) 2.37023 0.895862 0.447931 0.894068i \(-0.352161\pi\)
0.447931 + 0.894068i \(0.352161\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.44678 −0.815594
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) −0.743787 −0.214713
\(13\) −6.39183 −1.77278 −0.886388 0.462944i \(-0.846793\pi\)
−0.886388 + 0.462944i \(0.846793\pi\)
\(14\) 2.37023 0.633470
\(15\) 0.743787 0.192045
\(16\) 1.00000 0.250000
\(17\) 4.07984 0.989506 0.494753 0.869034i \(-0.335258\pi\)
0.494753 + 0.869034i \(0.335258\pi\)
\(18\) −2.44678 −0.576712
\(19\) 0.435288 0.0998619 0.0499309 0.998753i \(-0.484100\pi\)
0.0499309 + 0.998753i \(0.484100\pi\)
\(20\) −1.00000 −0.223607
\(21\) −1.76294 −0.384706
\(22\) 1.00000 0.213201
\(23\) 6.26363 1.30606 0.653029 0.757333i \(-0.273498\pi\)
0.653029 + 0.757333i \(0.273498\pi\)
\(24\) −0.743787 −0.151825
\(25\) 1.00000 0.200000
\(26\) −6.39183 −1.25354
\(27\) 4.05125 0.779663
\(28\) 2.37023 0.447931
\(29\) −1.79475 −0.333277 −0.166638 0.986018i \(-0.553291\pi\)
−0.166638 + 0.986018i \(0.553291\pi\)
\(30\) 0.743787 0.135796
\(31\) −8.03034 −1.44229 −0.721146 0.692783i \(-0.756384\pi\)
−0.721146 + 0.692783i \(0.756384\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.743787 −0.129477
\(34\) 4.07984 0.699687
\(35\) −2.37023 −0.400642
\(36\) −2.44678 −0.407797
\(37\) 2.46727 0.405617 0.202809 0.979218i \(-0.434993\pi\)
0.202809 + 0.979218i \(0.434993\pi\)
\(38\) 0.435288 0.0706130
\(39\) 4.75416 0.761275
\(40\) −1.00000 −0.158114
\(41\) 3.46869 0.541718 0.270859 0.962619i \(-0.412692\pi\)
0.270859 + 0.962619i \(0.412692\pi\)
\(42\) −1.76294 −0.272028
\(43\) 1.00000 0.152499
\(44\) 1.00000 0.150756
\(45\) 2.44678 0.364745
\(46\) 6.26363 0.923522
\(47\) 13.4587 1.96316 0.981579 0.191058i \(-0.0611920\pi\)
0.981579 + 0.191058i \(0.0611920\pi\)
\(48\) −0.743787 −0.107356
\(49\) −1.38202 −0.197432
\(50\) 1.00000 0.141421
\(51\) −3.03453 −0.424919
\(52\) −6.39183 −0.886388
\(53\) −3.17735 −0.436442 −0.218221 0.975899i \(-0.570025\pi\)
−0.218221 + 0.975899i \(0.570025\pi\)
\(54\) 4.05125 0.551305
\(55\) −1.00000 −0.134840
\(56\) 2.37023 0.316735
\(57\) −0.323761 −0.0428832
\(58\) −1.79475 −0.235662
\(59\) 3.31965 0.432182 0.216091 0.976373i \(-0.430669\pi\)
0.216091 + 0.976373i \(0.430669\pi\)
\(60\) 0.743787 0.0960225
\(61\) −7.47912 −0.957604 −0.478802 0.877923i \(-0.658929\pi\)
−0.478802 + 0.877923i \(0.658929\pi\)
\(62\) −8.03034 −1.01985
\(63\) −5.79943 −0.730659
\(64\) 1.00000 0.125000
\(65\) 6.39183 0.792809
\(66\) −0.743787 −0.0915539
\(67\) 10.3564 1.26524 0.632618 0.774464i \(-0.281980\pi\)
0.632618 + 0.774464i \(0.281980\pi\)
\(68\) 4.07984 0.494753
\(69\) −4.65881 −0.560854
\(70\) −2.37023 −0.283296
\(71\) 15.7728 1.87189 0.935943 0.352150i \(-0.114549\pi\)
0.935943 + 0.352150i \(0.114549\pi\)
\(72\) −2.44678 −0.288356
\(73\) −11.7977 −1.38082 −0.690411 0.723417i \(-0.742570\pi\)
−0.690411 + 0.723417i \(0.742570\pi\)
\(74\) 2.46727 0.286815
\(75\) −0.743787 −0.0858851
\(76\) 0.435288 0.0499309
\(77\) 2.37023 0.270112
\(78\) 4.75416 0.538303
\(79\) 10.9519 1.23218 0.616091 0.787675i \(-0.288715\pi\)
0.616091 + 0.787675i \(0.288715\pi\)
\(80\) −1.00000 −0.111803
\(81\) 4.32708 0.480786
\(82\) 3.46869 0.383053
\(83\) 15.5992 1.71223 0.856115 0.516785i \(-0.172872\pi\)
0.856115 + 0.516785i \(0.172872\pi\)
\(84\) −1.76294 −0.192353
\(85\) −4.07984 −0.442521
\(86\) 1.00000 0.107833
\(87\) 1.33491 0.143118
\(88\) 1.00000 0.106600
\(89\) 3.81948 0.404864 0.202432 0.979296i \(-0.435115\pi\)
0.202432 + 0.979296i \(0.435115\pi\)
\(90\) 2.44678 0.257913
\(91\) −15.1501 −1.58816
\(92\) 6.26363 0.653029
\(93\) 5.97287 0.619357
\(94\) 13.4587 1.38816
\(95\) −0.435288 −0.0446596
\(96\) −0.743787 −0.0759125
\(97\) 10.5689 1.07311 0.536555 0.843866i \(-0.319726\pi\)
0.536555 + 0.843866i \(0.319726\pi\)
\(98\) −1.38202 −0.139605
\(99\) −2.44678 −0.245911
\(100\) 1.00000 0.100000
\(101\) −12.6216 −1.25590 −0.627948 0.778255i \(-0.716105\pi\)
−0.627948 + 0.778255i \(0.716105\pi\)
\(102\) −3.03453 −0.300463
\(103\) 7.02093 0.691793 0.345896 0.938273i \(-0.387575\pi\)
0.345896 + 0.938273i \(0.387575\pi\)
\(104\) −6.39183 −0.626771
\(105\) 1.76294 0.172046
\(106\) −3.17735 −0.308611
\(107\) −18.2252 −1.76189 −0.880946 0.473217i \(-0.843093\pi\)
−0.880946 + 0.473217i \(0.843093\pi\)
\(108\) 4.05125 0.389831
\(109\) 1.96339 0.188059 0.0940293 0.995569i \(-0.470025\pi\)
0.0940293 + 0.995569i \(0.470025\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −1.83513 −0.174182
\(112\) 2.37023 0.223965
\(113\) 2.57016 0.241781 0.120890 0.992666i \(-0.461425\pi\)
0.120890 + 0.992666i \(0.461425\pi\)
\(114\) −0.323761 −0.0303230
\(115\) −6.26363 −0.584087
\(116\) −1.79475 −0.166638
\(117\) 15.6394 1.44586
\(118\) 3.31965 0.305599
\(119\) 9.67015 0.886461
\(120\) 0.743787 0.0678982
\(121\) 1.00000 0.0909091
\(122\) −7.47912 −0.677128
\(123\) −2.57997 −0.232628
\(124\) −8.03034 −0.721146
\(125\) −1.00000 −0.0894427
\(126\) −5.79943 −0.516654
\(127\) 4.26666 0.378605 0.189302 0.981919i \(-0.439377\pi\)
0.189302 + 0.981919i \(0.439377\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.743787 −0.0654868
\(130\) 6.39183 0.560601
\(131\) 16.4846 1.44027 0.720134 0.693835i \(-0.244080\pi\)
0.720134 + 0.693835i \(0.244080\pi\)
\(132\) −0.743787 −0.0647384
\(133\) 1.03173 0.0894624
\(134\) 10.3564 0.894657
\(135\) −4.05125 −0.348676
\(136\) 4.07984 0.349843
\(137\) −1.16436 −0.0994778 −0.0497389 0.998762i \(-0.515839\pi\)
−0.0497389 + 0.998762i \(0.515839\pi\)
\(138\) −4.65881 −0.396584
\(139\) −0.620186 −0.0526035 −0.0263017 0.999654i \(-0.508373\pi\)
−0.0263017 + 0.999654i \(0.508373\pi\)
\(140\) −2.37023 −0.200321
\(141\) −10.0104 −0.843030
\(142\) 15.7728 1.32362
\(143\) −6.39183 −0.534512
\(144\) −2.44678 −0.203898
\(145\) 1.79475 0.149046
\(146\) −11.7977 −0.976389
\(147\) 1.02793 0.0847823
\(148\) 2.46727 0.202809
\(149\) 9.96655 0.816492 0.408246 0.912872i \(-0.366141\pi\)
0.408246 + 0.912872i \(0.366141\pi\)
\(150\) −0.743787 −0.0607300
\(151\) 17.8260 1.45066 0.725330 0.688401i \(-0.241687\pi\)
0.725330 + 0.688401i \(0.241687\pi\)
\(152\) 0.435288 0.0353065
\(153\) −9.98247 −0.807035
\(154\) 2.37023 0.190998
\(155\) 8.03034 0.645013
\(156\) 4.75416 0.380638
\(157\) −0.927021 −0.0739843 −0.0369922 0.999316i \(-0.511778\pi\)
−0.0369922 + 0.999316i \(0.511778\pi\)
\(158\) 10.9519 0.871284
\(159\) 2.36327 0.187420
\(160\) −1.00000 −0.0790569
\(161\) 14.8462 1.17005
\(162\) 4.32708 0.339967
\(163\) −3.18442 −0.249423 −0.124711 0.992193i \(-0.539801\pi\)
−0.124711 + 0.992193i \(0.539801\pi\)
\(164\) 3.46869 0.270859
\(165\) 0.743787 0.0579037
\(166\) 15.5992 1.21073
\(167\) −23.9380 −1.85238 −0.926188 0.377062i \(-0.876934\pi\)
−0.926188 + 0.377062i \(0.876934\pi\)
\(168\) −1.76294 −0.136014
\(169\) 27.8555 2.14273
\(170\) −4.07984 −0.312909
\(171\) −1.06505 −0.0814467
\(172\) 1.00000 0.0762493
\(173\) 4.67961 0.355784 0.177892 0.984050i \(-0.443072\pi\)
0.177892 + 0.984050i \(0.443072\pi\)
\(174\) 1.33491 0.101199
\(175\) 2.37023 0.179172
\(176\) 1.00000 0.0753778
\(177\) −2.46911 −0.185590
\(178\) 3.81948 0.286282
\(179\) −16.3112 −1.21916 −0.609579 0.792725i \(-0.708662\pi\)
−0.609579 + 0.792725i \(0.708662\pi\)
\(180\) 2.44678 0.182372
\(181\) −16.2790 −1.21001 −0.605003 0.796223i \(-0.706828\pi\)
−0.605003 + 0.796223i \(0.706828\pi\)
\(182\) −15.1501 −1.12300
\(183\) 5.56288 0.411220
\(184\) 6.26363 0.461761
\(185\) −2.46727 −0.181397
\(186\) 5.97287 0.437952
\(187\) 4.07984 0.298347
\(188\) 13.4587 0.981579
\(189\) 9.60237 0.698470
\(190\) −0.435288 −0.0315791
\(191\) −0.748643 −0.0541699 −0.0270850 0.999633i \(-0.508622\pi\)
−0.0270850 + 0.999633i \(0.508622\pi\)
\(192\) −0.743787 −0.0536782
\(193\) −3.19938 −0.230296 −0.115148 0.993348i \(-0.536734\pi\)
−0.115148 + 0.993348i \(0.536734\pi\)
\(194\) 10.5689 0.758803
\(195\) −4.75416 −0.340453
\(196\) −1.38202 −0.0987159
\(197\) 16.7313 1.19206 0.596028 0.802964i \(-0.296745\pi\)
0.596028 + 0.802964i \(0.296745\pi\)
\(198\) −2.44678 −0.173885
\(199\) 25.8675 1.83370 0.916849 0.399235i \(-0.130724\pi\)
0.916849 + 0.399235i \(0.130724\pi\)
\(200\) 1.00000 0.0707107
\(201\) −7.70296 −0.543325
\(202\) −12.6216 −0.888053
\(203\) −4.25397 −0.298570
\(204\) −3.03453 −0.212460
\(205\) −3.46869 −0.242264
\(206\) 7.02093 0.489171
\(207\) −15.3257 −1.06521
\(208\) −6.39183 −0.443194
\(209\) 0.435288 0.0301095
\(210\) 1.76294 0.121655
\(211\) −1.91869 −0.132088 −0.0660442 0.997817i \(-0.521038\pi\)
−0.0660442 + 0.997817i \(0.521038\pi\)
\(212\) −3.17735 −0.218221
\(213\) −11.7316 −0.803836
\(214\) −18.2252 −1.24585
\(215\) −1.00000 −0.0681994
\(216\) 4.05125 0.275652
\(217\) −19.0337 −1.29209
\(218\) 1.96339 0.132978
\(219\) 8.77501 0.592960
\(220\) −1.00000 −0.0674200
\(221\) −26.0777 −1.75417
\(222\) −1.83513 −0.123166
\(223\) 6.34358 0.424797 0.212399 0.977183i \(-0.431872\pi\)
0.212399 + 0.977183i \(0.431872\pi\)
\(224\) 2.37023 0.158367
\(225\) −2.44678 −0.163119
\(226\) 2.57016 0.170965
\(227\) 6.30747 0.418642 0.209321 0.977847i \(-0.432875\pi\)
0.209321 + 0.977847i \(0.432875\pi\)
\(228\) −0.323761 −0.0214416
\(229\) −1.07394 −0.0709677 −0.0354838 0.999370i \(-0.511297\pi\)
−0.0354838 + 0.999370i \(0.511297\pi\)
\(230\) −6.26363 −0.413012
\(231\) −1.76294 −0.115993
\(232\) −1.79475 −0.117831
\(233\) −12.8886 −0.844360 −0.422180 0.906512i \(-0.638735\pi\)
−0.422180 + 0.906512i \(0.638735\pi\)
\(234\) 15.6394 1.02238
\(235\) −13.4587 −0.877951
\(236\) 3.31965 0.216091
\(237\) −8.14586 −0.529130
\(238\) 9.67015 0.626822
\(239\) 23.8230 1.54098 0.770490 0.637452i \(-0.220012\pi\)
0.770490 + 0.637452i \(0.220012\pi\)
\(240\) 0.743787 0.0480113
\(241\) −23.7819 −1.53193 −0.765965 0.642882i \(-0.777738\pi\)
−0.765965 + 0.642882i \(0.777738\pi\)
\(242\) 1.00000 0.0642824
\(243\) −15.3722 −0.986125
\(244\) −7.47912 −0.478802
\(245\) 1.38202 0.0882942
\(246\) −2.57997 −0.164493
\(247\) −2.78229 −0.177033
\(248\) −8.03034 −0.509927
\(249\) −11.6025 −0.735275
\(250\) −1.00000 −0.0632456
\(251\) 28.8494 1.82096 0.910480 0.413554i \(-0.135713\pi\)
0.910480 + 0.413554i \(0.135713\pi\)
\(252\) −5.79943 −0.365330
\(253\) 6.26363 0.393791
\(254\) 4.26666 0.267714
\(255\) 3.03453 0.190030
\(256\) 1.00000 0.0625000
\(257\) −14.9517 −0.932662 −0.466331 0.884610i \(-0.654424\pi\)
−0.466331 + 0.884610i \(0.654424\pi\)
\(258\) −0.743787 −0.0463062
\(259\) 5.84800 0.363377
\(260\) 6.39183 0.396405
\(261\) 4.39136 0.271818
\(262\) 16.4846 1.01842
\(263\) −1.97089 −0.121530 −0.0607650 0.998152i \(-0.519354\pi\)
−0.0607650 + 0.998152i \(0.519354\pi\)
\(264\) −0.743787 −0.0457769
\(265\) 3.17735 0.195183
\(266\) 1.03173 0.0632595
\(267\) −2.84088 −0.173859
\(268\) 10.3564 0.632618
\(269\) 1.29375 0.0788816 0.0394408 0.999222i \(-0.487442\pi\)
0.0394408 + 0.999222i \(0.487442\pi\)
\(270\) −4.05125 −0.246551
\(271\) −0.608675 −0.0369744 −0.0184872 0.999829i \(-0.505885\pi\)
−0.0184872 + 0.999829i \(0.505885\pi\)
\(272\) 4.07984 0.247377
\(273\) 11.2684 0.681997
\(274\) −1.16436 −0.0703415
\(275\) 1.00000 0.0603023
\(276\) −4.65881 −0.280427
\(277\) 25.2431 1.51671 0.758357 0.651840i \(-0.226003\pi\)
0.758357 + 0.651840i \(0.226003\pi\)
\(278\) −0.620186 −0.0371963
\(279\) 19.6485 1.17632
\(280\) −2.37023 −0.141648
\(281\) −5.40227 −0.322273 −0.161136 0.986932i \(-0.551516\pi\)
−0.161136 + 0.986932i \(0.551516\pi\)
\(282\) −10.0104 −0.596112
\(283\) 11.6987 0.695418 0.347709 0.937603i \(-0.386960\pi\)
0.347709 + 0.937603i \(0.386960\pi\)
\(284\) 15.7728 0.935943
\(285\) 0.323761 0.0191780
\(286\) −6.39183 −0.377957
\(287\) 8.22158 0.485305
\(288\) −2.44678 −0.144178
\(289\) −0.354914 −0.0208773
\(290\) 1.79475 0.105391
\(291\) −7.86101 −0.460821
\(292\) −11.7977 −0.690411
\(293\) −11.9728 −0.699460 −0.349730 0.936851i \(-0.613727\pi\)
−0.349730 + 0.936851i \(0.613727\pi\)
\(294\) 1.02793 0.0599502
\(295\) −3.31965 −0.193277
\(296\) 2.46727 0.143407
\(297\) 4.05125 0.235077
\(298\) 9.96655 0.577347
\(299\) −40.0361 −2.31535
\(300\) −0.743787 −0.0429426
\(301\) 2.37023 0.136618
\(302\) 17.8260 1.02577
\(303\) 9.38779 0.539314
\(304\) 0.435288 0.0249655
\(305\) 7.47912 0.428253
\(306\) −9.98247 −0.570660
\(307\) −2.62894 −0.150041 −0.0750207 0.997182i \(-0.523902\pi\)
−0.0750207 + 0.997182i \(0.523902\pi\)
\(308\) 2.37023 0.135056
\(309\) −5.22208 −0.297074
\(310\) 8.03034 0.456093
\(311\) 31.2463 1.77182 0.885908 0.463861i \(-0.153536\pi\)
0.885908 + 0.463861i \(0.153536\pi\)
\(312\) 4.75416 0.269151
\(313\) 8.54031 0.482727 0.241364 0.970435i \(-0.422405\pi\)
0.241364 + 0.970435i \(0.422405\pi\)
\(314\) −0.927021 −0.0523148
\(315\) 5.79943 0.326761
\(316\) 10.9519 0.616091
\(317\) −3.00276 −0.168652 −0.0843260 0.996438i \(-0.526874\pi\)
−0.0843260 + 0.996438i \(0.526874\pi\)
\(318\) 2.36327 0.132526
\(319\) −1.79475 −0.100487
\(320\) −1.00000 −0.0559017
\(321\) 13.5556 0.756602
\(322\) 14.8462 0.827348
\(323\) 1.77590 0.0988139
\(324\) 4.32708 0.240393
\(325\) −6.39183 −0.354555
\(326\) −3.18442 −0.176369
\(327\) −1.46034 −0.0807572
\(328\) 3.46869 0.191526
\(329\) 31.9002 1.75872
\(330\) 0.743787 0.0409441
\(331\) 17.2705 0.949271 0.474636 0.880182i \(-0.342580\pi\)
0.474636 + 0.880182i \(0.342580\pi\)
\(332\) 15.5992 0.856115
\(333\) −6.03688 −0.330819
\(334\) −23.9380 −1.30983
\(335\) −10.3564 −0.565831
\(336\) −1.76294 −0.0961765
\(337\) 23.7259 1.29243 0.646217 0.763154i \(-0.276350\pi\)
0.646217 + 0.763154i \(0.276350\pi\)
\(338\) 27.8555 1.51514
\(339\) −1.91166 −0.103827
\(340\) −4.07984 −0.221260
\(341\) −8.03034 −0.434867
\(342\) −1.06505 −0.0575915
\(343\) −19.8673 −1.07273
\(344\) 1.00000 0.0539164
\(345\) 4.65881 0.250822
\(346\) 4.67961 0.251577
\(347\) 28.5607 1.53322 0.766610 0.642113i \(-0.221942\pi\)
0.766610 + 0.642113i \(0.221942\pi\)
\(348\) 1.33491 0.0715588
\(349\) −21.1705 −1.13323 −0.566615 0.823983i \(-0.691747\pi\)
−0.566615 + 0.823983i \(0.691747\pi\)
\(350\) 2.37023 0.126694
\(351\) −25.8949 −1.38217
\(352\) 1.00000 0.0533002
\(353\) −3.04772 −0.162214 −0.0811068 0.996705i \(-0.525845\pi\)
−0.0811068 + 0.996705i \(0.525845\pi\)
\(354\) −2.46911 −0.131232
\(355\) −15.7728 −0.837133
\(356\) 3.81948 0.202432
\(357\) −7.19253 −0.380669
\(358\) −16.3112 −0.862075
\(359\) −7.77059 −0.410116 −0.205058 0.978750i \(-0.565738\pi\)
−0.205058 + 0.978750i \(0.565738\pi\)
\(360\) 2.44678 0.128957
\(361\) −18.8105 −0.990028
\(362\) −16.2790 −0.855604
\(363\) −0.743787 −0.0390387
\(364\) −15.1501 −0.794081
\(365\) 11.7977 0.617522
\(366\) 5.56288 0.290776
\(367\) 25.1694 1.31383 0.656916 0.753964i \(-0.271860\pi\)
0.656916 + 0.753964i \(0.271860\pi\)
\(368\) 6.26363 0.326514
\(369\) −8.48712 −0.441822
\(370\) −2.46727 −0.128267
\(371\) −7.53104 −0.390992
\(372\) 5.97287 0.309679
\(373\) 9.13802 0.473149 0.236574 0.971613i \(-0.423975\pi\)
0.236574 + 0.971613i \(0.423975\pi\)
\(374\) 4.07984 0.210963
\(375\) 0.743787 0.0384090
\(376\) 13.4587 0.694081
\(377\) 11.4717 0.590825
\(378\) 9.60237 0.493893
\(379\) −21.1229 −1.08501 −0.542505 0.840053i \(-0.682524\pi\)
−0.542505 + 0.840053i \(0.682524\pi\)
\(380\) −0.435288 −0.0223298
\(381\) −3.17349 −0.162583
\(382\) −0.748643 −0.0383039
\(383\) −24.4665 −1.25018 −0.625091 0.780552i \(-0.714938\pi\)
−0.625091 + 0.780552i \(0.714938\pi\)
\(384\) −0.743787 −0.0379562
\(385\) −2.37023 −0.120798
\(386\) −3.19938 −0.162844
\(387\) −2.44678 −0.124377
\(388\) 10.5689 0.536555
\(389\) 20.4998 1.03938 0.519690 0.854355i \(-0.326047\pi\)
0.519690 + 0.854355i \(0.326047\pi\)
\(390\) −4.75416 −0.240736
\(391\) 25.5546 1.29235
\(392\) −1.38202 −0.0698027
\(393\) −12.2611 −0.618488
\(394\) 16.7313 0.842911
\(395\) −10.9519 −0.551048
\(396\) −2.44678 −0.122955
\(397\) 6.08973 0.305635 0.152817 0.988254i \(-0.451165\pi\)
0.152817 + 0.988254i \(0.451165\pi\)
\(398\) 25.8675 1.29662
\(399\) −0.767388 −0.0384175
\(400\) 1.00000 0.0500000
\(401\) 10.6349 0.531080 0.265540 0.964100i \(-0.414450\pi\)
0.265540 + 0.964100i \(0.414450\pi\)
\(402\) −7.70296 −0.384189
\(403\) 51.3286 2.55686
\(404\) −12.6216 −0.627948
\(405\) −4.32708 −0.215014
\(406\) −4.25397 −0.211121
\(407\) 2.46727 0.122298
\(408\) −3.03453 −0.150232
\(409\) −22.1299 −1.09425 −0.547126 0.837050i \(-0.684278\pi\)
−0.547126 + 0.837050i \(0.684278\pi\)
\(410\) −3.46869 −0.171306
\(411\) 0.866035 0.0427183
\(412\) 7.02093 0.345896
\(413\) 7.86832 0.387175
\(414\) −15.3257 −0.753219
\(415\) −15.5992 −0.765732
\(416\) −6.39183 −0.313385
\(417\) 0.461286 0.0225893
\(418\) 0.435288 0.0212906
\(419\) −6.59799 −0.322333 −0.161166 0.986927i \(-0.551526\pi\)
−0.161166 + 0.986927i \(0.551526\pi\)
\(420\) 1.76294 0.0860229
\(421\) 34.6188 1.68722 0.843609 0.536957i \(-0.180426\pi\)
0.843609 + 0.536957i \(0.180426\pi\)
\(422\) −1.91869 −0.0934005
\(423\) −32.9306 −1.60114
\(424\) −3.17735 −0.154306
\(425\) 4.07984 0.197901
\(426\) −11.7316 −0.568398
\(427\) −17.7272 −0.857880
\(428\) −18.2252 −0.880946
\(429\) 4.75416 0.229533
\(430\) −1.00000 −0.0482243
\(431\) −0.278037 −0.0133926 −0.00669629 0.999978i \(-0.502132\pi\)
−0.00669629 + 0.999978i \(0.502132\pi\)
\(432\) 4.05125 0.194916
\(433\) 18.8648 0.906583 0.453292 0.891362i \(-0.350250\pi\)
0.453292 + 0.891362i \(0.350250\pi\)
\(434\) −19.0337 −0.913649
\(435\) −1.33491 −0.0640041
\(436\) 1.96339 0.0940293
\(437\) 2.72648 0.130425
\(438\) 8.77501 0.419286
\(439\) 32.4407 1.54831 0.774155 0.632996i \(-0.218175\pi\)
0.774155 + 0.632996i \(0.218175\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 3.38151 0.161024
\(442\) −26.0777 −1.24039
\(443\) −13.2400 −0.629049 −0.314525 0.949249i \(-0.601845\pi\)
−0.314525 + 0.949249i \(0.601845\pi\)
\(444\) −1.83513 −0.0870912
\(445\) −3.81948 −0.181061
\(446\) 6.34358 0.300377
\(447\) −7.41299 −0.350623
\(448\) 2.37023 0.111983
\(449\) −21.9325 −1.03506 −0.517530 0.855665i \(-0.673148\pi\)
−0.517530 + 0.855665i \(0.673148\pi\)
\(450\) −2.44678 −0.115342
\(451\) 3.46869 0.163334
\(452\) 2.57016 0.120890
\(453\) −13.2588 −0.622951
\(454\) 6.30747 0.296024
\(455\) 15.1501 0.710247
\(456\) −0.323761 −0.0151615
\(457\) 5.29284 0.247589 0.123794 0.992308i \(-0.460494\pi\)
0.123794 + 0.992308i \(0.460494\pi\)
\(458\) −1.07394 −0.0501817
\(459\) 16.5284 0.771481
\(460\) −6.26363 −0.292043
\(461\) −26.5996 −1.23887 −0.619434 0.785049i \(-0.712638\pi\)
−0.619434 + 0.785049i \(0.712638\pi\)
\(462\) −1.76294 −0.0820196
\(463\) −4.36551 −0.202882 −0.101441 0.994842i \(-0.532345\pi\)
−0.101441 + 0.994842i \(0.532345\pi\)
\(464\) −1.79475 −0.0833192
\(465\) −5.97287 −0.276985
\(466\) −12.8886 −0.597053
\(467\) −6.47548 −0.299650 −0.149825 0.988713i \(-0.547871\pi\)
−0.149825 + 0.988713i \(0.547871\pi\)
\(468\) 15.6394 0.722932
\(469\) 24.5470 1.13348
\(470\) −13.4587 −0.620805
\(471\) 0.689506 0.0317708
\(472\) 3.31965 0.152799
\(473\) 1.00000 0.0459800
\(474\) −8.14586 −0.374152
\(475\) 0.435288 0.0199724
\(476\) 9.67015 0.443230
\(477\) 7.77428 0.355960
\(478\) 23.8230 1.08964
\(479\) 6.30021 0.287864 0.143932 0.989588i \(-0.454025\pi\)
0.143932 + 0.989588i \(0.454025\pi\)
\(480\) 0.743787 0.0339491
\(481\) −15.7704 −0.719068
\(482\) −23.7819 −1.08324
\(483\) −11.0424 −0.502448
\(484\) 1.00000 0.0454545
\(485\) −10.5689 −0.479909
\(486\) −15.3722 −0.697295
\(487\) 6.41963 0.290901 0.145451 0.989366i \(-0.453537\pi\)
0.145451 + 0.989366i \(0.453537\pi\)
\(488\) −7.47912 −0.338564
\(489\) 2.36853 0.107109
\(490\) 1.38202 0.0624334
\(491\) −18.5957 −0.839214 −0.419607 0.907706i \(-0.637832\pi\)
−0.419607 + 0.907706i \(0.637832\pi\)
\(492\) −2.57997 −0.116314
\(493\) −7.32229 −0.329779
\(494\) −2.78229 −0.125181
\(495\) 2.44678 0.109975
\(496\) −8.03034 −0.360573
\(497\) 37.3851 1.67695
\(498\) −11.6025 −0.519918
\(499\) 19.8768 0.889809 0.444904 0.895578i \(-0.353238\pi\)
0.444904 + 0.895578i \(0.353238\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 17.8048 0.795458
\(502\) 28.8494 1.28761
\(503\) −23.6174 −1.05305 −0.526525 0.850160i \(-0.676505\pi\)
−0.526525 + 0.850160i \(0.676505\pi\)
\(504\) −5.79943 −0.258327
\(505\) 12.6216 0.561654
\(506\) 6.26363 0.278452
\(507\) −20.7186 −0.920145
\(508\) 4.26666 0.189302
\(509\) 2.47997 0.109923 0.0549614 0.998488i \(-0.482496\pi\)
0.0549614 + 0.998488i \(0.482496\pi\)
\(510\) 3.03453 0.134371
\(511\) −27.9633 −1.23703
\(512\) 1.00000 0.0441942
\(513\) 1.76346 0.0778585
\(514\) −14.9517 −0.659492
\(515\) −7.02093 −0.309379
\(516\) −0.743787 −0.0327434
\(517\) 13.4587 0.591914
\(518\) 5.84800 0.256946
\(519\) −3.48063 −0.152783
\(520\) 6.39183 0.280300
\(521\) −2.16403 −0.0948080 −0.0474040 0.998876i \(-0.515095\pi\)
−0.0474040 + 0.998876i \(0.515095\pi\)
\(522\) 4.39136 0.192205
\(523\) −17.2625 −0.754836 −0.377418 0.926043i \(-0.623188\pi\)
−0.377418 + 0.926043i \(0.623188\pi\)
\(524\) 16.4846 0.720134
\(525\) −1.76294 −0.0769412
\(526\) −1.97089 −0.0859347
\(527\) −32.7625 −1.42716
\(528\) −0.743787 −0.0323692
\(529\) 16.2331 0.705785
\(530\) 3.17735 0.138015
\(531\) −8.12246 −0.352485
\(532\) 1.03173 0.0447312
\(533\) −22.1713 −0.960345
\(534\) −2.84088 −0.122937
\(535\) 18.2252 0.787942
\(536\) 10.3564 0.447329
\(537\) 12.1321 0.523538
\(538\) 1.29375 0.0557777
\(539\) −1.38202 −0.0595279
\(540\) −4.05125 −0.174338
\(541\) 0.218195 0.00938095 0.00469047 0.999989i \(-0.498507\pi\)
0.00469047 + 0.999989i \(0.498507\pi\)
\(542\) −0.608675 −0.0261448
\(543\) 12.1081 0.519608
\(544\) 4.07984 0.174922
\(545\) −1.96339 −0.0841024
\(546\) 11.2684 0.482245
\(547\) −35.6010 −1.52219 −0.761095 0.648641i \(-0.775338\pi\)
−0.761095 + 0.648641i \(0.775338\pi\)
\(548\) −1.16436 −0.0497389
\(549\) 18.2998 0.781015
\(550\) 1.00000 0.0426401
\(551\) −0.781233 −0.0332816
\(552\) −4.65881 −0.198292
\(553\) 25.9584 1.10386
\(554\) 25.2431 1.07248
\(555\) 1.83513 0.0778967
\(556\) −0.620186 −0.0263017
\(557\) −16.9034 −0.716220 −0.358110 0.933679i \(-0.616579\pi\)
−0.358110 + 0.933679i \(0.616579\pi\)
\(558\) 19.6485 0.831787
\(559\) −6.39183 −0.270346
\(560\) −2.37023 −0.100160
\(561\) −3.03453 −0.128118
\(562\) −5.40227 −0.227881
\(563\) 18.1930 0.766741 0.383371 0.923595i \(-0.374763\pi\)
0.383371 + 0.923595i \(0.374763\pi\)
\(564\) −10.0104 −0.421515
\(565\) −2.57016 −0.108128
\(566\) 11.6987 0.491735
\(567\) 10.2562 0.430718
\(568\) 15.7728 0.661812
\(569\) 2.86491 0.120103 0.0600516 0.998195i \(-0.480873\pi\)
0.0600516 + 0.998195i \(0.480873\pi\)
\(570\) 0.323761 0.0135609
\(571\) −23.8161 −0.996671 −0.498335 0.866984i \(-0.666055\pi\)
−0.498335 + 0.866984i \(0.666055\pi\)
\(572\) −6.39183 −0.267256
\(573\) 0.556831 0.0232620
\(574\) 8.22158 0.343162
\(575\) 6.26363 0.261211
\(576\) −2.44678 −0.101949
\(577\) −4.31064 −0.179454 −0.0897272 0.995966i \(-0.528600\pi\)
−0.0897272 + 0.995966i \(0.528600\pi\)
\(578\) −0.354914 −0.0147625
\(579\) 2.37966 0.0988951
\(580\) 1.79475 0.0745230
\(581\) 36.9735 1.53392
\(582\) −7.86101 −0.325849
\(583\) −3.17735 −0.131592
\(584\) −11.7977 −0.488194
\(585\) −15.6394 −0.646610
\(586\) −11.9728 −0.494593
\(587\) −30.9067 −1.27565 −0.637827 0.770180i \(-0.720167\pi\)
−0.637827 + 0.770180i \(0.720167\pi\)
\(588\) 1.02793 0.0423912
\(589\) −3.49551 −0.144030
\(590\) −3.31965 −0.136668
\(591\) −12.4445 −0.511899
\(592\) 2.46727 0.101404
\(593\) −40.2599 −1.65328 −0.826639 0.562733i \(-0.809750\pi\)
−0.826639 + 0.562733i \(0.809750\pi\)
\(594\) 4.05125 0.166225
\(595\) −9.67015 −0.396437
\(596\) 9.96655 0.408246
\(597\) −19.2399 −0.787437
\(598\) −40.0361 −1.63720
\(599\) −43.3369 −1.77070 −0.885349 0.464927i \(-0.846081\pi\)
−0.885349 + 0.464927i \(0.846081\pi\)
\(600\) −0.743787 −0.0303650
\(601\) −3.49531 −0.142577 −0.0712883 0.997456i \(-0.522711\pi\)
−0.0712883 + 0.997456i \(0.522711\pi\)
\(602\) 2.37023 0.0966032
\(603\) −25.3399 −1.03192
\(604\) 17.8260 0.725330
\(605\) −1.00000 −0.0406558
\(606\) 9.38779 0.381353
\(607\) −7.07265 −0.287070 −0.143535 0.989645i \(-0.545847\pi\)
−0.143535 + 0.989645i \(0.545847\pi\)
\(608\) 0.435288 0.0176532
\(609\) 3.16405 0.128214
\(610\) 7.47912 0.302821
\(611\) −86.0259 −3.48024
\(612\) −9.98247 −0.403517
\(613\) 15.4997 0.626027 0.313013 0.949749i \(-0.398661\pi\)
0.313013 + 0.949749i \(0.398661\pi\)
\(614\) −2.62894 −0.106095
\(615\) 2.57997 0.104034
\(616\) 2.37023 0.0954992
\(617\) −46.6801 −1.87927 −0.939635 0.342178i \(-0.888836\pi\)
−0.939635 + 0.342178i \(0.888836\pi\)
\(618\) −5.22208 −0.210063
\(619\) −39.8885 −1.60325 −0.801626 0.597825i \(-0.796032\pi\)
−0.801626 + 0.597825i \(0.796032\pi\)
\(620\) 8.03034 0.322506
\(621\) 25.3755 1.01828
\(622\) 31.2463 1.25286
\(623\) 9.05304 0.362702
\(624\) 4.75416 0.190319
\(625\) 1.00000 0.0400000
\(626\) 8.54031 0.341340
\(627\) −0.323761 −0.0129298
\(628\) −0.927021 −0.0369922
\(629\) 10.0661 0.401361
\(630\) 5.79943 0.231055
\(631\) 19.8822 0.791498 0.395749 0.918359i \(-0.370485\pi\)
0.395749 + 0.918359i \(0.370485\pi\)
\(632\) 10.9519 0.435642
\(633\) 1.42710 0.0567221
\(634\) −3.00276 −0.119255
\(635\) −4.26666 −0.169317
\(636\) 2.36327 0.0937098
\(637\) 8.83366 0.350002
\(638\) −1.79475 −0.0710548
\(639\) −38.5926 −1.52670
\(640\) −1.00000 −0.0395285
\(641\) −6.83084 −0.269802 −0.134901 0.990859i \(-0.543072\pi\)
−0.134901 + 0.990859i \(0.543072\pi\)
\(642\) 13.5556 0.534998
\(643\) −41.1340 −1.62217 −0.811084 0.584930i \(-0.801122\pi\)
−0.811084 + 0.584930i \(0.801122\pi\)
\(644\) 14.8462 0.585023
\(645\) 0.743787 0.0292866
\(646\) 1.77590 0.0698720
\(647\) −31.7247 −1.24723 −0.623613 0.781734i \(-0.714336\pi\)
−0.623613 + 0.781734i \(0.714336\pi\)
\(648\) 4.32708 0.169984
\(649\) 3.31965 0.130308
\(650\) −6.39183 −0.250708
\(651\) 14.1570 0.554859
\(652\) −3.18442 −0.124711
\(653\) 13.6939 0.535885 0.267942 0.963435i \(-0.413656\pi\)
0.267942 + 0.963435i \(0.413656\pi\)
\(654\) −1.46034 −0.0571040
\(655\) −16.4846 −0.644108
\(656\) 3.46869 0.135430
\(657\) 28.8665 1.12619
\(658\) 31.9002 1.24360
\(659\) −17.8299 −0.694555 −0.347277 0.937762i \(-0.612894\pi\)
−0.347277 + 0.937762i \(0.612894\pi\)
\(660\) 0.743787 0.0289519
\(661\) −38.9843 −1.51632 −0.758158 0.652071i \(-0.773900\pi\)
−0.758158 + 0.652071i \(0.773900\pi\)
\(662\) 17.2705 0.671236
\(663\) 19.3962 0.753287
\(664\) 15.5992 0.605365
\(665\) −1.03173 −0.0400088
\(666\) −6.03688 −0.233924
\(667\) −11.2417 −0.435279
\(668\) −23.9380 −0.926188
\(669\) −4.71827 −0.182419
\(670\) −10.3564 −0.400103
\(671\) −7.47912 −0.288728
\(672\) −1.76294 −0.0680071
\(673\) 7.35240 0.283414 0.141707 0.989909i \(-0.454741\pi\)
0.141707 + 0.989909i \(0.454741\pi\)
\(674\) 23.7259 0.913889
\(675\) 4.05125 0.155933
\(676\) 27.8555 1.07137
\(677\) −35.8656 −1.37843 −0.689214 0.724558i \(-0.742044\pi\)
−0.689214 + 0.724558i \(0.742044\pi\)
\(678\) −1.91166 −0.0734167
\(679\) 25.0507 0.961357
\(680\) −4.07984 −0.156455
\(681\) −4.69142 −0.179776
\(682\) −8.03034 −0.307498
\(683\) −13.0707 −0.500138 −0.250069 0.968228i \(-0.580453\pi\)
−0.250069 + 0.968228i \(0.580453\pi\)
\(684\) −1.06505 −0.0407233
\(685\) 1.16436 0.0444878
\(686\) −19.8673 −0.758537
\(687\) 0.798780 0.0304753
\(688\) 1.00000 0.0381246
\(689\) 20.3091 0.773714
\(690\) 4.65881 0.177358
\(691\) 9.37181 0.356520 0.178260 0.983983i \(-0.442953\pi\)
0.178260 + 0.983983i \(0.442953\pi\)
\(692\) 4.67961 0.177892
\(693\) −5.79943 −0.220302
\(694\) 28.5607 1.08415
\(695\) 0.620186 0.0235250
\(696\) 1.33491 0.0505997
\(697\) 14.1517 0.536034
\(698\) −21.1705 −0.801314
\(699\) 9.58637 0.362590
\(700\) 2.37023 0.0895862
\(701\) 14.2696 0.538955 0.269478 0.963007i \(-0.413149\pi\)
0.269478 + 0.963007i \(0.413149\pi\)
\(702\) −25.8949 −0.977339
\(703\) 1.07397 0.0405057
\(704\) 1.00000 0.0376889
\(705\) 10.0104 0.377015
\(706\) −3.04772 −0.114702
\(707\) −29.9161 −1.12511
\(708\) −2.46911 −0.0927949
\(709\) −19.7298 −0.740968 −0.370484 0.928839i \(-0.620808\pi\)
−0.370484 + 0.928839i \(0.620808\pi\)
\(710\) −15.7728 −0.591943
\(711\) −26.7968 −1.00496
\(712\) 3.81948 0.143141
\(713\) −50.2991 −1.88372
\(714\) −7.19253 −0.269174
\(715\) 6.39183 0.239041
\(716\) −16.3112 −0.609579
\(717\) −17.7192 −0.661736
\(718\) −7.77059 −0.289996
\(719\) −1.52100 −0.0567236 −0.0283618 0.999598i \(-0.509029\pi\)
−0.0283618 + 0.999598i \(0.509029\pi\)
\(720\) 2.44678 0.0911861
\(721\) 16.6412 0.619751
\(722\) −18.8105 −0.700055
\(723\) 17.6887 0.657850
\(724\) −16.2790 −0.605003
\(725\) −1.79475 −0.0666554
\(726\) −0.743787 −0.0276045
\(727\) 13.8389 0.513258 0.256629 0.966510i \(-0.417388\pi\)
0.256629 + 0.966510i \(0.417388\pi\)
\(728\) −15.1501 −0.561500
\(729\) −1.54762 −0.0573193
\(730\) 11.7977 0.436654
\(731\) 4.07984 0.150898
\(732\) 5.56288 0.205610
\(733\) 13.3314 0.492405 0.246203 0.969218i \(-0.420817\pi\)
0.246203 + 0.969218i \(0.420817\pi\)
\(734\) 25.1694 0.929020
\(735\) −1.02793 −0.0379158
\(736\) 6.26363 0.230880
\(737\) 10.3564 0.381483
\(738\) −8.48712 −0.312415
\(739\) 43.2074 1.58941 0.794704 0.606997i \(-0.207626\pi\)
0.794704 + 0.606997i \(0.207626\pi\)
\(740\) −2.46727 −0.0906987
\(741\) 2.06943 0.0760224
\(742\) −7.53104 −0.276473
\(743\) 12.8432 0.471172 0.235586 0.971854i \(-0.424299\pi\)
0.235586 + 0.971854i \(0.424299\pi\)
\(744\) 5.97287 0.218976
\(745\) −9.96655 −0.365146
\(746\) 9.13802 0.334567
\(747\) −38.1677 −1.39648
\(748\) 4.07984 0.149174
\(749\) −43.1978 −1.57841
\(750\) 0.743787 0.0271593
\(751\) −23.6911 −0.864500 −0.432250 0.901754i \(-0.642280\pi\)
−0.432250 + 0.901754i \(0.642280\pi\)
\(752\) 13.4587 0.490789
\(753\) −21.4578 −0.781967
\(754\) 11.4717 0.417776
\(755\) −17.8260 −0.648755
\(756\) 9.60237 0.349235
\(757\) −26.5599 −0.965337 −0.482668 0.875803i \(-0.660332\pi\)
−0.482668 + 0.875803i \(0.660332\pi\)
\(758\) −21.1229 −0.767218
\(759\) −4.65881 −0.169104
\(760\) −0.435288 −0.0157895
\(761\) 3.38269 0.122623 0.0613113 0.998119i \(-0.480472\pi\)
0.0613113 + 0.998119i \(0.480472\pi\)
\(762\) −3.17349 −0.114963
\(763\) 4.65368 0.168474
\(764\) −0.748643 −0.0270850
\(765\) 9.98247 0.360917
\(766\) −24.4665 −0.884011
\(767\) −21.2186 −0.766161
\(768\) −0.743787 −0.0268391
\(769\) 44.6319 1.60947 0.804735 0.593635i \(-0.202308\pi\)
0.804735 + 0.593635i \(0.202308\pi\)
\(770\) −2.37023 −0.0854171
\(771\) 11.1209 0.400509
\(772\) −3.19938 −0.115148
\(773\) 1.50754 0.0542224 0.0271112 0.999632i \(-0.491369\pi\)
0.0271112 + 0.999632i \(0.491369\pi\)
\(774\) −2.44678 −0.0879477
\(775\) −8.03034 −0.288458
\(776\) 10.5689 0.379401
\(777\) −4.34966 −0.156043
\(778\) 20.4998 0.734953
\(779\) 1.50988 0.0540970
\(780\) −4.75416 −0.170226
\(781\) 15.7728 0.564395
\(782\) 25.5546 0.913831
\(783\) −7.27097 −0.259843
\(784\) −1.38202 −0.0493580
\(785\) 0.927021 0.0330868
\(786\) −12.2611 −0.437337
\(787\) 7.66602 0.273264 0.136632 0.990622i \(-0.456372\pi\)
0.136632 + 0.990622i \(0.456372\pi\)
\(788\) 16.7313 0.596028
\(789\) 1.46592 0.0521881
\(790\) −10.9519 −0.389650
\(791\) 6.09187 0.216602
\(792\) −2.44678 −0.0869426
\(793\) 47.8053 1.69762
\(794\) 6.08973 0.216116
\(795\) −2.36327 −0.0838166
\(796\) 25.8675 0.916849
\(797\) −31.2532 −1.10704 −0.553522 0.832834i \(-0.686717\pi\)
−0.553522 + 0.832834i \(0.686717\pi\)
\(798\) −0.767388 −0.0271652
\(799\) 54.9094 1.94256
\(800\) 1.00000 0.0353553
\(801\) −9.34543 −0.330205
\(802\) 10.6349 0.375530
\(803\) −11.7977 −0.416334
\(804\) −7.70296 −0.271662
\(805\) −14.8462 −0.523261
\(806\) 51.3286 1.80797
\(807\) −0.962278 −0.0338738
\(808\) −12.6216 −0.444026
\(809\) 38.1785 1.34228 0.671142 0.741328i \(-0.265804\pi\)
0.671142 + 0.741328i \(0.265804\pi\)
\(810\) −4.32708 −0.152038
\(811\) 1.52266 0.0534677 0.0267338 0.999643i \(-0.491489\pi\)
0.0267338 + 0.999643i \(0.491489\pi\)
\(812\) −4.25397 −0.149285
\(813\) 0.452725 0.0158778
\(814\) 2.46727 0.0864779
\(815\) 3.18442 0.111545
\(816\) −3.03453 −0.106230
\(817\) 0.435288 0.0152288
\(818\) −22.1299 −0.773753
\(819\) 37.0690 1.29529
\(820\) −3.46869 −0.121132
\(821\) −49.8391 −1.73940 −0.869698 0.493584i \(-0.835686\pi\)
−0.869698 + 0.493584i \(0.835686\pi\)
\(822\) 0.866035 0.0302064
\(823\) −11.7603 −0.409937 −0.204968 0.978769i \(-0.565709\pi\)
−0.204968 + 0.978769i \(0.565709\pi\)
\(824\) 7.02093 0.244586
\(825\) −0.743787 −0.0258953
\(826\) 7.86832 0.273774
\(827\) −21.3694 −0.743087 −0.371544 0.928416i \(-0.621171\pi\)
−0.371544 + 0.928416i \(0.621171\pi\)
\(828\) −15.3257 −0.532606
\(829\) −1.52148 −0.0528431 −0.0264215 0.999651i \(-0.508411\pi\)
−0.0264215 + 0.999651i \(0.508411\pi\)
\(830\) −15.5992 −0.541455
\(831\) −18.7755 −0.651316
\(832\) −6.39183 −0.221597
\(833\) −5.63843 −0.195360
\(834\) 0.461286 0.0159730
\(835\) 23.9380 0.828408
\(836\) 0.435288 0.0150547
\(837\) −32.5329 −1.12450
\(838\) −6.59799 −0.227924
\(839\) 32.3221 1.11588 0.557941 0.829880i \(-0.311591\pi\)
0.557941 + 0.829880i \(0.311591\pi\)
\(840\) 1.76294 0.0608274
\(841\) −25.7789 −0.888927
\(842\) 34.6188 1.19304
\(843\) 4.01814 0.138392
\(844\) −1.91869 −0.0660442
\(845\) −27.8555 −0.958259
\(846\) −32.9306 −1.13218
\(847\) 2.37023 0.0814420
\(848\) −3.17735 −0.109111
\(849\) −8.70137 −0.298630
\(850\) 4.07984 0.139937
\(851\) 15.4541 0.529759
\(852\) −11.7316 −0.401918
\(853\) 13.0236 0.445919 0.222959 0.974828i \(-0.428428\pi\)
0.222959 + 0.974828i \(0.428428\pi\)
\(854\) −17.7272 −0.606613
\(855\) 1.06505 0.0364241
\(856\) −18.2252 −0.622923
\(857\) −0.260487 −0.00889805 −0.00444903 0.999990i \(-0.501416\pi\)
−0.00444903 + 0.999990i \(0.501416\pi\)
\(858\) 4.75416 0.162304
\(859\) 26.5239 0.904985 0.452493 0.891768i \(-0.350535\pi\)
0.452493 + 0.891768i \(0.350535\pi\)
\(860\) −1.00000 −0.0340997
\(861\) −6.11511 −0.208402
\(862\) −0.278037 −0.00946999
\(863\) 48.7179 1.65838 0.829188 0.558969i \(-0.188803\pi\)
0.829188 + 0.558969i \(0.188803\pi\)
\(864\) 4.05125 0.137826
\(865\) −4.67961 −0.159111
\(866\) 18.8648 0.641051
\(867\) 0.263980 0.00896524
\(868\) −19.0337 −0.646047
\(869\) 10.9519 0.371517
\(870\) −1.33491 −0.0452578
\(871\) −66.1964 −2.24298
\(872\) 1.96339 0.0664888
\(873\) −25.8598 −0.875221
\(874\) 2.72648 0.0922246
\(875\) −2.37023 −0.0801283
\(876\) 8.77501 0.296480
\(877\) −24.8095 −0.837757 −0.418878 0.908042i \(-0.637577\pi\)
−0.418878 + 0.908042i \(0.637577\pi\)
\(878\) 32.4407 1.09482
\(879\) 8.90523 0.300366
\(880\) −1.00000 −0.0337100
\(881\) 36.9709 1.24558 0.622791 0.782389i \(-0.285999\pi\)
0.622791 + 0.782389i \(0.285999\pi\)
\(882\) 3.38151 0.113861
\(883\) −9.31541 −0.313488 −0.156744 0.987639i \(-0.550100\pi\)
−0.156744 + 0.987639i \(0.550100\pi\)
\(884\) −26.0777 −0.877086
\(885\) 2.46911 0.0829983
\(886\) −13.2400 −0.444805
\(887\) −1.50628 −0.0505761 −0.0252880 0.999680i \(-0.508050\pi\)
−0.0252880 + 0.999680i \(0.508050\pi\)
\(888\) −1.83513 −0.0615828
\(889\) 10.1130 0.339178
\(890\) −3.81948 −0.128029
\(891\) 4.32708 0.144963
\(892\) 6.34358 0.212399
\(893\) 5.85842 0.196045
\(894\) −7.41299 −0.247928
\(895\) 16.3112 0.545224
\(896\) 2.37023 0.0791837
\(897\) 29.7783 0.994269
\(898\) −21.9325 −0.731898
\(899\) 14.4125 0.480683
\(900\) −2.44678 −0.0815594
\(901\) −12.9631 −0.431863
\(902\) 3.46869 0.115495
\(903\) −1.76294 −0.0586671
\(904\) 2.57016 0.0854824
\(905\) 16.2790 0.541131
\(906\) −13.2588 −0.440493
\(907\) −46.3625 −1.53944 −0.769721 0.638381i \(-0.779604\pi\)
−0.769721 + 0.638381i \(0.779604\pi\)
\(908\) 6.30747 0.209321
\(909\) 30.8823 1.02430
\(910\) 15.1501 0.502221
\(911\) 25.6279 0.849091 0.424545 0.905407i \(-0.360434\pi\)
0.424545 + 0.905407i \(0.360434\pi\)
\(912\) −0.323761 −0.0107208
\(913\) 15.5992 0.516257
\(914\) 5.29284 0.175072
\(915\) −5.56288 −0.183903
\(916\) −1.07394 −0.0354838
\(917\) 39.0723 1.29028
\(918\) 16.5284 0.545519
\(919\) 37.5643 1.23913 0.619565 0.784945i \(-0.287309\pi\)
0.619565 + 0.784945i \(0.287309\pi\)
\(920\) −6.26363 −0.206506
\(921\) 1.95537 0.0644317
\(922\) −26.5996 −0.876012
\(923\) −100.817 −3.31844
\(924\) −1.76294 −0.0579966
\(925\) 2.46727 0.0811234
\(926\) −4.36551 −0.143460
\(927\) −17.1787 −0.564222
\(928\) −1.79475 −0.0589156
\(929\) −21.5879 −0.708277 −0.354138 0.935193i \(-0.615226\pi\)
−0.354138 + 0.935193i \(0.615226\pi\)
\(930\) −5.97287 −0.195858
\(931\) −0.601578 −0.0197159
\(932\) −12.8886 −0.422180
\(933\) −23.2406 −0.760863
\(934\) −6.47548 −0.211884
\(935\) −4.07984 −0.133425
\(936\) 15.6394 0.511190
\(937\) 6.58836 0.215232 0.107616 0.994193i \(-0.465678\pi\)
0.107616 + 0.994193i \(0.465678\pi\)
\(938\) 24.5470 0.801489
\(939\) −6.35218 −0.207295
\(940\) −13.4587 −0.438975
\(941\) 57.0170 1.85870 0.929350 0.369200i \(-0.120368\pi\)
0.929350 + 0.369200i \(0.120368\pi\)
\(942\) 0.689506 0.0224653
\(943\) 21.7266 0.707515
\(944\) 3.31965 0.108045
\(945\) −9.60237 −0.312365
\(946\) 1.00000 0.0325128
\(947\) 14.9046 0.484333 0.242166 0.970235i \(-0.422142\pi\)
0.242166 + 0.970235i \(0.422142\pi\)
\(948\) −8.14586 −0.264565
\(949\) 75.4092 2.44789
\(950\) 0.435288 0.0141226
\(951\) 2.23342 0.0724235
\(952\) 9.67015 0.313411
\(953\) 14.1245 0.457539 0.228769 0.973481i \(-0.426530\pi\)
0.228769 + 0.973481i \(0.426530\pi\)
\(954\) 7.77428 0.251701
\(955\) 0.748643 0.0242255
\(956\) 23.8230 0.770490
\(957\) 1.33491 0.0431516
\(958\) 6.30021 0.203551
\(959\) −2.75979 −0.0891184
\(960\) 0.743787 0.0240056
\(961\) 33.4864 1.08021
\(962\) −15.7704 −0.508458
\(963\) 44.5930 1.43699
\(964\) −23.7819 −0.765965
\(965\) 3.19938 0.102992
\(966\) −11.0424 −0.355284
\(967\) −31.1000 −1.00011 −0.500054 0.865994i \(-0.666687\pi\)
−0.500054 + 0.865994i \(0.666687\pi\)
\(968\) 1.00000 0.0321412
\(969\) −1.32089 −0.0424332
\(970\) −10.5689 −0.339347
\(971\) 31.7306 1.01828 0.509142 0.860683i \(-0.329963\pi\)
0.509142 + 0.860683i \(0.329963\pi\)
\(972\) −15.3722 −0.493062
\(973\) −1.46998 −0.0471254
\(974\) 6.41963 0.205698
\(975\) 4.75416 0.152255
\(976\) −7.47912 −0.239401
\(977\) −11.4581 −0.366578 −0.183289 0.983059i \(-0.558674\pi\)
−0.183289 + 0.983059i \(0.558674\pi\)
\(978\) 2.36853 0.0757372
\(979\) 3.81948 0.122071
\(980\) 1.38202 0.0441471
\(981\) −4.80398 −0.153379
\(982\) −18.5957 −0.593414
\(983\) −20.9511 −0.668236 −0.334118 0.942531i \(-0.608438\pi\)
−0.334118 + 0.942531i \(0.608438\pi\)
\(984\) −2.57997 −0.0822463
\(985\) −16.7313 −0.533104
\(986\) −7.32229 −0.233189
\(987\) −23.7270 −0.755238
\(988\) −2.78229 −0.0885163
\(989\) 6.26363 0.199172
\(990\) 2.44678 0.0777638
\(991\) −31.1769 −0.990368 −0.495184 0.868788i \(-0.664899\pi\)
−0.495184 + 0.868788i \(0.664899\pi\)
\(992\) −8.03034 −0.254964
\(993\) −12.8456 −0.407642
\(994\) 37.3851 1.18578
\(995\) −25.8675 −0.820054
\(996\) −11.6025 −0.367638
\(997\) −32.3131 −1.02337 −0.511684 0.859174i \(-0.670978\pi\)
−0.511684 + 0.859174i \(0.670978\pi\)
\(998\) 19.8768 0.629190
\(999\) 9.99553 0.316244
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.bf.1.6 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bf.1.6 13 1.1 even 1 trivial