Properties

Label 4730.2.a.be.1.1
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 12
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.03435\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.03435 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.03435 q^{6} -3.44511 q^{7} +1.00000 q^{8} +6.20730 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.03435 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.03435 q^{6} -3.44511 q^{7} +1.00000 q^{8} +6.20730 q^{9} +1.00000 q^{10} -1.00000 q^{11} -3.03435 q^{12} +3.01153 q^{13} -3.44511 q^{14} -3.03435 q^{15} +1.00000 q^{16} +8.05622 q^{17} +6.20730 q^{18} -1.97164 q^{19} +1.00000 q^{20} +10.4537 q^{21} -1.00000 q^{22} -1.01153 q^{23} -3.03435 q^{24} +1.00000 q^{25} +3.01153 q^{26} -9.73209 q^{27} -3.44511 q^{28} -7.47434 q^{29} -3.03435 q^{30} +3.58845 q^{31} +1.00000 q^{32} +3.03435 q^{33} +8.05622 q^{34} -3.44511 q^{35} +6.20730 q^{36} +0.814968 q^{37} -1.97164 q^{38} -9.13803 q^{39} +1.00000 q^{40} -8.79033 q^{41} +10.4537 q^{42} +1.00000 q^{43} -1.00000 q^{44} +6.20730 q^{45} -1.01153 q^{46} -2.28907 q^{47} -3.03435 q^{48} +4.86875 q^{49} +1.00000 q^{50} -24.4454 q^{51} +3.01153 q^{52} -4.19135 q^{53} -9.73209 q^{54} -1.00000 q^{55} -3.44511 q^{56} +5.98266 q^{57} -7.47434 q^{58} -0.747496 q^{59} -3.03435 q^{60} -0.594147 q^{61} +3.58845 q^{62} -21.3848 q^{63} +1.00000 q^{64} +3.01153 q^{65} +3.03435 q^{66} +3.95796 q^{67} +8.05622 q^{68} +3.06933 q^{69} -3.44511 q^{70} -5.26792 q^{71} +6.20730 q^{72} +6.70688 q^{73} +0.814968 q^{74} -3.03435 q^{75} -1.97164 q^{76} +3.44511 q^{77} -9.13803 q^{78} +7.02527 q^{79} +1.00000 q^{80} +10.9087 q^{81} -8.79033 q^{82} +12.1548 q^{83} +10.4537 q^{84} +8.05622 q^{85} +1.00000 q^{86} +22.6798 q^{87} -1.00000 q^{88} +11.2814 q^{89} +6.20730 q^{90} -10.3750 q^{91} -1.01153 q^{92} -10.8886 q^{93} -2.28907 q^{94} -1.97164 q^{95} -3.03435 q^{96} -13.1215 q^{97} +4.86875 q^{98} -6.20730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 12q^{2} + 3q^{3} + 12q^{4} + 12q^{5} + 3q^{6} + 8q^{7} + 12q^{8} + 25q^{9} + O(q^{10}) \) \( 12q + 12q^{2} + 3q^{3} + 12q^{4} + 12q^{5} + 3q^{6} + 8q^{7} + 12q^{8} + 25q^{9} + 12q^{10} - 12q^{11} + 3q^{12} + 16q^{13} + 8q^{14} + 3q^{15} + 12q^{16} + 18q^{17} + 25q^{18} - 4q^{19} + 12q^{20} + 4q^{21} - 12q^{22} + 8q^{23} + 3q^{24} + 12q^{25} + 16q^{26} + 6q^{27} + 8q^{28} + 20q^{29} + 3q^{30} + 5q^{31} + 12q^{32} - 3q^{33} + 18q^{34} + 8q^{35} + 25q^{36} + 19q^{37} - 4q^{38} + 6q^{39} + 12q^{40} + 16q^{41} + 4q^{42} + 12q^{43} - 12q^{44} + 25q^{45} + 8q^{46} - q^{47} + 3q^{48} + 52q^{49} + 12q^{50} + q^{51} + 16q^{52} + 11q^{53} + 6q^{54} - 12q^{55} + 8q^{56} + 9q^{57} + 20q^{58} - 11q^{59} + 3q^{60} + 18q^{61} + 5q^{62} + 15q^{63} + 12q^{64} + 16q^{65} - 3q^{66} - 10q^{67} + 18q^{68} + 8q^{70} - 2q^{71} + 25q^{72} + 29q^{73} + 19q^{74} + 3q^{75} - 4q^{76} - 8q^{77} + 6q^{78} + 2q^{79} + 12q^{80} - 8q^{81} + 16q^{82} + 26q^{83} + 4q^{84} + 18q^{85} + 12q^{86} - 4q^{87} - 12q^{88} + 41q^{89} + 25q^{90} - 4q^{91} + 8q^{92} + 5q^{93} - q^{94} - 4q^{95} + 3q^{96} - 7q^{97} + 52q^{98} - 25q^{99} + O(q^{100}) \)

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
\(3\) −3.03435 −1.75188 −0.875942 0.482416i \(-0.839760\pi\)
−0.875942 + 0.482416i \(0.839760\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −3.03435 −1.23877
\(7\) −3.44511 −1.30213 −0.651064 0.759023i \(-0.725677\pi\)
−0.651064 + 0.759023i \(0.725677\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.20730 2.06910
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) −3.03435 −0.875942
\(13\) 3.01153 0.835247 0.417623 0.908620i \(-0.362863\pi\)
0.417623 + 0.908620i \(0.362863\pi\)
\(14\) −3.44511 −0.920743
\(15\) −3.03435 −0.783467
\(16\) 1.00000 0.250000
\(17\) 8.05622 1.95392 0.976961 0.213420i \(-0.0684602\pi\)
0.976961 + 0.213420i \(0.0684602\pi\)
\(18\) 6.20730 1.46308
\(19\) −1.97164 −0.452326 −0.226163 0.974090i \(-0.572618\pi\)
−0.226163 + 0.974090i \(0.572618\pi\)
\(20\) 1.00000 0.223607
\(21\) 10.4537 2.28118
\(22\) −1.00000 −0.213201
\(23\) −1.01153 −0.210918 −0.105459 0.994424i \(-0.533631\pi\)
−0.105459 + 0.994424i \(0.533631\pi\)
\(24\) −3.03435 −0.619385
\(25\) 1.00000 0.200000
\(26\) 3.01153 0.590609
\(27\) −9.73209 −1.87294
\(28\) −3.44511 −0.651064
\(29\) −7.47434 −1.38795 −0.693975 0.719999i \(-0.744142\pi\)
−0.693975 + 0.719999i \(0.744142\pi\)
\(30\) −3.03435 −0.553995
\(31\) 3.58845 0.644504 0.322252 0.946654i \(-0.395560\pi\)
0.322252 + 0.946654i \(0.395560\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.03435 0.528213
\(34\) 8.05622 1.38163
\(35\) −3.44511 −0.582329
\(36\) 6.20730 1.03455
\(37\) 0.814968 0.133980 0.0669900 0.997754i \(-0.478660\pi\)
0.0669900 + 0.997754i \(0.478660\pi\)
\(38\) −1.97164 −0.319843
\(39\) −9.13803 −1.46326
\(40\) 1.00000 0.158114
\(41\) −8.79033 −1.37282 −0.686410 0.727215i \(-0.740814\pi\)
−0.686410 + 0.727215i \(0.740814\pi\)
\(42\) 10.4537 1.61304
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) 6.20730 0.925330
\(46\) −1.01153 −0.149141
\(47\) −2.28907 −0.333895 −0.166948 0.985966i \(-0.553391\pi\)
−0.166948 + 0.985966i \(0.553391\pi\)
\(48\) −3.03435 −0.437971
\(49\) 4.86875 0.695536
\(50\) 1.00000 0.141421
\(51\) −24.4454 −3.42305
\(52\) 3.01153 0.417623
\(53\) −4.19135 −0.575726 −0.287863 0.957672i \(-0.592945\pi\)
−0.287863 + 0.957672i \(0.592945\pi\)
\(54\) −9.73209 −1.32437
\(55\) −1.00000 −0.134840
\(56\) −3.44511 −0.460372
\(57\) 5.98266 0.792422
\(58\) −7.47434 −0.981429
\(59\) −0.747496 −0.0973156 −0.0486578 0.998816i \(-0.515494\pi\)
−0.0486578 + 0.998816i \(0.515494\pi\)
\(60\) −3.03435 −0.391733
\(61\) −0.594147 −0.0760727 −0.0380363 0.999276i \(-0.512110\pi\)
−0.0380363 + 0.999276i \(0.512110\pi\)
\(62\) 3.58845 0.455733
\(63\) −21.3848 −2.69423
\(64\) 1.00000 0.125000
\(65\) 3.01153 0.373534
\(66\) 3.03435 0.373503
\(67\) 3.95796 0.483541 0.241771 0.970333i \(-0.422272\pi\)
0.241771 + 0.970333i \(0.422272\pi\)
\(68\) 8.05622 0.976961
\(69\) 3.06933 0.369503
\(70\) −3.44511 −0.411769
\(71\) −5.26792 −0.625187 −0.312594 0.949887i \(-0.601198\pi\)
−0.312594 + 0.949887i \(0.601198\pi\)
\(72\) 6.20730 0.731538
\(73\) 6.70688 0.784981 0.392491 0.919756i \(-0.371614\pi\)
0.392491 + 0.919756i \(0.371614\pi\)
\(74\) 0.814968 0.0947381
\(75\) −3.03435 −0.350377
\(76\) −1.97164 −0.226163
\(77\) 3.44511 0.392606
\(78\) −9.13803 −1.03468
\(79\) 7.02527 0.790404 0.395202 0.918594i \(-0.370675\pi\)
0.395202 + 0.918594i \(0.370675\pi\)
\(80\) 1.00000 0.111803
\(81\) 10.9087 1.21208
\(82\) −8.79033 −0.970730
\(83\) 12.1548 1.33416 0.667079 0.744987i \(-0.267544\pi\)
0.667079 + 0.744987i \(0.267544\pi\)
\(84\) 10.4537 1.14059
\(85\) 8.05622 0.873820
\(86\) 1.00000 0.107833
\(87\) 22.6798 2.43153
\(88\) −1.00000 −0.106600
\(89\) 11.2814 1.19583 0.597914 0.801560i \(-0.295996\pi\)
0.597914 + 0.801560i \(0.295996\pi\)
\(90\) 6.20730 0.654307
\(91\) −10.3750 −1.08760
\(92\) −1.01153 −0.105459
\(93\) −10.8886 −1.12910
\(94\) −2.28907 −0.236099
\(95\) −1.97164 −0.202286
\(96\) −3.03435 −0.309692
\(97\) −13.1215 −1.33229 −0.666143 0.745824i \(-0.732056\pi\)
−0.666143 + 0.745824i \(0.732056\pi\)
\(98\) 4.86875 0.491818
\(99\) −6.20730 −0.623857
\(100\) 1.00000 0.100000
\(101\) 2.38586 0.237402 0.118701 0.992930i \(-0.462127\pi\)
0.118701 + 0.992930i \(0.462127\pi\)
\(102\) −24.4454 −2.42046
\(103\) 8.69704 0.856945 0.428472 0.903555i \(-0.359052\pi\)
0.428472 + 0.903555i \(0.359052\pi\)
\(104\) 3.01153 0.295304
\(105\) 10.4537 1.02017
\(106\) −4.19135 −0.407100
\(107\) −0.158326 −0.0153060 −0.00765299 0.999971i \(-0.502436\pi\)
−0.00765299 + 0.999971i \(0.502436\pi\)
\(108\) −9.73209 −0.936471
\(109\) 17.8523 1.70994 0.854970 0.518678i \(-0.173575\pi\)
0.854970 + 0.518678i \(0.173575\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −2.47290 −0.234717
\(112\) −3.44511 −0.325532
\(113\) 14.1561 1.33169 0.665847 0.746089i \(-0.268070\pi\)
0.665847 + 0.746089i \(0.268070\pi\)
\(114\) 5.98266 0.560327
\(115\) −1.01153 −0.0943252
\(116\) −7.47434 −0.693975
\(117\) 18.6935 1.72821
\(118\) −0.747496 −0.0688125
\(119\) −27.7545 −2.54425
\(120\) −3.03435 −0.276997
\(121\) 1.00000 0.0909091
\(122\) −0.594147 −0.0537915
\(123\) 26.6730 2.40502
\(124\) 3.58845 0.322252
\(125\) 1.00000 0.0894427
\(126\) −21.3848 −1.90511
\(127\) 5.67047 0.503173 0.251586 0.967835i \(-0.419048\pi\)
0.251586 + 0.967835i \(0.419048\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.03435 −0.267160
\(130\) 3.01153 0.264128
\(131\) −7.81393 −0.682707 −0.341353 0.939935i \(-0.610885\pi\)
−0.341353 + 0.939935i \(0.610885\pi\)
\(132\) 3.03435 0.264107
\(133\) 6.79251 0.588986
\(134\) 3.95796 0.341915
\(135\) −9.73209 −0.837605
\(136\) 8.05622 0.690815
\(137\) 11.7760 1.00609 0.503045 0.864260i \(-0.332213\pi\)
0.503045 + 0.864260i \(0.332213\pi\)
\(138\) 3.06933 0.261278
\(139\) −14.3383 −1.21616 −0.608078 0.793877i \(-0.708059\pi\)
−0.608078 + 0.793877i \(0.708059\pi\)
\(140\) −3.44511 −0.291165
\(141\) 6.94585 0.584946
\(142\) −5.26792 −0.442074
\(143\) −3.01153 −0.251836
\(144\) 6.20730 0.517275
\(145\) −7.47434 −0.620710
\(146\) 6.70688 0.555066
\(147\) −14.7735 −1.21850
\(148\) 0.814968 0.0669900
\(149\) −8.21509 −0.673006 −0.336503 0.941682i \(-0.609244\pi\)
−0.336503 + 0.941682i \(0.609244\pi\)
\(150\) −3.03435 −0.247754
\(151\) 9.95698 0.810288 0.405144 0.914253i \(-0.367221\pi\)
0.405144 + 0.914253i \(0.367221\pi\)
\(152\) −1.97164 −0.159921
\(153\) 50.0074 4.04286
\(154\) 3.44511 0.277615
\(155\) 3.58845 0.288231
\(156\) −9.13803 −0.731628
\(157\) 1.44307 0.115169 0.0575846 0.998341i \(-0.481660\pi\)
0.0575846 + 0.998341i \(0.481660\pi\)
\(158\) 7.02527 0.558900
\(159\) 12.7180 1.00861
\(160\) 1.00000 0.0790569
\(161\) 3.48481 0.274642
\(162\) 10.9087 0.857068
\(163\) −3.41087 −0.267160 −0.133580 0.991038i \(-0.542647\pi\)
−0.133580 + 0.991038i \(0.542647\pi\)
\(164\) −8.79033 −0.686410
\(165\) 3.03435 0.236224
\(166\) 12.1548 0.943392
\(167\) 1.97518 0.152844 0.0764222 0.997076i \(-0.475650\pi\)
0.0764222 + 0.997076i \(0.475650\pi\)
\(168\) 10.4537 0.806518
\(169\) −3.93071 −0.302363
\(170\) 8.05622 0.617884
\(171\) −12.2386 −0.935907
\(172\) 1.00000 0.0762493
\(173\) 9.06789 0.689419 0.344709 0.938709i \(-0.387977\pi\)
0.344709 + 0.938709i \(0.387977\pi\)
\(174\) 22.6798 1.71935
\(175\) −3.44511 −0.260425
\(176\) −1.00000 −0.0753778
\(177\) 2.26817 0.170486
\(178\) 11.2814 0.845579
\(179\) 4.50260 0.336540 0.168270 0.985741i \(-0.446182\pi\)
0.168270 + 0.985741i \(0.446182\pi\)
\(180\) 6.20730 0.462665
\(181\) 21.3984 1.59053 0.795264 0.606263i \(-0.207332\pi\)
0.795264 + 0.606263i \(0.207332\pi\)
\(182\) −10.3750 −0.769048
\(183\) 1.80285 0.133271
\(184\) −1.01153 −0.0745707
\(185\) 0.814968 0.0599176
\(186\) −10.8886 −0.798392
\(187\) −8.05622 −0.589129
\(188\) −2.28907 −0.166948
\(189\) 33.5281 2.43881
\(190\) −1.97164 −0.143038
\(191\) 23.5905 1.70695 0.853474 0.521136i \(-0.174492\pi\)
0.853474 + 0.521136i \(0.174492\pi\)
\(192\) −3.03435 −0.218986
\(193\) 18.2524 1.31383 0.656917 0.753963i \(-0.271860\pi\)
0.656917 + 0.753963i \(0.271860\pi\)
\(194\) −13.1215 −0.942068
\(195\) −9.13803 −0.654388
\(196\) 4.86875 0.347768
\(197\) −16.3169 −1.16253 −0.581265 0.813714i \(-0.697442\pi\)
−0.581265 + 0.813714i \(0.697442\pi\)
\(198\) −6.20730 −0.441134
\(199\) 1.88014 0.133279 0.0666397 0.997777i \(-0.478772\pi\)
0.0666397 + 0.997777i \(0.478772\pi\)
\(200\) 1.00000 0.0707107
\(201\) −12.0098 −0.847109
\(202\) 2.38586 0.167868
\(203\) 25.7499 1.80729
\(204\) −24.4454 −1.71152
\(205\) −8.79033 −0.613944
\(206\) 8.69704 0.605951
\(207\) −6.27885 −0.436410
\(208\) 3.01153 0.208812
\(209\) 1.97164 0.136381
\(210\) 10.4537 0.721372
\(211\) −5.48675 −0.377724 −0.188862 0.982004i \(-0.560480\pi\)
−0.188862 + 0.982004i \(0.560480\pi\)
\(212\) −4.19135 −0.287863
\(213\) 15.9847 1.09526
\(214\) −0.158326 −0.0108230
\(215\) 1.00000 0.0681994
\(216\) −9.73209 −0.662185
\(217\) −12.3626 −0.839227
\(218\) 17.8523 1.20911
\(219\) −20.3511 −1.37520
\(220\) −1.00000 −0.0674200
\(221\) 24.2615 1.63201
\(222\) −2.47290 −0.165970
\(223\) −5.95482 −0.398764 −0.199382 0.979922i \(-0.563894\pi\)
−0.199382 + 0.979922i \(0.563894\pi\)
\(224\) −3.44511 −0.230186
\(225\) 6.20730 0.413820
\(226\) 14.1561 0.941649
\(227\) 16.6824 1.10725 0.553623 0.832767i \(-0.313245\pi\)
0.553623 + 0.832767i \(0.313245\pi\)
\(228\) 5.98266 0.396211
\(229\) −20.8066 −1.37494 −0.687469 0.726214i \(-0.741278\pi\)
−0.687469 + 0.726214i \(0.741278\pi\)
\(230\) −1.01153 −0.0666980
\(231\) −10.4537 −0.687801
\(232\) −7.47434 −0.490715
\(233\) 6.22241 0.407643 0.203822 0.979008i \(-0.434664\pi\)
0.203822 + 0.979008i \(0.434664\pi\)
\(234\) 18.6935 1.22203
\(235\) −2.28907 −0.149322
\(236\) −0.747496 −0.0486578
\(237\) −21.3171 −1.38470
\(238\) −27.7545 −1.79906
\(239\) 1.42446 0.0921408 0.0460704 0.998938i \(-0.485330\pi\)
0.0460704 + 0.998938i \(0.485330\pi\)
\(240\) −3.03435 −0.195867
\(241\) −13.8015 −0.889034 −0.444517 0.895770i \(-0.646625\pi\)
−0.444517 + 0.895770i \(0.646625\pi\)
\(242\) 1.00000 0.0642824
\(243\) −3.90458 −0.250479
\(244\) −0.594147 −0.0380363
\(245\) 4.86875 0.311053
\(246\) 26.6730 1.70061
\(247\) −5.93765 −0.377804
\(248\) 3.58845 0.227867
\(249\) −36.8818 −2.33729
\(250\) 1.00000 0.0632456
\(251\) 11.7815 0.743642 0.371821 0.928305i \(-0.378734\pi\)
0.371821 + 0.928305i \(0.378734\pi\)
\(252\) −21.3848 −1.34712
\(253\) 1.01153 0.0635941
\(254\) 5.67047 0.355797
\(255\) −24.4454 −1.53083
\(256\) 1.00000 0.0625000
\(257\) 2.93713 0.183213 0.0916066 0.995795i \(-0.470800\pi\)
0.0916066 + 0.995795i \(0.470800\pi\)
\(258\) −3.03435 −0.188911
\(259\) −2.80765 −0.174459
\(260\) 3.01153 0.186767
\(261\) −46.3955 −2.87181
\(262\) −7.81393 −0.482746
\(263\) 16.1661 0.996842 0.498421 0.866935i \(-0.333913\pi\)
0.498421 + 0.866935i \(0.333913\pi\)
\(264\) 3.03435 0.186752
\(265\) −4.19135 −0.257473
\(266\) 6.79251 0.416476
\(267\) −34.2318 −2.09495
\(268\) 3.95796 0.241771
\(269\) −7.51028 −0.457910 −0.228955 0.973437i \(-0.573531\pi\)
−0.228955 + 0.973437i \(0.573531\pi\)
\(270\) −9.73209 −0.592276
\(271\) −5.81531 −0.353255 −0.176628 0.984278i \(-0.556519\pi\)
−0.176628 + 0.984278i \(0.556519\pi\)
\(272\) 8.05622 0.488480
\(273\) 31.4815 1.90535
\(274\) 11.7760 0.711412
\(275\) −1.00000 −0.0603023
\(276\) 3.06933 0.184752
\(277\) −14.0947 −0.846868 −0.423434 0.905927i \(-0.639175\pi\)
−0.423434 + 0.905927i \(0.639175\pi\)
\(278\) −14.3383 −0.859952
\(279\) 22.2746 1.33354
\(280\) −3.44511 −0.205884
\(281\) 28.9769 1.72862 0.864310 0.502960i \(-0.167756\pi\)
0.864310 + 0.502960i \(0.167756\pi\)
\(282\) 6.94585 0.413619
\(283\) −5.85843 −0.348248 −0.174124 0.984724i \(-0.555709\pi\)
−0.174124 + 0.984724i \(0.555709\pi\)
\(284\) −5.26792 −0.312594
\(285\) 5.98266 0.354382
\(286\) −3.01153 −0.178075
\(287\) 30.2836 1.78759
\(288\) 6.20730 0.365769
\(289\) 47.9027 2.81781
\(290\) −7.47434 −0.438908
\(291\) 39.8152 2.33401
\(292\) 6.70688 0.392491
\(293\) 22.6998 1.32614 0.663068 0.748559i \(-0.269254\pi\)
0.663068 + 0.748559i \(0.269254\pi\)
\(294\) −14.7735 −0.861609
\(295\) −0.747496 −0.0435209
\(296\) 0.814968 0.0473690
\(297\) 9.73209 0.564713
\(298\) −8.21509 −0.475887
\(299\) −3.04623 −0.176168
\(300\) −3.03435 −0.175188
\(301\) −3.44511 −0.198573
\(302\) 9.95698 0.572960
\(303\) −7.23954 −0.415901
\(304\) −1.97164 −0.113081
\(305\) −0.594147 −0.0340207
\(306\) 50.0074 2.85873
\(307\) 23.5995 1.34690 0.673448 0.739234i \(-0.264812\pi\)
0.673448 + 0.739234i \(0.264812\pi\)
\(308\) 3.44511 0.196303
\(309\) −26.3899 −1.50127
\(310\) 3.58845 0.203810
\(311\) −33.5297 −1.90130 −0.950649 0.310269i \(-0.899581\pi\)
−0.950649 + 0.310269i \(0.899581\pi\)
\(312\) −9.13803 −0.517339
\(313\) 13.5130 0.763801 0.381901 0.924203i \(-0.375270\pi\)
0.381901 + 0.924203i \(0.375270\pi\)
\(314\) 1.44307 0.0814370
\(315\) −21.3848 −1.20490
\(316\) 7.02527 0.395202
\(317\) 32.4963 1.82518 0.912588 0.408881i \(-0.134081\pi\)
0.912588 + 0.408881i \(0.134081\pi\)
\(318\) 12.7180 0.713192
\(319\) 7.47434 0.418483
\(320\) 1.00000 0.0559017
\(321\) 0.480418 0.0268143
\(322\) 3.48481 0.194201
\(323\) −15.8840 −0.883809
\(324\) 10.9087 0.606039
\(325\) 3.01153 0.167049
\(326\) −3.41087 −0.188911
\(327\) −54.1702 −2.99562
\(328\) −8.79033 −0.485365
\(329\) 7.88608 0.434774
\(330\) 3.03435 0.167036
\(331\) −4.30112 −0.236411 −0.118206 0.992989i \(-0.537714\pi\)
−0.118206 + 0.992989i \(0.537714\pi\)
\(332\) 12.1548 0.667079
\(333\) 5.05875 0.277218
\(334\) 1.97518 0.108077
\(335\) 3.95796 0.216246
\(336\) 10.4537 0.570294
\(337\) −1.53439 −0.0835837 −0.0417919 0.999126i \(-0.513307\pi\)
−0.0417919 + 0.999126i \(0.513307\pi\)
\(338\) −3.93071 −0.213803
\(339\) −42.9546 −2.33297
\(340\) 8.05622 0.436910
\(341\) −3.58845 −0.194325
\(342\) −12.2386 −0.661786
\(343\) 7.34238 0.396451
\(344\) 1.00000 0.0539164
\(345\) 3.06933 0.165247
\(346\) 9.06789 0.487493
\(347\) −11.3937 −0.611645 −0.305823 0.952089i \(-0.598931\pi\)
−0.305823 + 0.952089i \(0.598931\pi\)
\(348\) 22.6798 1.21576
\(349\) 19.2716 1.03159 0.515793 0.856713i \(-0.327497\pi\)
0.515793 + 0.856713i \(0.327497\pi\)
\(350\) −3.44511 −0.184149
\(351\) −29.3084 −1.56437
\(352\) −1.00000 −0.0533002
\(353\) 17.3056 0.921086 0.460543 0.887637i \(-0.347655\pi\)
0.460543 + 0.887637i \(0.347655\pi\)
\(354\) 2.26817 0.120552
\(355\) −5.26792 −0.279592
\(356\) 11.2814 0.597914
\(357\) 84.2171 4.45724
\(358\) 4.50260 0.237970
\(359\) 31.0300 1.63770 0.818850 0.574007i \(-0.194612\pi\)
0.818850 + 0.574007i \(0.194612\pi\)
\(360\) 6.20730 0.327154
\(361\) −15.1126 −0.795402
\(362\) 21.3984 1.12467
\(363\) −3.03435 −0.159262
\(364\) −10.3750 −0.543799
\(365\) 6.70688 0.351054
\(366\) 1.80285 0.0942365
\(367\) 26.2176 1.36855 0.684273 0.729226i \(-0.260119\pi\)
0.684273 + 0.729226i \(0.260119\pi\)
\(368\) −1.01153 −0.0527294
\(369\) −54.5643 −2.84050
\(370\) 0.814968 0.0423682
\(371\) 14.4396 0.749669
\(372\) −10.8886 −0.564549
\(373\) 3.10048 0.160537 0.0802685 0.996773i \(-0.474422\pi\)
0.0802685 + 0.996773i \(0.474422\pi\)
\(374\) −8.05622 −0.416577
\(375\) −3.03435 −0.156693
\(376\) −2.28907 −0.118050
\(377\) −22.5092 −1.15928
\(378\) 33.5281 1.72450
\(379\) 16.3697 0.840855 0.420427 0.907326i \(-0.361880\pi\)
0.420427 + 0.907326i \(0.361880\pi\)
\(380\) −1.97164 −0.101143
\(381\) −17.2062 −0.881501
\(382\) 23.5905 1.20699
\(383\) 1.84411 0.0942298 0.0471149 0.998889i \(-0.484997\pi\)
0.0471149 + 0.998889i \(0.484997\pi\)
\(384\) −3.03435 −0.154846
\(385\) 3.44511 0.175579
\(386\) 18.2524 0.929021
\(387\) 6.20730 0.315535
\(388\) −13.1215 −0.666143
\(389\) −2.69523 −0.136654 −0.0683269 0.997663i \(-0.521766\pi\)
−0.0683269 + 0.997663i \(0.521766\pi\)
\(390\) −9.13803 −0.462722
\(391\) −8.14908 −0.412116
\(392\) 4.86875 0.245909
\(393\) 23.7102 1.19602
\(394\) −16.3169 −0.822033
\(395\) 7.02527 0.353480
\(396\) −6.20730 −0.311929
\(397\) 31.5646 1.58418 0.792092 0.610402i \(-0.208992\pi\)
0.792092 + 0.610402i \(0.208992\pi\)
\(398\) 1.88014 0.0942428
\(399\) −20.6109 −1.03184
\(400\) 1.00000 0.0500000
\(401\) −20.9312 −1.04525 −0.522626 0.852562i \(-0.675048\pi\)
−0.522626 + 0.852562i \(0.675048\pi\)
\(402\) −12.0098 −0.598996
\(403\) 10.8067 0.538320
\(404\) 2.38586 0.118701
\(405\) 10.9087 0.542058
\(406\) 25.7499 1.27795
\(407\) −0.814968 −0.0403965
\(408\) −24.4454 −1.21023
\(409\) −26.4274 −1.30675 −0.653376 0.757034i \(-0.726648\pi\)
−0.653376 + 0.757034i \(0.726648\pi\)
\(410\) −8.79033 −0.434124
\(411\) −35.7325 −1.76255
\(412\) 8.69704 0.428472
\(413\) 2.57520 0.126717
\(414\) −6.27885 −0.308588
\(415\) 12.1548 0.596653
\(416\) 3.01153 0.147652
\(417\) 43.5074 2.13056
\(418\) 1.97164 0.0964361
\(419\) −21.0841 −1.03003 −0.515014 0.857182i \(-0.672213\pi\)
−0.515014 + 0.857182i \(0.672213\pi\)
\(420\) 10.4537 0.510087
\(421\) −30.4110 −1.48214 −0.741070 0.671428i \(-0.765681\pi\)
−0.741070 + 0.671428i \(0.765681\pi\)
\(422\) −5.48675 −0.267091
\(423\) −14.2089 −0.690863
\(424\) −4.19135 −0.203550
\(425\) 8.05622 0.390784
\(426\) 15.9847 0.774463
\(427\) 2.04690 0.0990563
\(428\) −0.158326 −0.00765299
\(429\) 9.13803 0.441188
\(430\) 1.00000 0.0482243
\(431\) 21.1977 1.02106 0.510529 0.859861i \(-0.329450\pi\)
0.510529 + 0.859861i \(0.329450\pi\)
\(432\) −9.73209 −0.468235
\(433\) 25.0369 1.20320 0.601599 0.798798i \(-0.294530\pi\)
0.601599 + 0.798798i \(0.294530\pi\)
\(434\) −12.3626 −0.593423
\(435\) 22.6798 1.08741
\(436\) 17.8523 0.854970
\(437\) 1.99437 0.0954035
\(438\) −20.3511 −0.972411
\(439\) 17.1204 0.817113 0.408557 0.912733i \(-0.366032\pi\)
0.408557 + 0.912733i \(0.366032\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 30.2218 1.43913
\(442\) 24.2615 1.15400
\(443\) −26.7844 −1.27256 −0.636282 0.771457i \(-0.719528\pi\)
−0.636282 + 0.771457i \(0.719528\pi\)
\(444\) −2.47290 −0.117359
\(445\) 11.2814 0.534791
\(446\) −5.95482 −0.281969
\(447\) 24.9275 1.17903
\(448\) −3.44511 −0.162766
\(449\) −37.7530 −1.78167 −0.890837 0.454323i \(-0.849881\pi\)
−0.890837 + 0.454323i \(0.849881\pi\)
\(450\) 6.20730 0.292615
\(451\) 8.79033 0.413921
\(452\) 14.1561 0.665847
\(453\) −30.2130 −1.41953
\(454\) 16.6824 0.782942
\(455\) −10.3750 −0.486389
\(456\) 5.98266 0.280164
\(457\) −35.4827 −1.65981 −0.829905 0.557904i \(-0.811606\pi\)
−0.829905 + 0.557904i \(0.811606\pi\)
\(458\) −20.8066 −0.972228
\(459\) −78.4039 −3.65958
\(460\) −1.01153 −0.0471626
\(461\) −31.8589 −1.48381 −0.741907 0.670502i \(-0.766079\pi\)
−0.741907 + 0.670502i \(0.766079\pi\)
\(462\) −10.4537 −0.486349
\(463\) 25.0415 1.16378 0.581888 0.813269i \(-0.302314\pi\)
0.581888 + 0.813269i \(0.302314\pi\)
\(464\) −7.47434 −0.346988
\(465\) −10.8886 −0.504948
\(466\) 6.22241 0.288247
\(467\) 7.52638 0.348279 0.174140 0.984721i \(-0.444286\pi\)
0.174140 + 0.984721i \(0.444286\pi\)
\(468\) 18.6935 0.864105
\(469\) −13.6356 −0.629632
\(470\) −2.28907 −0.105587
\(471\) −4.37878 −0.201763
\(472\) −0.747496 −0.0344063
\(473\) −1.00000 −0.0459800
\(474\) −21.3171 −0.979129
\(475\) −1.97164 −0.0904651
\(476\) −27.7545 −1.27213
\(477\) −26.0170 −1.19124
\(478\) 1.42446 0.0651534
\(479\) −8.55601 −0.390934 −0.195467 0.980710i \(-0.562622\pi\)
−0.195467 + 0.980710i \(0.562622\pi\)
\(480\) −3.03435 −0.138499
\(481\) 2.45430 0.111906
\(482\) −13.8015 −0.628642
\(483\) −10.5742 −0.481141
\(484\) 1.00000 0.0454545
\(485\) −13.1215 −0.595816
\(486\) −3.90458 −0.177115
\(487\) −9.24248 −0.418817 −0.209408 0.977828i \(-0.567154\pi\)
−0.209408 + 0.977828i \(0.567154\pi\)
\(488\) −0.594147 −0.0268957
\(489\) 10.3498 0.468033
\(490\) 4.86875 0.219948
\(491\) 34.7025 1.56610 0.783050 0.621958i \(-0.213663\pi\)
0.783050 + 0.621958i \(0.213663\pi\)
\(492\) 26.6730 1.20251
\(493\) −60.2150 −2.71195
\(494\) −5.93765 −0.267147
\(495\) −6.20730 −0.278998
\(496\) 3.58845 0.161126
\(497\) 18.1485 0.814074
\(498\) −36.8818 −1.65271
\(499\) 13.6098 0.609259 0.304629 0.952471i \(-0.401467\pi\)
0.304629 + 0.952471i \(0.401467\pi\)
\(500\) 1.00000 0.0447214
\(501\) −5.99341 −0.267766
\(502\) 11.7815 0.525834
\(503\) −10.9154 −0.486691 −0.243346 0.969940i \(-0.578245\pi\)
−0.243346 + 0.969940i \(0.578245\pi\)
\(504\) −21.3848 −0.952555
\(505\) 2.38586 0.106169
\(506\) 1.01153 0.0449678
\(507\) 11.9272 0.529705
\(508\) 5.67047 0.251586
\(509\) −38.3303 −1.69896 −0.849479 0.527622i \(-0.823084\pi\)
−0.849479 + 0.527622i \(0.823084\pi\)
\(510\) −24.4454 −1.08246
\(511\) −23.1059 −1.02215
\(512\) 1.00000 0.0441942
\(513\) 19.1882 0.847180
\(514\) 2.93713 0.129551
\(515\) 8.69704 0.383237
\(516\) −3.03435 −0.133580
\(517\) 2.28907 0.100673
\(518\) −2.80765 −0.123361
\(519\) −27.5152 −1.20778
\(520\) 3.01153 0.132064
\(521\) 21.4920 0.941583 0.470792 0.882244i \(-0.343968\pi\)
0.470792 + 0.882244i \(0.343968\pi\)
\(522\) −46.3955 −2.03068
\(523\) −45.0225 −1.96870 −0.984348 0.176235i \(-0.943608\pi\)
−0.984348 + 0.176235i \(0.943608\pi\)
\(524\) −7.81393 −0.341353
\(525\) 10.4537 0.456236
\(526\) 16.1661 0.704874
\(527\) 28.9093 1.25931
\(528\) 3.03435 0.132053
\(529\) −21.9768 −0.955514
\(530\) −4.19135 −0.182061
\(531\) −4.63993 −0.201356
\(532\) 6.79251 0.294493
\(533\) −26.4723 −1.14664
\(534\) −34.2318 −1.48136
\(535\) −0.158326 −0.00684504
\(536\) 3.95796 0.170958
\(537\) −13.6625 −0.589579
\(538\) −7.51028 −0.323791
\(539\) −4.86875 −0.209712
\(540\) −9.73209 −0.418803
\(541\) 43.5568 1.87265 0.936327 0.351128i \(-0.114202\pi\)
0.936327 + 0.351128i \(0.114202\pi\)
\(542\) −5.81531 −0.249789
\(543\) −64.9302 −2.78642
\(544\) 8.05622 0.345408
\(545\) 17.8523 0.764708
\(546\) 31.4815 1.34728
\(547\) −1.74771 −0.0747267 −0.0373633 0.999302i \(-0.511896\pi\)
−0.0373633 + 0.999302i \(0.511896\pi\)
\(548\) 11.7760 0.503045
\(549\) −3.68805 −0.157402
\(550\) −1.00000 −0.0426401
\(551\) 14.7367 0.627805
\(552\) 3.06933 0.130639
\(553\) −24.2028 −1.02921
\(554\) −14.0947 −0.598826
\(555\) −2.47290 −0.104969
\(556\) −14.3383 −0.608078
\(557\) 27.7103 1.17412 0.587061 0.809542i \(-0.300285\pi\)
0.587061 + 0.809542i \(0.300285\pi\)
\(558\) 22.2746 0.942958
\(559\) 3.01153 0.127374
\(560\) −3.44511 −0.145582
\(561\) 24.4454 1.03209
\(562\) 28.9769 1.22232
\(563\) 31.7218 1.33691 0.668457 0.743751i \(-0.266955\pi\)
0.668457 + 0.743751i \(0.266955\pi\)
\(564\) 6.94585 0.292473
\(565\) 14.1561 0.595551
\(566\) −5.85843 −0.246248
\(567\) −37.5816 −1.57828
\(568\) −5.26792 −0.221037
\(569\) −27.2360 −1.14179 −0.570895 0.821023i \(-0.693404\pi\)
−0.570895 + 0.821023i \(0.693404\pi\)
\(570\) 5.98266 0.250586
\(571\) 32.7621 1.37105 0.685526 0.728048i \(-0.259572\pi\)
0.685526 + 0.728048i \(0.259572\pi\)
\(572\) −3.01153 −0.125918
\(573\) −71.5819 −2.99038
\(574\) 30.2836 1.26401
\(575\) −1.01153 −0.0421835
\(576\) 6.20730 0.258638
\(577\) −13.0091 −0.541576 −0.270788 0.962639i \(-0.587284\pi\)
−0.270788 + 0.962639i \(0.587284\pi\)
\(578\) 47.9027 1.99249
\(579\) −55.3841 −2.30169
\(580\) −7.47434 −0.310355
\(581\) −41.8744 −1.73724
\(582\) 39.8152 1.65040
\(583\) 4.19135 0.173588
\(584\) 6.70688 0.277533
\(585\) 18.6935 0.772879
\(586\) 22.6998 0.937719
\(587\) −15.4139 −0.636199 −0.318100 0.948057i \(-0.603045\pi\)
−0.318100 + 0.948057i \(0.603045\pi\)
\(588\) −14.7735 −0.609249
\(589\) −7.07513 −0.291526
\(590\) −0.747496 −0.0307739
\(591\) 49.5112 2.03662
\(592\) 0.814968 0.0334950
\(593\) 16.4405 0.675129 0.337564 0.941302i \(-0.390397\pi\)
0.337564 + 0.941302i \(0.390397\pi\)
\(594\) 9.73209 0.399313
\(595\) −27.7545 −1.13783
\(596\) −8.21509 −0.336503
\(597\) −5.70500 −0.233490
\(598\) −3.04623 −0.124570
\(599\) 4.52286 0.184799 0.0923995 0.995722i \(-0.470546\pi\)
0.0923995 + 0.995722i \(0.470546\pi\)
\(600\) −3.03435 −0.123877
\(601\) −37.8833 −1.54529 −0.772646 0.634837i \(-0.781067\pi\)
−0.772646 + 0.634837i \(0.781067\pi\)
\(602\) −3.44511 −0.140412
\(603\) 24.5682 1.00050
\(604\) 9.95698 0.405144
\(605\) 1.00000 0.0406558
\(606\) −7.23954 −0.294086
\(607\) −27.3697 −1.11090 −0.555450 0.831550i \(-0.687454\pi\)
−0.555450 + 0.831550i \(0.687454\pi\)
\(608\) −1.97164 −0.0799606
\(609\) −78.1343 −3.16616
\(610\) −0.594147 −0.0240563
\(611\) −6.89359 −0.278885
\(612\) 50.0074 2.02143
\(613\) −9.72740 −0.392886 −0.196443 0.980515i \(-0.562939\pi\)
−0.196443 + 0.980515i \(0.562939\pi\)
\(614\) 23.5995 0.952400
\(615\) 26.6730 1.07556
\(616\) 3.44511 0.138807
\(617\) −26.8861 −1.08239 −0.541197 0.840896i \(-0.682029\pi\)
−0.541197 + 0.840896i \(0.682029\pi\)
\(618\) −26.3899 −1.06156
\(619\) 15.1651 0.609538 0.304769 0.952426i \(-0.401421\pi\)
0.304769 + 0.952426i \(0.401421\pi\)
\(620\) 3.58845 0.144116
\(621\) 9.84426 0.395037
\(622\) −33.5297 −1.34442
\(623\) −38.8657 −1.55712
\(624\) −9.13803 −0.365814
\(625\) 1.00000 0.0400000
\(626\) 13.5130 0.540089
\(627\) −5.98266 −0.238924
\(628\) 1.44307 0.0575846
\(629\) 6.56556 0.261786
\(630\) −21.3848 −0.851991
\(631\) 40.8146 1.62480 0.812402 0.583098i \(-0.198160\pi\)
0.812402 + 0.583098i \(0.198160\pi\)
\(632\) 7.02527 0.279450
\(633\) 16.6488 0.661729
\(634\) 32.4963 1.29059
\(635\) 5.67047 0.225026
\(636\) 12.7180 0.504303
\(637\) 14.6624 0.580944
\(638\) 7.47434 0.295912
\(639\) −32.6996 −1.29358
\(640\) 1.00000 0.0395285
\(641\) 10.5834 0.418017 0.209009 0.977914i \(-0.432976\pi\)
0.209009 + 0.977914i \(0.432976\pi\)
\(642\) 0.480418 0.0189606
\(643\) 26.6338 1.05033 0.525167 0.850999i \(-0.324003\pi\)
0.525167 + 0.850999i \(0.324003\pi\)
\(644\) 3.48481 0.137321
\(645\) −3.03435 −0.119478
\(646\) −15.8840 −0.624947
\(647\) −24.4855 −0.962624 −0.481312 0.876549i \(-0.659840\pi\)
−0.481312 + 0.876549i \(0.659840\pi\)
\(648\) 10.9087 0.428534
\(649\) 0.747496 0.0293418
\(650\) 3.01153 0.118122
\(651\) 37.5124 1.47023
\(652\) −3.41087 −0.133580
\(653\) −6.10760 −0.239009 −0.119504 0.992834i \(-0.538131\pi\)
−0.119504 + 0.992834i \(0.538131\pi\)
\(654\) −54.1702 −2.11822
\(655\) −7.81393 −0.305316
\(656\) −8.79033 −0.343205
\(657\) 41.6317 1.62421
\(658\) 7.88608 0.307432
\(659\) −1.81431 −0.0706755 −0.0353377 0.999375i \(-0.511251\pi\)
−0.0353377 + 0.999375i \(0.511251\pi\)
\(660\) 3.03435 0.118112
\(661\) −4.07311 −0.158425 −0.0792127 0.996858i \(-0.525241\pi\)
−0.0792127 + 0.996858i \(0.525241\pi\)
\(662\) −4.30112 −0.167168
\(663\) −73.6180 −2.85909
\(664\) 12.1548 0.471696
\(665\) 6.79251 0.263402
\(666\) 5.05875 0.196023
\(667\) 7.56049 0.292743
\(668\) 1.97518 0.0764222
\(669\) 18.0690 0.698589
\(670\) 3.95796 0.152909
\(671\) 0.594147 0.0229368
\(672\) 10.4537 0.403259
\(673\) 37.7126 1.45372 0.726858 0.686788i \(-0.240980\pi\)
0.726858 + 0.686788i \(0.240980\pi\)
\(674\) −1.53439 −0.0591026
\(675\) −9.73209 −0.374588
\(676\) −3.93071 −0.151181
\(677\) −41.5508 −1.59693 −0.798463 0.602043i \(-0.794353\pi\)
−0.798463 + 0.602043i \(0.794353\pi\)
\(678\) −42.9546 −1.64966
\(679\) 45.2049 1.73481
\(680\) 8.05622 0.308942
\(681\) −50.6202 −1.93977
\(682\) −3.58845 −0.137409
\(683\) 16.0110 0.612642 0.306321 0.951928i \(-0.400902\pi\)
0.306321 + 0.951928i \(0.400902\pi\)
\(684\) −12.2386 −0.467954
\(685\) 11.7760 0.449937
\(686\) 7.34238 0.280333
\(687\) 63.1345 2.40873
\(688\) 1.00000 0.0381246
\(689\) −12.6224 −0.480873
\(690\) 3.06933 0.116847
\(691\) −10.1084 −0.384540 −0.192270 0.981342i \(-0.561585\pi\)
−0.192270 + 0.981342i \(0.561585\pi\)
\(692\) 9.06789 0.344709
\(693\) 21.3848 0.812342
\(694\) −11.3937 −0.432498
\(695\) −14.3383 −0.543881
\(696\) 22.6798 0.859675
\(697\) −70.8169 −2.68238
\(698\) 19.2716 0.729442
\(699\) −18.8810 −0.714144
\(700\) −3.44511 −0.130213
\(701\) 38.0510 1.43717 0.718583 0.695441i \(-0.244791\pi\)
0.718583 + 0.695441i \(0.244791\pi\)
\(702\) −29.3084 −1.10618
\(703\) −1.60682 −0.0606025
\(704\) −1.00000 −0.0376889
\(705\) 6.94585 0.261596
\(706\) 17.3056 0.651306
\(707\) −8.21953 −0.309127
\(708\) 2.26817 0.0852429
\(709\) 49.2891 1.85109 0.925545 0.378638i \(-0.123607\pi\)
0.925545 + 0.378638i \(0.123607\pi\)
\(710\) −5.26792 −0.197702
\(711\) 43.6080 1.63543
\(712\) 11.2814 0.422789
\(713\) −3.62981 −0.135937
\(714\) 84.2171 3.15175
\(715\) −3.01153 −0.112625
\(716\) 4.50260 0.168270
\(717\) −4.32232 −0.161420
\(718\) 31.0300 1.15803
\(719\) −28.1770 −1.05083 −0.525413 0.850847i \(-0.676089\pi\)
−0.525413 + 0.850847i \(0.676089\pi\)
\(720\) 6.20730 0.231333
\(721\) −29.9622 −1.11585
\(722\) −15.1126 −0.562434
\(723\) 41.8787 1.55749
\(724\) 21.3984 0.795264
\(725\) −7.47434 −0.277590
\(726\) −3.03435 −0.112615
\(727\) 43.0471 1.59653 0.798264 0.602308i \(-0.205752\pi\)
0.798264 + 0.602308i \(0.205752\pi\)
\(728\) −10.3750 −0.384524
\(729\) −20.8782 −0.773267
\(730\) 6.70688 0.248233
\(731\) 8.05622 0.297970
\(732\) 1.80285 0.0666353
\(733\) 17.3492 0.640807 0.320403 0.947281i \(-0.396182\pi\)
0.320403 + 0.947281i \(0.396182\pi\)
\(734\) 26.2176 0.967709
\(735\) −14.7735 −0.544929
\(736\) −1.01153 −0.0372853
\(737\) −3.95796 −0.145793
\(738\) −54.5643 −2.00854
\(739\) −14.8976 −0.548018 −0.274009 0.961727i \(-0.588350\pi\)
−0.274009 + 0.961727i \(0.588350\pi\)
\(740\) 0.814968 0.0299588
\(741\) 18.0169 0.661868
\(742\) 14.4396 0.530096
\(743\) 38.5777 1.41528 0.707639 0.706575i \(-0.249761\pi\)
0.707639 + 0.706575i \(0.249761\pi\)
\(744\) −10.8886 −0.399196
\(745\) −8.21509 −0.300978
\(746\) 3.10048 0.113517
\(747\) 75.4482 2.76051
\(748\) −8.05622 −0.294565
\(749\) 0.545451 0.0199303
\(750\) −3.03435 −0.110799
\(751\) 9.30941 0.339705 0.169853 0.985469i \(-0.445671\pi\)
0.169853 + 0.985469i \(0.445671\pi\)
\(752\) −2.28907 −0.0834738
\(753\) −35.7492 −1.30277
\(754\) −22.5092 −0.819736
\(755\) 9.95698 0.362372
\(756\) 33.5281 1.21940
\(757\) 35.2626 1.28164 0.640820 0.767691i \(-0.278594\pi\)
0.640820 + 0.767691i \(0.278594\pi\)
\(758\) 16.3697 0.594574
\(759\) −3.06933 −0.111409
\(760\) −1.97164 −0.0715190
\(761\) 36.1965 1.31212 0.656062 0.754707i \(-0.272221\pi\)
0.656062 + 0.754707i \(0.272221\pi\)
\(762\) −17.2062 −0.623315
\(763\) −61.5030 −2.22656
\(764\) 23.5905 0.853474
\(765\) 50.0074 1.80802
\(766\) 1.84411 0.0666305
\(767\) −2.25110 −0.0812826
\(768\) −3.03435 −0.109493
\(769\) −26.5292 −0.956667 −0.478334 0.878178i \(-0.658759\pi\)
−0.478334 + 0.878178i \(0.658759\pi\)
\(770\) 3.44511 0.124153
\(771\) −8.91229 −0.320968
\(772\) 18.2524 0.656917
\(773\) −33.2115 −1.19453 −0.597267 0.802043i \(-0.703747\pi\)
−0.597267 + 0.802043i \(0.703747\pi\)
\(774\) 6.20730 0.223117
\(775\) 3.58845 0.128901
\(776\) −13.1215 −0.471034
\(777\) 8.51940 0.305632
\(778\) −2.69523 −0.0966288
\(779\) 17.3314 0.620961
\(780\) −9.13803 −0.327194
\(781\) 5.26792 0.188501
\(782\) −8.14908 −0.291410
\(783\) 72.7410 2.59955
\(784\) 4.86875 0.173884
\(785\) 1.44307 0.0515053
\(786\) 23.7102 0.845716
\(787\) −15.6797 −0.558922 −0.279461 0.960157i \(-0.590156\pi\)
−0.279461 + 0.960157i \(0.590156\pi\)
\(788\) −16.3169 −0.581265
\(789\) −49.0535 −1.74635
\(790\) 7.02527 0.249948
\(791\) −48.7692 −1.73403
\(792\) −6.20730 −0.220567
\(793\) −1.78929 −0.0635395
\(794\) 31.5646 1.12019
\(795\) 12.7180 0.451062
\(796\) 1.88014 0.0666397
\(797\) 16.3162 0.577951 0.288975 0.957337i \(-0.406685\pi\)
0.288975 + 0.957337i \(0.406685\pi\)
\(798\) −20.6109 −0.729618
\(799\) −18.4413 −0.652405
\(800\) 1.00000 0.0353553
\(801\) 70.0272 2.47429
\(802\) −20.9312 −0.739105
\(803\) −6.70688 −0.236681
\(804\) −12.0098 −0.423554
\(805\) 3.48481 0.122823
\(806\) 10.8067 0.380650
\(807\) 22.7889 0.802206
\(808\) 2.38586 0.0839342
\(809\) 10.8237 0.380543 0.190271 0.981732i \(-0.439063\pi\)
0.190271 + 0.981732i \(0.439063\pi\)
\(810\) 10.9087 0.383293
\(811\) −14.4504 −0.507424 −0.253712 0.967280i \(-0.581651\pi\)
−0.253712 + 0.967280i \(0.581651\pi\)
\(812\) 25.7499 0.903644
\(813\) 17.6457 0.618862
\(814\) −0.814968 −0.0285646
\(815\) −3.41087 −0.119478
\(816\) −24.4454 −0.855761
\(817\) −1.97164 −0.0689790
\(818\) −26.4274 −0.924013
\(819\) −64.4009 −2.25035
\(820\) −8.79033 −0.306972
\(821\) 39.2959 1.37144 0.685718 0.727867i \(-0.259488\pi\)
0.685718 + 0.727867i \(0.259488\pi\)
\(822\) −35.7325 −1.24631
\(823\) −23.6733 −0.825199 −0.412600 0.910913i \(-0.635379\pi\)
−0.412600 + 0.910913i \(0.635379\pi\)
\(824\) 8.69704 0.302976
\(825\) 3.03435 0.105643
\(826\) 2.57520 0.0896027
\(827\) −42.8341 −1.48949 −0.744744 0.667351i \(-0.767428\pi\)
−0.744744 + 0.667351i \(0.767428\pi\)
\(828\) −6.27885 −0.218205
\(829\) −25.9312 −0.900628 −0.450314 0.892870i \(-0.648688\pi\)
−0.450314 + 0.892870i \(0.648688\pi\)
\(830\) 12.1548 0.421898
\(831\) 42.7683 1.48362
\(832\) 3.01153 0.104406
\(833\) 39.2237 1.35902
\(834\) 43.5074 1.50654
\(835\) 1.97518 0.0683541
\(836\) 1.97164 0.0681907
\(837\) −34.9231 −1.20712
\(838\) −21.0841 −0.728339
\(839\) −3.95871 −0.136670 −0.0683350 0.997662i \(-0.521769\pi\)
−0.0683350 + 0.997662i \(0.521769\pi\)
\(840\) 10.4537 0.360686
\(841\) 26.8658 0.926406
\(842\) −30.4110 −1.04803
\(843\) −87.9263 −3.02834
\(844\) −5.48675 −0.188862
\(845\) −3.93071 −0.135221
\(846\) −14.2089 −0.488514
\(847\) −3.44511 −0.118375
\(848\) −4.19135 −0.143932
\(849\) 17.7766 0.610090
\(850\) 8.05622 0.276326
\(851\) −0.824361 −0.0282587
\(852\) 15.9847 0.547628
\(853\) −37.4187 −1.28119 −0.640595 0.767879i \(-0.721312\pi\)
−0.640595 + 0.767879i \(0.721312\pi\)
\(854\) 2.04690 0.0700434
\(855\) −12.2386 −0.418551
\(856\) −0.158326 −0.00541148
\(857\) 27.3132 0.933003 0.466501 0.884521i \(-0.345514\pi\)
0.466501 + 0.884521i \(0.345514\pi\)
\(858\) 9.13803 0.311967
\(859\) 13.2220 0.451130 0.225565 0.974228i \(-0.427577\pi\)
0.225565 + 0.974228i \(0.427577\pi\)
\(860\) 1.00000 0.0340997
\(861\) −91.8912 −3.13164
\(862\) 21.1977 0.721997
\(863\) −8.08216 −0.275120 −0.137560 0.990493i \(-0.543926\pi\)
−0.137560 + 0.990493i \(0.543926\pi\)
\(864\) −9.73209 −0.331092
\(865\) 9.06789 0.308317
\(866\) 25.0369 0.850790
\(867\) −145.354 −4.93648
\(868\) −12.3626 −0.419613
\(869\) −7.02527 −0.238316
\(870\) 22.6798 0.768917
\(871\) 11.9195 0.403876
\(872\) 17.8523 0.604555
\(873\) −81.4491 −2.75663
\(874\) 1.99437 0.0674604
\(875\) −3.44511 −0.116466
\(876\) −20.3511 −0.687599
\(877\) −44.3666 −1.49815 −0.749076 0.662484i \(-0.769502\pi\)
−0.749076 + 0.662484i \(0.769502\pi\)
\(878\) 17.1204 0.577786
\(879\) −68.8792 −2.32324
\(880\) −1.00000 −0.0337100
\(881\) −1.04662 −0.0352615 −0.0176307 0.999845i \(-0.505612\pi\)
−0.0176307 + 0.999845i \(0.505612\pi\)
\(882\) 30.2218 1.01762
\(883\) −15.4009 −0.518281 −0.259140 0.965840i \(-0.583439\pi\)
−0.259140 + 0.965840i \(0.583439\pi\)
\(884\) 24.2615 0.816003
\(885\) 2.26817 0.0762436
\(886\) −26.7844 −0.899838
\(887\) −52.4559 −1.76130 −0.880648 0.473771i \(-0.842892\pi\)
−0.880648 + 0.473771i \(0.842892\pi\)
\(888\) −2.47290 −0.0829851
\(889\) −19.5354 −0.655195
\(890\) 11.2814 0.378154
\(891\) −10.9087 −0.365455
\(892\) −5.95482 −0.199382
\(893\) 4.51322 0.151029
\(894\) 24.9275 0.833700
\(895\) 4.50260 0.150505
\(896\) −3.44511 −0.115093
\(897\) 9.24335 0.308627
\(898\) −37.7530 −1.25983
\(899\) −26.8213 −0.894540
\(900\) 6.20730 0.206910
\(901\) −33.7664 −1.12492
\(902\) 8.79033 0.292686
\(903\) 10.4537 0.347876
\(904\) 14.1561 0.470825
\(905\) 21.3984 0.711306
\(906\) −30.2130 −1.00376
\(907\) −35.8803 −1.19139 −0.595694 0.803212i \(-0.703123\pi\)
−0.595694 + 0.803212i \(0.703123\pi\)
\(908\) 16.6824 0.553623
\(909\) 14.8097 0.491208
\(910\) −10.3750 −0.343929
\(911\) 40.0836 1.32803 0.664015 0.747720i \(-0.268851\pi\)
0.664015 + 0.747720i \(0.268851\pi\)
\(912\) 5.98266 0.198106
\(913\) −12.1548 −0.402264
\(914\) −35.4827 −1.17366
\(915\) 1.80285 0.0596004
\(916\) −20.8066 −0.687469
\(917\) 26.9198 0.888971
\(918\) −78.4039 −2.58771
\(919\) 48.9039 1.61319 0.806596 0.591104i \(-0.201308\pi\)
0.806596 + 0.591104i \(0.201308\pi\)
\(920\) −1.01153 −0.0333490
\(921\) −71.6093 −2.35961
\(922\) −31.8589 −1.04922
\(923\) −15.8645 −0.522186
\(924\) −10.4537 −0.343900
\(925\) 0.814968 0.0267960
\(926\) 25.0415 0.822914
\(927\) 53.9852 1.77311
\(928\) −7.47434 −0.245357
\(929\) −35.4865 −1.16427 −0.582137 0.813091i \(-0.697783\pi\)
−0.582137 + 0.813091i \(0.697783\pi\)
\(930\) −10.8886 −0.357052
\(931\) −9.59943 −0.314609
\(932\) 6.22241 0.203822
\(933\) 101.741 3.33085
\(934\) 7.52638 0.246271
\(935\) −8.05622 −0.263467
\(936\) 18.6935 0.611015
\(937\) −5.43303 −0.177489 −0.0887446 0.996054i \(-0.528285\pi\)
−0.0887446 + 0.996054i \(0.528285\pi\)
\(938\) −13.6356 −0.445217
\(939\) −41.0033 −1.33809
\(940\) −2.28907 −0.0746612
\(941\) 0.702205 0.0228912 0.0114456 0.999934i \(-0.496357\pi\)
0.0114456 + 0.999934i \(0.496357\pi\)
\(942\) −4.37878 −0.142668
\(943\) 8.89165 0.289552
\(944\) −0.747496 −0.0243289
\(945\) 33.5281 1.09067
\(946\) −1.00000 −0.0325128
\(947\) −46.2283 −1.50222 −0.751110 0.660178i \(-0.770481\pi\)
−0.751110 + 0.660178i \(0.770481\pi\)
\(948\) −21.3171 −0.692349
\(949\) 20.1980 0.655653
\(950\) −1.97164 −0.0639685
\(951\) −98.6053 −3.19750
\(952\) −27.7545 −0.899530
\(953\) −47.7755 −1.54760 −0.773800 0.633430i \(-0.781646\pi\)
−0.773800 + 0.633430i \(0.781646\pi\)
\(954\) −26.0170 −0.842331
\(955\) 23.5905 0.763370
\(956\) 1.42446 0.0460704
\(957\) −22.6798 −0.733134
\(958\) −8.55601 −0.276432
\(959\) −40.5695 −1.31006
\(960\) −3.03435 −0.0979333
\(961\) −18.1230 −0.584614
\(962\) 2.45430 0.0791297
\(963\) −0.982780 −0.0316696
\(964\) −13.8015 −0.444517
\(965\) 18.2524 0.587564
\(966\) −10.5742 −0.340218
\(967\) 55.6766 1.79044 0.895220 0.445625i \(-0.147019\pi\)
0.895220 + 0.445625i \(0.147019\pi\)
\(968\) 1.00000 0.0321412
\(969\) 48.1976 1.54833
\(970\) −13.1215 −0.421306
\(971\) 34.5148 1.10763 0.553816 0.832639i \(-0.313171\pi\)
0.553816 + 0.832639i \(0.313171\pi\)
\(972\) −3.90458 −0.125240
\(973\) 49.3968 1.58359
\(974\) −9.24248 −0.296148
\(975\) −9.13803 −0.292651
\(976\) −0.594147 −0.0190182
\(977\) 5.20212 0.166431 0.0832153 0.996532i \(-0.473481\pi\)
0.0832153 + 0.996532i \(0.473481\pi\)
\(978\) 10.3498 0.330950
\(979\) −11.2814 −0.360556
\(980\) 4.86875 0.155527
\(981\) 110.815 3.53804
\(982\) 34.7025 1.10740
\(983\) 4.79649 0.152984 0.0764921 0.997070i \(-0.475628\pi\)
0.0764921 + 0.997070i \(0.475628\pi\)
\(984\) 26.6730 0.850304
\(985\) −16.3169 −0.519899
\(986\) −60.2150 −1.91763
\(987\) −23.9292 −0.761674
\(988\) −5.93765 −0.188902
\(989\) −1.01153 −0.0321646
\(990\) −6.20730 −0.197281
\(991\) 32.7118 1.03912 0.519562 0.854433i \(-0.326095\pi\)
0.519562 + 0.854433i \(0.326095\pi\)
\(992\) 3.58845 0.113933
\(993\) 13.0511 0.414165
\(994\) 18.1485 0.575637
\(995\) 1.88014 0.0596044
\(996\) −36.8818 −1.16865
\(997\) −22.3139 −0.706688 −0.353344 0.935493i \(-0.614956\pi\)
−0.353344 + 0.935493i \(0.614956\pi\)
\(998\) 13.6098 0.430811
\(999\) −7.93134 −0.250937
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.be.1.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.be.1.1 12 1.1 even 1 trivial