Properties

Label 1859.2.a.t.1.14
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.17546 q^{2} -1.22926 q^{3} -0.618298 q^{4} -1.06938 q^{5} -1.44494 q^{6} -3.67782 q^{7} -3.07770 q^{8} -1.48892 q^{9} +O(q^{10})\) \(q+1.17546 q^{2} -1.22926 q^{3} -0.618298 q^{4} -1.06938 q^{5} -1.44494 q^{6} -3.67782 q^{7} -3.07770 q^{8} -1.48892 q^{9} -1.25701 q^{10} +1.00000 q^{11} +0.760050 q^{12} -4.32312 q^{14} +1.31454 q^{15} -2.38111 q^{16} +4.61281 q^{17} -1.75016 q^{18} -6.56325 q^{19} +0.661193 q^{20} +4.52100 q^{21} +1.17546 q^{22} +6.89013 q^{23} +3.78330 q^{24} -3.85644 q^{25} +5.51805 q^{27} +2.27399 q^{28} -7.50948 q^{29} +1.54519 q^{30} -4.02002 q^{31} +3.35650 q^{32} -1.22926 q^{33} +5.42216 q^{34} +3.93297 q^{35} +0.920595 q^{36} +4.37781 q^{37} -7.71483 q^{38} +3.29122 q^{40} +7.56827 q^{41} +5.31425 q^{42} +3.03588 q^{43} -0.618298 q^{44} +1.59221 q^{45} +8.09906 q^{46} -2.86516 q^{47} +2.92701 q^{48} +6.52636 q^{49} -4.53308 q^{50} -5.67034 q^{51} +11.3481 q^{53} +6.48624 q^{54} -1.06938 q^{55} +11.3192 q^{56} +8.06795 q^{57} -8.82708 q^{58} +7.28662 q^{59} -0.812779 q^{60} -2.10752 q^{61} -4.72536 q^{62} +5.47597 q^{63} +8.70765 q^{64} -1.44494 q^{66} -6.17708 q^{67} -2.85209 q^{68} -8.46977 q^{69} +4.62304 q^{70} +10.0122 q^{71} +4.58244 q^{72} +7.21487 q^{73} +5.14593 q^{74} +4.74057 q^{75} +4.05805 q^{76} -3.67782 q^{77} -15.1525 q^{79} +2.54630 q^{80} -2.31637 q^{81} +8.89618 q^{82} -3.56754 q^{83} -2.79533 q^{84} -4.93282 q^{85} +3.56855 q^{86} +9.23111 q^{87} -3.07770 q^{88} +3.36383 q^{89} +1.87158 q^{90} -4.26015 q^{92} +4.94165 q^{93} -3.36788 q^{94} +7.01858 q^{95} -4.12602 q^{96} -18.1156 q^{97} +7.67147 q^{98} -1.48892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.17546 0.831174 0.415587 0.909553i \(-0.363576\pi\)
0.415587 + 0.909553i \(0.363576\pi\)
\(3\) −1.22926 −0.709714 −0.354857 0.934921i \(-0.615470\pi\)
−0.354857 + 0.934921i \(0.615470\pi\)
\(4\) −0.618298 −0.309149
\(5\) −1.06938 −0.478239 −0.239120 0.970990i \(-0.576859\pi\)
−0.239120 + 0.970990i \(0.576859\pi\)
\(6\) −1.44494 −0.589896
\(7\) −3.67782 −1.39009 −0.695043 0.718968i \(-0.744615\pi\)
−0.695043 + 0.718968i \(0.744615\pi\)
\(8\) −3.07770 −1.08813
\(9\) −1.48892 −0.496306
\(10\) −1.25701 −0.397500
\(11\) 1.00000 0.301511
\(12\) 0.760050 0.219407
\(13\) 0 0
\(14\) −4.32312 −1.15540
\(15\) 1.31454 0.339413
\(16\) −2.38111 −0.595278
\(17\) 4.61281 1.11877 0.559385 0.828908i \(-0.311037\pi\)
0.559385 + 0.828908i \(0.311037\pi\)
\(18\) −1.75016 −0.412517
\(19\) −6.56325 −1.50571 −0.752857 0.658184i \(-0.771325\pi\)
−0.752857 + 0.658184i \(0.771325\pi\)
\(20\) 0.661193 0.147847
\(21\) 4.52100 0.986563
\(22\) 1.17546 0.250609
\(23\) 6.89013 1.43669 0.718346 0.695686i \(-0.244900\pi\)
0.718346 + 0.695686i \(0.244900\pi\)
\(24\) 3.78330 0.772262
\(25\) −3.85644 −0.771287
\(26\) 0 0
\(27\) 5.51805 1.06195
\(28\) 2.27399 0.429744
\(29\) −7.50948 −1.39447 −0.697237 0.716840i \(-0.745588\pi\)
−0.697237 + 0.716840i \(0.745588\pi\)
\(30\) 1.54519 0.282112
\(31\) −4.02002 −0.722016 −0.361008 0.932563i \(-0.617567\pi\)
−0.361008 + 0.932563i \(0.617567\pi\)
\(32\) 3.35650 0.593352
\(33\) −1.22926 −0.213987
\(34\) 5.42216 0.929893
\(35\) 3.93297 0.664793
\(36\) 0.920595 0.153432
\(37\) 4.37781 0.719707 0.359854 0.933009i \(-0.382827\pi\)
0.359854 + 0.933009i \(0.382827\pi\)
\(38\) −7.71483 −1.25151
\(39\) 0 0
\(40\) 3.29122 0.520387
\(41\) 7.56827 1.18197 0.590983 0.806684i \(-0.298740\pi\)
0.590983 + 0.806684i \(0.298740\pi\)
\(42\) 5.31425 0.820006
\(43\) 3.03588 0.462967 0.231483 0.972839i \(-0.425642\pi\)
0.231483 + 0.972839i \(0.425642\pi\)
\(44\) −0.618298 −0.0932120
\(45\) 1.59221 0.237353
\(46\) 8.09906 1.19414
\(47\) −2.86516 −0.417927 −0.208963 0.977923i \(-0.567009\pi\)
−0.208963 + 0.977923i \(0.567009\pi\)
\(48\) 2.92701 0.422477
\(49\) 6.52636 0.932338
\(50\) −4.53308 −0.641074
\(51\) −5.67034 −0.794007
\(52\) 0 0
\(53\) 11.3481 1.55879 0.779393 0.626536i \(-0.215528\pi\)
0.779393 + 0.626536i \(0.215528\pi\)
\(54\) 6.48624 0.882665
\(55\) −1.06938 −0.144195
\(56\) 11.3192 1.51260
\(57\) 8.06795 1.06863
\(58\) −8.82708 −1.15905
\(59\) 7.28662 0.948638 0.474319 0.880353i \(-0.342694\pi\)
0.474319 + 0.880353i \(0.342694\pi\)
\(60\) −0.812779 −0.104929
\(61\) −2.10752 −0.269841 −0.134920 0.990856i \(-0.543078\pi\)
−0.134920 + 0.990856i \(0.543078\pi\)
\(62\) −4.72536 −0.600121
\(63\) 5.47597 0.689908
\(64\) 8.70765 1.08846
\(65\) 0 0
\(66\) −1.44494 −0.177860
\(67\) −6.17708 −0.754650 −0.377325 0.926081i \(-0.623156\pi\)
−0.377325 + 0.926081i \(0.623156\pi\)
\(68\) −2.85209 −0.345867
\(69\) −8.46977 −1.01964
\(70\) 4.62304 0.552559
\(71\) 10.0122 1.18823 0.594116 0.804379i \(-0.297502\pi\)
0.594116 + 0.804379i \(0.297502\pi\)
\(72\) 4.58244 0.540046
\(73\) 7.21487 0.844437 0.422219 0.906494i \(-0.361251\pi\)
0.422219 + 0.906494i \(0.361251\pi\)
\(74\) 5.14593 0.598202
\(75\) 4.74057 0.547393
\(76\) 4.05805 0.465490
\(77\) −3.67782 −0.419127
\(78\) 0 0
\(79\) −15.1525 −1.70479 −0.852395 0.522898i \(-0.824851\pi\)
−0.852395 + 0.522898i \(0.824851\pi\)
\(80\) 2.54630 0.284685
\(81\) −2.31637 −0.257375
\(82\) 8.89618 0.982419
\(83\) −3.56754 −0.391588 −0.195794 0.980645i \(-0.562728\pi\)
−0.195794 + 0.980645i \(0.562728\pi\)
\(84\) −2.79533 −0.304995
\(85\) −4.93282 −0.535039
\(86\) 3.56855 0.384806
\(87\) 9.23111 0.989678
\(88\) −3.07770 −0.328084
\(89\) 3.36383 0.356566 0.178283 0.983979i \(-0.442946\pi\)
0.178283 + 0.983979i \(0.442946\pi\)
\(90\) 1.87158 0.197282
\(91\) 0 0
\(92\) −4.26015 −0.444152
\(93\) 4.94165 0.512425
\(94\) −3.36788 −0.347370
\(95\) 7.01858 0.720091
\(96\) −4.12602 −0.421110
\(97\) −18.1156 −1.83936 −0.919679 0.392671i \(-0.871551\pi\)
−0.919679 + 0.392671i \(0.871551\pi\)
\(98\) 7.67147 0.774935
\(99\) −1.48892 −0.149642
\(100\) 2.38443 0.238443
\(101\) 13.1809 1.31155 0.655773 0.754958i \(-0.272343\pi\)
0.655773 + 0.754958i \(0.272343\pi\)
\(102\) −6.66525 −0.659958
\(103\) 5.35159 0.527308 0.263654 0.964617i \(-0.415072\pi\)
0.263654 + 0.964617i \(0.415072\pi\)
\(104\) 0 0
\(105\) −4.83465 −0.471813
\(106\) 13.3393 1.29562
\(107\) 8.40679 0.812715 0.406358 0.913714i \(-0.366799\pi\)
0.406358 + 0.913714i \(0.366799\pi\)
\(108\) −3.41180 −0.328301
\(109\) −12.9301 −1.23848 −0.619240 0.785202i \(-0.712559\pi\)
−0.619240 + 0.785202i \(0.712559\pi\)
\(110\) −1.25701 −0.119851
\(111\) −5.38147 −0.510786
\(112\) 8.75730 0.827487
\(113\) 2.38626 0.224480 0.112240 0.993681i \(-0.464197\pi\)
0.112240 + 0.993681i \(0.464197\pi\)
\(114\) 9.48354 0.888215
\(115\) −7.36814 −0.687082
\(116\) 4.64310 0.431101
\(117\) 0 0
\(118\) 8.56512 0.788483
\(119\) −16.9651 −1.55519
\(120\) −4.04576 −0.369326
\(121\) 1.00000 0.0909091
\(122\) −2.47730 −0.224285
\(123\) −9.30338 −0.838857
\(124\) 2.48557 0.223211
\(125\) 9.47086 0.847099
\(126\) 6.43677 0.573433
\(127\) 11.3039 1.00306 0.501529 0.865141i \(-0.332771\pi\)
0.501529 + 0.865141i \(0.332771\pi\)
\(128\) 3.52247 0.311346
\(129\) −3.73188 −0.328574
\(130\) 0 0
\(131\) −8.65899 −0.756540 −0.378270 0.925695i \(-0.623481\pi\)
−0.378270 + 0.925695i \(0.623481\pi\)
\(132\) 0.760050 0.0661538
\(133\) 24.1385 2.09307
\(134\) −7.26090 −0.627246
\(135\) −5.90087 −0.507866
\(136\) −14.1968 −1.21737
\(137\) −7.29319 −0.623099 −0.311550 0.950230i \(-0.600848\pi\)
−0.311550 + 0.950230i \(0.600848\pi\)
\(138\) −9.95586 −0.847499
\(139\) −12.3363 −1.04635 −0.523176 0.852225i \(-0.675253\pi\)
−0.523176 + 0.852225i \(0.675253\pi\)
\(140\) −2.43175 −0.205520
\(141\) 3.52203 0.296608
\(142\) 11.7689 0.987628
\(143\) 0 0
\(144\) 3.54528 0.295440
\(145\) 8.03045 0.666893
\(146\) 8.48078 0.701874
\(147\) −8.02260 −0.661693
\(148\) −2.70679 −0.222497
\(149\) 0.138812 0.0113719 0.00568597 0.999984i \(-0.498190\pi\)
0.00568597 + 0.999984i \(0.498190\pi\)
\(150\) 5.57234 0.454979
\(151\) −21.2786 −1.73163 −0.865813 0.500368i \(-0.833198\pi\)
−0.865813 + 0.500368i \(0.833198\pi\)
\(152\) 20.1997 1.63841
\(153\) −6.86809 −0.555252
\(154\) −4.32312 −0.348367
\(155\) 4.29891 0.345296
\(156\) 0 0
\(157\) 15.4984 1.23691 0.618453 0.785822i \(-0.287760\pi\)
0.618453 + 0.785822i \(0.287760\pi\)
\(158\) −17.8111 −1.41698
\(159\) −13.9498 −1.10629
\(160\) −3.58936 −0.283764
\(161\) −25.3407 −1.99712
\(162\) −2.72280 −0.213923
\(163\) 1.31961 0.103360 0.0516799 0.998664i \(-0.483542\pi\)
0.0516799 + 0.998664i \(0.483542\pi\)
\(164\) −4.67945 −0.365403
\(165\) 1.31454 0.102337
\(166\) −4.19349 −0.325478
\(167\) −6.49802 −0.502832 −0.251416 0.967879i \(-0.580896\pi\)
−0.251416 + 0.967879i \(0.580896\pi\)
\(168\) −13.9143 −1.07351
\(169\) 0 0
\(170\) −5.79832 −0.444711
\(171\) 9.77214 0.747294
\(172\) −1.87708 −0.143126
\(173\) 2.23420 0.169863 0.0849314 0.996387i \(-0.472933\pi\)
0.0849314 + 0.996387i \(0.472933\pi\)
\(174\) 10.8508 0.822595
\(175\) 14.1833 1.07216
\(176\) −2.38111 −0.179483
\(177\) −8.95716 −0.673262
\(178\) 3.95404 0.296368
\(179\) 12.7708 0.954531 0.477265 0.878759i \(-0.341628\pi\)
0.477265 + 0.878759i \(0.341628\pi\)
\(180\) −0.984462 −0.0733774
\(181\) 15.3012 1.13733 0.568665 0.822569i \(-0.307460\pi\)
0.568665 + 0.822569i \(0.307460\pi\)
\(182\) 0 0
\(183\) 2.59070 0.191510
\(184\) −21.2058 −1.56331
\(185\) −4.68152 −0.344192
\(186\) 5.80870 0.425915
\(187\) 4.61281 0.337322
\(188\) 1.77152 0.129202
\(189\) −20.2944 −1.47620
\(190\) 8.25005 0.598521
\(191\) −10.0060 −0.724010 −0.362005 0.932176i \(-0.617908\pi\)
−0.362005 + 0.932176i \(0.617908\pi\)
\(192\) −10.7040 −0.772493
\(193\) −10.8911 −0.783958 −0.391979 0.919974i \(-0.628209\pi\)
−0.391979 + 0.919974i \(0.628209\pi\)
\(194\) −21.2941 −1.52883
\(195\) 0 0
\(196\) −4.03524 −0.288231
\(197\) −2.41459 −0.172033 −0.0860163 0.996294i \(-0.527414\pi\)
−0.0860163 + 0.996294i \(0.527414\pi\)
\(198\) −1.75016 −0.124378
\(199\) 0.0512234 0.00363113 0.00181557 0.999998i \(-0.499422\pi\)
0.00181557 + 0.999998i \(0.499422\pi\)
\(200\) 11.8690 0.839262
\(201\) 7.59324 0.535586
\(202\) 15.4936 1.09012
\(203\) 27.6185 1.93844
\(204\) 3.50596 0.245466
\(205\) −8.09332 −0.565262
\(206\) 6.29057 0.438285
\(207\) −10.2588 −0.713038
\(208\) 0 0
\(209\) −6.56325 −0.453990
\(210\) −5.68293 −0.392159
\(211\) 25.6713 1.76728 0.883641 0.468165i \(-0.155085\pi\)
0.883641 + 0.468165i \(0.155085\pi\)
\(212\) −7.01653 −0.481897
\(213\) −12.3076 −0.843305
\(214\) 9.88183 0.675508
\(215\) −3.24649 −0.221409
\(216\) −16.9829 −1.15554
\(217\) 14.7849 1.00366
\(218\) −15.1988 −1.02939
\(219\) −8.86896 −0.599309
\(220\) 0.661193 0.0445776
\(221\) 0 0
\(222\) −6.32569 −0.424553
\(223\) 5.80464 0.388708 0.194354 0.980931i \(-0.437739\pi\)
0.194354 + 0.980931i \(0.437739\pi\)
\(224\) −12.3446 −0.824809
\(225\) 5.74192 0.382794
\(226\) 2.80494 0.186582
\(227\) 3.73623 0.247983 0.123991 0.992283i \(-0.460431\pi\)
0.123991 + 0.992283i \(0.460431\pi\)
\(228\) −4.98840 −0.330365
\(229\) 18.5146 1.22348 0.611739 0.791060i \(-0.290470\pi\)
0.611739 + 0.791060i \(0.290470\pi\)
\(230\) −8.66093 −0.571085
\(231\) 4.52100 0.297460
\(232\) 23.1119 1.51737
\(233\) 15.2245 0.997387 0.498694 0.866778i \(-0.333813\pi\)
0.498694 + 0.866778i \(0.333813\pi\)
\(234\) 0 0
\(235\) 3.06393 0.199869
\(236\) −4.50531 −0.293270
\(237\) 18.6264 1.20991
\(238\) −19.9417 −1.29263
\(239\) 24.2441 1.56822 0.784110 0.620622i \(-0.213120\pi\)
0.784110 + 0.620622i \(0.213120\pi\)
\(240\) −3.13007 −0.202045
\(241\) 14.5797 0.939162 0.469581 0.882889i \(-0.344405\pi\)
0.469581 + 0.882889i \(0.344405\pi\)
\(242\) 1.17546 0.0755613
\(243\) −13.7067 −0.879287
\(244\) 1.30308 0.0834210
\(245\) −6.97913 −0.445880
\(246\) −10.9357 −0.697237
\(247\) 0 0
\(248\) 12.3724 0.785648
\(249\) 4.38544 0.277916
\(250\) 11.1326 0.704087
\(251\) −20.3766 −1.28616 −0.643079 0.765800i \(-0.722343\pi\)
−0.643079 + 0.765800i \(0.722343\pi\)
\(252\) −3.38578 −0.213284
\(253\) 6.89013 0.433179
\(254\) 13.2872 0.833715
\(255\) 6.06372 0.379725
\(256\) −13.2748 −0.829674
\(257\) −2.30300 −0.143657 −0.0718287 0.997417i \(-0.522883\pi\)
−0.0718287 + 0.997417i \(0.522883\pi\)
\(258\) −4.38667 −0.273102
\(259\) −16.1008 −1.00045
\(260\) 0 0
\(261\) 11.1810 0.692086
\(262\) −10.1783 −0.628817
\(263\) −4.84720 −0.298891 −0.149446 0.988770i \(-0.547749\pi\)
−0.149446 + 0.988770i \(0.547749\pi\)
\(264\) 3.78330 0.232846
\(265\) −12.1354 −0.745472
\(266\) 28.3738 1.73971
\(267\) −4.13503 −0.253060
\(268\) 3.81928 0.233299
\(269\) 25.1720 1.53476 0.767381 0.641191i \(-0.221559\pi\)
0.767381 + 0.641191i \(0.221559\pi\)
\(270\) −6.93622 −0.422125
\(271\) −8.88098 −0.539481 −0.269740 0.962933i \(-0.586938\pi\)
−0.269740 + 0.962933i \(0.586938\pi\)
\(272\) −10.9836 −0.665979
\(273\) 0 0
\(274\) −8.57284 −0.517904
\(275\) −3.85644 −0.232552
\(276\) 5.23684 0.315221
\(277\) 19.1219 1.14892 0.574462 0.818531i \(-0.305211\pi\)
0.574462 + 0.818531i \(0.305211\pi\)
\(278\) −14.5008 −0.869701
\(279\) 5.98547 0.358341
\(280\) −12.1045 −0.723382
\(281\) −0.195636 −0.0116706 −0.00583532 0.999983i \(-0.501857\pi\)
−0.00583532 + 0.999983i \(0.501857\pi\)
\(282\) 4.14000 0.246533
\(283\) −9.94140 −0.590955 −0.295478 0.955350i \(-0.595479\pi\)
−0.295478 + 0.955350i \(0.595479\pi\)
\(284\) −6.19054 −0.367341
\(285\) −8.62767 −0.511059
\(286\) 0 0
\(287\) −27.8347 −1.64303
\(288\) −4.99756 −0.294484
\(289\) 4.27797 0.251645
\(290\) 9.43946 0.554304
\(291\) 22.2688 1.30542
\(292\) −4.46094 −0.261057
\(293\) −2.74298 −0.160247 −0.0801234 0.996785i \(-0.525531\pi\)
−0.0801234 + 0.996785i \(0.525531\pi\)
\(294\) −9.43024 −0.549983
\(295\) −7.79214 −0.453676
\(296\) −13.4736 −0.783136
\(297\) 5.51805 0.320190
\(298\) 0.163168 0.00945207
\(299\) 0 0
\(300\) −2.93108 −0.169226
\(301\) −11.1654 −0.643563
\(302\) −25.0121 −1.43928
\(303\) −16.2027 −0.930823
\(304\) 15.6278 0.896318
\(305\) 2.25373 0.129048
\(306\) −8.07315 −0.461511
\(307\) −29.7166 −1.69602 −0.848008 0.529983i \(-0.822198\pi\)
−0.848008 + 0.529983i \(0.822198\pi\)
\(308\) 2.27399 0.129573
\(309\) −6.57850 −0.374238
\(310\) 5.05318 0.287002
\(311\) 12.2907 0.696941 0.348471 0.937320i \(-0.386701\pi\)
0.348471 + 0.937320i \(0.386701\pi\)
\(312\) 0 0
\(313\) −0.838781 −0.0474107 −0.0237054 0.999719i \(-0.507546\pi\)
−0.0237054 + 0.999719i \(0.507546\pi\)
\(314\) 18.2177 1.02808
\(315\) −5.85587 −0.329941
\(316\) 9.36877 0.527035
\(317\) 3.62055 0.203351 0.101675 0.994818i \(-0.467580\pi\)
0.101675 + 0.994818i \(0.467580\pi\)
\(318\) −16.3974 −0.919522
\(319\) −7.50948 −0.420450
\(320\) −9.31175 −0.520543
\(321\) −10.3341 −0.576795
\(322\) −29.7869 −1.65996
\(323\) −30.2750 −1.68455
\(324\) 1.43221 0.0795672
\(325\) 0 0
\(326\) 1.55115 0.0859100
\(327\) 15.8945 0.878967
\(328\) −23.2929 −1.28613
\(329\) 10.5375 0.580954
\(330\) 1.54519 0.0850598
\(331\) 2.09287 0.115035 0.0575174 0.998345i \(-0.481682\pi\)
0.0575174 + 0.998345i \(0.481682\pi\)
\(332\) 2.20580 0.121059
\(333\) −6.51819 −0.357195
\(334\) −7.63815 −0.417941
\(335\) 6.60562 0.360903
\(336\) −10.7650 −0.587279
\(337\) 21.8264 1.18896 0.594479 0.804111i \(-0.297358\pi\)
0.594479 + 0.804111i \(0.297358\pi\)
\(338\) 0 0
\(339\) −2.93333 −0.159317
\(340\) 3.04995 0.165407
\(341\) −4.02002 −0.217696
\(342\) 11.4867 0.621132
\(343\) 1.74195 0.0940563
\(344\) −9.34352 −0.503769
\(345\) 9.05736 0.487632
\(346\) 2.62620 0.141186
\(347\) −29.8757 −1.60381 −0.801907 0.597449i \(-0.796181\pi\)
−0.801907 + 0.597449i \(0.796181\pi\)
\(348\) −5.70758 −0.305958
\(349\) −2.72847 −0.146052 −0.0730259 0.997330i \(-0.523266\pi\)
−0.0730259 + 0.997330i \(0.523266\pi\)
\(350\) 16.6719 0.891148
\(351\) 0 0
\(352\) 3.35650 0.178902
\(353\) 33.1863 1.76633 0.883164 0.469063i \(-0.155408\pi\)
0.883164 + 0.469063i \(0.155408\pi\)
\(354\) −10.5288 −0.559598
\(355\) −10.7068 −0.568259
\(356\) −2.07985 −0.110232
\(357\) 20.8545 1.10374
\(358\) 15.0115 0.793382
\(359\) 22.1247 1.16769 0.583847 0.811863i \(-0.301547\pi\)
0.583847 + 0.811863i \(0.301547\pi\)
\(360\) −4.90035 −0.258271
\(361\) 24.0763 1.26717
\(362\) 17.9859 0.945320
\(363\) −1.22926 −0.0645195
\(364\) 0 0
\(365\) −7.71541 −0.403843
\(366\) 3.04525 0.159178
\(367\) −26.9673 −1.40768 −0.703840 0.710358i \(-0.748533\pi\)
−0.703840 + 0.710358i \(0.748533\pi\)
\(368\) −16.4062 −0.855230
\(369\) −11.2685 −0.586616
\(370\) −5.50293 −0.286084
\(371\) −41.7364 −2.16685
\(372\) −3.05541 −0.158416
\(373\) −19.4916 −1.00924 −0.504618 0.863343i \(-0.668367\pi\)
−0.504618 + 0.863343i \(0.668367\pi\)
\(374\) 5.42216 0.280373
\(375\) −11.6422 −0.601198
\(376\) 8.81811 0.454759
\(377\) 0 0
\(378\) −23.8552 −1.22698
\(379\) −35.8631 −1.84216 −0.921081 0.389370i \(-0.872693\pi\)
−0.921081 + 0.389370i \(0.872693\pi\)
\(380\) −4.33958 −0.222616
\(381\) −13.8954 −0.711884
\(382\) −11.7617 −0.601779
\(383\) 30.1820 1.54223 0.771114 0.636697i \(-0.219700\pi\)
0.771114 + 0.636697i \(0.219700\pi\)
\(384\) −4.33004 −0.220966
\(385\) 3.93297 0.200443
\(386\) −12.8020 −0.651606
\(387\) −4.52017 −0.229773
\(388\) 11.2008 0.568636
\(389\) 24.7916 1.25698 0.628492 0.777816i \(-0.283673\pi\)
0.628492 + 0.777816i \(0.283673\pi\)
\(390\) 0 0
\(391\) 31.7828 1.60733
\(392\) −20.0862 −1.01451
\(393\) 10.6442 0.536927
\(394\) −2.83825 −0.142989
\(395\) 16.2037 0.815298
\(396\) 0.920595 0.0462616
\(397\) −26.5220 −1.33110 −0.665550 0.746353i \(-0.731803\pi\)
−0.665550 + 0.746353i \(0.731803\pi\)
\(398\) 0.0602110 0.00301810
\(399\) −29.6725 −1.48548
\(400\) 9.18260 0.459130
\(401\) 10.9423 0.546432 0.273216 0.961953i \(-0.411913\pi\)
0.273216 + 0.961953i \(0.411913\pi\)
\(402\) 8.92554 0.445165
\(403\) 0 0
\(404\) −8.14972 −0.405463
\(405\) 2.47707 0.123087
\(406\) 32.4644 1.61118
\(407\) 4.37781 0.217000
\(408\) 17.4516 0.863983
\(409\) 32.8872 1.62617 0.813083 0.582147i \(-0.197787\pi\)
0.813083 + 0.582147i \(0.197787\pi\)
\(410\) −9.51336 −0.469831
\(411\) 8.96523 0.442222
\(412\) −3.30888 −0.163017
\(413\) −26.7989 −1.31869
\(414\) −12.0588 −0.592659
\(415\) 3.81504 0.187273
\(416\) 0 0
\(417\) 15.1645 0.742611
\(418\) −7.71483 −0.377345
\(419\) 10.4527 0.510650 0.255325 0.966855i \(-0.417818\pi\)
0.255325 + 0.966855i \(0.417818\pi\)
\(420\) 2.98925 0.145861
\(421\) 13.9640 0.680566 0.340283 0.940323i \(-0.389477\pi\)
0.340283 + 0.940323i \(0.389477\pi\)
\(422\) 30.1755 1.46892
\(423\) 4.26599 0.207419
\(424\) −34.9261 −1.69616
\(425\) −17.7890 −0.862893
\(426\) −14.4671 −0.700934
\(427\) 7.75109 0.375101
\(428\) −5.19790 −0.251250
\(429\) 0 0
\(430\) −3.81612 −0.184029
\(431\) 11.3165 0.545097 0.272549 0.962142i \(-0.412133\pi\)
0.272549 + 0.962142i \(0.412133\pi\)
\(432\) −13.1391 −0.632155
\(433\) −35.6680 −1.71409 −0.857047 0.515238i \(-0.827704\pi\)
−0.857047 + 0.515238i \(0.827704\pi\)
\(434\) 17.3790 0.834220
\(435\) −9.87152 −0.473303
\(436\) 7.99466 0.382875
\(437\) −45.2217 −2.16325
\(438\) −10.4251 −0.498130
\(439\) 13.2650 0.633104 0.316552 0.948575i \(-0.397475\pi\)
0.316552 + 0.948575i \(0.397475\pi\)
\(440\) 3.29122 0.156903
\(441\) −9.71722 −0.462725
\(442\) 0 0
\(443\) 33.9842 1.61464 0.807319 0.590115i \(-0.200917\pi\)
0.807319 + 0.590115i \(0.200917\pi\)
\(444\) 3.32735 0.157909
\(445\) −3.59720 −0.170524
\(446\) 6.82312 0.323084
\(447\) −0.170637 −0.00807083
\(448\) −32.0252 −1.51305
\(449\) −10.8215 −0.510700 −0.255350 0.966849i \(-0.582191\pi\)
−0.255350 + 0.966849i \(0.582191\pi\)
\(450\) 6.74938 0.318169
\(451\) 7.56827 0.356376
\(452\) −1.47542 −0.0693978
\(453\) 26.1569 1.22896
\(454\) 4.39179 0.206117
\(455\) 0 0
\(456\) −24.8307 −1.16281
\(457\) −27.7721 −1.29912 −0.649562 0.760308i \(-0.725048\pi\)
−0.649562 + 0.760308i \(0.725048\pi\)
\(458\) 21.7631 1.01692
\(459\) 25.4537 1.18808
\(460\) 4.55570 0.212411
\(461\) 3.29026 0.153243 0.0766214 0.997060i \(-0.475587\pi\)
0.0766214 + 0.997060i \(0.475587\pi\)
\(462\) 5.31425 0.247241
\(463\) −14.1359 −0.656950 −0.328475 0.944513i \(-0.606535\pi\)
−0.328475 + 0.944513i \(0.606535\pi\)
\(464\) 17.8809 0.830100
\(465\) −5.28448 −0.245062
\(466\) 17.8957 0.829003
\(467\) 11.3193 0.523796 0.261898 0.965096i \(-0.415652\pi\)
0.261898 + 0.965096i \(0.415652\pi\)
\(468\) 0 0
\(469\) 22.7182 1.04903
\(470\) 3.60152 0.166126
\(471\) −19.0516 −0.877849
\(472\) −22.4260 −1.03224
\(473\) 3.03588 0.139590
\(474\) 21.8945 1.00565
\(475\) 25.3108 1.16134
\(476\) 10.4895 0.480784
\(477\) −16.8964 −0.773634
\(478\) 28.4979 1.30346
\(479\) 26.9047 1.22931 0.614654 0.788797i \(-0.289296\pi\)
0.614654 + 0.788797i \(0.289296\pi\)
\(480\) 4.41226 0.201391
\(481\) 0 0
\(482\) 17.1379 0.780608
\(483\) 31.1503 1.41739
\(484\) −0.618298 −0.0281045
\(485\) 19.3724 0.879653
\(486\) −16.1117 −0.730841
\(487\) −39.8486 −1.80571 −0.902856 0.429944i \(-0.858533\pi\)
−0.902856 + 0.429944i \(0.858533\pi\)
\(488\) 6.48632 0.293622
\(489\) −1.62214 −0.0733559
\(490\) −8.20368 −0.370604
\(491\) −1.66711 −0.0752356 −0.0376178 0.999292i \(-0.511977\pi\)
−0.0376178 + 0.999292i \(0.511977\pi\)
\(492\) 5.75226 0.259332
\(493\) −34.6398 −1.56010
\(494\) 0 0
\(495\) 1.59221 0.0715646
\(496\) 9.57210 0.429800
\(497\) −36.8231 −1.65174
\(498\) 5.15490 0.230996
\(499\) 25.1675 1.12665 0.563327 0.826234i \(-0.309521\pi\)
0.563327 + 0.826234i \(0.309521\pi\)
\(500\) −5.85581 −0.261880
\(501\) 7.98776 0.356867
\(502\) −23.9518 −1.06902
\(503\) 10.5616 0.470919 0.235459 0.971884i \(-0.424341\pi\)
0.235459 + 0.971884i \(0.424341\pi\)
\(504\) −16.8534 −0.750710
\(505\) −14.0953 −0.627233
\(506\) 8.09906 0.360047
\(507\) 0 0
\(508\) −6.98917 −0.310094
\(509\) −22.9522 −1.01734 −0.508670 0.860962i \(-0.669863\pi\)
−0.508670 + 0.860962i \(0.669863\pi\)
\(510\) 7.12765 0.315618
\(511\) −26.5350 −1.17384
\(512\) −22.6489 −1.00095
\(513\) −36.2164 −1.59899
\(514\) −2.70708 −0.119404
\(515\) −5.72286 −0.252179
\(516\) 2.30742 0.101578
\(517\) −2.86516 −0.126010
\(518\) −18.9258 −0.831552
\(519\) −2.74641 −0.120554
\(520\) 0 0
\(521\) 21.3081 0.933524 0.466762 0.884383i \(-0.345420\pi\)
0.466762 + 0.884383i \(0.345420\pi\)
\(522\) 13.1428 0.575244
\(523\) 22.0155 0.962671 0.481335 0.876536i \(-0.340152\pi\)
0.481335 + 0.876536i \(0.340152\pi\)
\(524\) 5.35384 0.233884
\(525\) −17.4350 −0.760924
\(526\) −5.69768 −0.248431
\(527\) −18.5435 −0.807770
\(528\) 2.92701 0.127382
\(529\) 24.4739 1.06408
\(530\) −14.2647 −0.619618
\(531\) −10.8492 −0.470814
\(532\) −14.9248 −0.647071
\(533\) 0 0
\(534\) −4.86055 −0.210337
\(535\) −8.99001 −0.388672
\(536\) 19.0112 0.821158
\(537\) −15.6986 −0.677444
\(538\) 29.5886 1.27566
\(539\) 6.52636 0.281110
\(540\) 3.64850 0.157006
\(541\) 25.7702 1.10795 0.553975 0.832534i \(-0.313110\pi\)
0.553975 + 0.832534i \(0.313110\pi\)
\(542\) −10.4392 −0.448403
\(543\) −18.8092 −0.807179
\(544\) 15.4829 0.663824
\(545\) 13.8271 0.592290
\(546\) 0 0
\(547\) 26.4584 1.13128 0.565640 0.824652i \(-0.308629\pi\)
0.565640 + 0.824652i \(0.308629\pi\)
\(548\) 4.50936 0.192631
\(549\) 3.13793 0.133923
\(550\) −4.53308 −0.193291
\(551\) 49.2866 2.09968
\(552\) 26.0674 1.10950
\(553\) 55.7282 2.36981
\(554\) 22.4770 0.954956
\(555\) 5.75481 0.244278
\(556\) 7.62752 0.323479
\(557\) 18.4881 0.783365 0.391682 0.920100i \(-0.371893\pi\)
0.391682 + 0.920100i \(0.371893\pi\)
\(558\) 7.03567 0.297844
\(559\) 0 0
\(560\) −9.36484 −0.395737
\(561\) −5.67034 −0.239402
\(562\) −0.229961 −0.00970034
\(563\) 12.2594 0.516673 0.258336 0.966055i \(-0.416826\pi\)
0.258336 + 0.966055i \(0.416826\pi\)
\(564\) −2.17767 −0.0916962
\(565\) −2.55180 −0.107355
\(566\) −11.6857 −0.491187
\(567\) 8.51920 0.357773
\(568\) −30.8146 −1.29295
\(569\) −15.0610 −0.631390 −0.315695 0.948861i \(-0.602238\pi\)
−0.315695 + 0.948861i \(0.602238\pi\)
\(570\) −10.1415 −0.424779
\(571\) 30.4829 1.27567 0.637834 0.770174i \(-0.279830\pi\)
0.637834 + 0.770174i \(0.279830\pi\)
\(572\) 0 0
\(573\) 12.3000 0.513840
\(574\) −32.7186 −1.36565
\(575\) −26.5713 −1.10810
\(576\) −12.9650 −0.540207
\(577\) 46.1063 1.91943 0.959715 0.280975i \(-0.0906577\pi\)
0.959715 + 0.280975i \(0.0906577\pi\)
\(578\) 5.02858 0.209161
\(579\) 13.3880 0.556386
\(580\) −4.96521 −0.206169
\(581\) 13.1208 0.544341
\(582\) 26.1760 1.08503
\(583\) 11.3481 0.469992
\(584\) −22.2052 −0.918858
\(585\) 0 0
\(586\) −3.22426 −0.133193
\(587\) 23.9638 0.989090 0.494545 0.869152i \(-0.335335\pi\)
0.494545 + 0.869152i \(0.335335\pi\)
\(588\) 4.96036 0.204562
\(589\) 26.3844 1.08715
\(590\) −9.15933 −0.377084
\(591\) 2.96817 0.122094
\(592\) −10.4240 −0.428426
\(593\) 39.1542 1.60787 0.803936 0.594716i \(-0.202735\pi\)
0.803936 + 0.594716i \(0.202735\pi\)
\(594\) 6.48624 0.266134
\(595\) 18.1420 0.743751
\(596\) −0.0858274 −0.00351563
\(597\) −0.0629669 −0.00257706
\(598\) 0 0
\(599\) −42.5743 −1.73954 −0.869770 0.493457i \(-0.835733\pi\)
−0.869770 + 0.493457i \(0.835733\pi\)
\(600\) −14.5900 −0.595636
\(601\) 44.5295 1.81640 0.908198 0.418540i \(-0.137458\pi\)
0.908198 + 0.418540i \(0.137458\pi\)
\(602\) −13.1245 −0.534914
\(603\) 9.19716 0.374537
\(604\) 13.1565 0.535331
\(605\) −1.06938 −0.0434763
\(606\) −19.0456 −0.773677
\(607\) 39.1704 1.58988 0.794939 0.606690i \(-0.207503\pi\)
0.794939 + 0.606690i \(0.207503\pi\)
\(608\) −22.0296 −0.893417
\(609\) −33.9504 −1.37574
\(610\) 2.64917 0.107262
\(611\) 0 0
\(612\) 4.24653 0.171656
\(613\) 6.12204 0.247267 0.123633 0.992328i \(-0.460545\pi\)
0.123633 + 0.992328i \(0.460545\pi\)
\(614\) −34.9306 −1.40969
\(615\) 9.94881 0.401175
\(616\) 11.3192 0.456065
\(617\) −8.47140 −0.341046 −0.170523 0.985354i \(-0.554546\pi\)
−0.170523 + 0.985354i \(0.554546\pi\)
\(618\) −7.73275 −0.311057
\(619\) −42.4986 −1.70816 −0.854082 0.520139i \(-0.825880\pi\)
−0.854082 + 0.520139i \(0.825880\pi\)
\(620\) −2.65801 −0.106748
\(621\) 38.0201 1.52569
\(622\) 14.4472 0.579280
\(623\) −12.3716 −0.495657
\(624\) 0 0
\(625\) 9.15428 0.366171
\(626\) −0.985952 −0.0394066
\(627\) 8.06795 0.322203
\(628\) −9.58262 −0.382388
\(629\) 20.1940 0.805186
\(630\) −6.88333 −0.274238
\(631\) −34.2480 −1.36339 −0.681696 0.731636i \(-0.738757\pi\)
−0.681696 + 0.731636i \(0.738757\pi\)
\(632\) 46.6349 1.85504
\(633\) −31.5567 −1.25427
\(634\) 4.25581 0.169020
\(635\) −12.0881 −0.479701
\(636\) 8.62515 0.342009
\(637\) 0 0
\(638\) −8.82708 −0.349467
\(639\) −14.9074 −0.589726
\(640\) −3.76685 −0.148898
\(641\) 14.6005 0.576685 0.288342 0.957527i \(-0.406896\pi\)
0.288342 + 0.957527i \(0.406896\pi\)
\(642\) −12.1473 −0.479418
\(643\) 1.58929 0.0626756 0.0313378 0.999509i \(-0.490023\pi\)
0.0313378 + 0.999509i \(0.490023\pi\)
\(644\) 15.6681 0.617409
\(645\) 3.99079 0.157137
\(646\) −35.5870 −1.40015
\(647\) −15.5801 −0.612516 −0.306258 0.951949i \(-0.599077\pi\)
−0.306258 + 0.951949i \(0.599077\pi\)
\(648\) 7.12910 0.280057
\(649\) 7.28662 0.286025
\(650\) 0 0
\(651\) −18.1745 −0.712315
\(652\) −0.815912 −0.0319536
\(653\) −47.8185 −1.87128 −0.935642 0.352951i \(-0.885178\pi\)
−0.935642 + 0.352951i \(0.885178\pi\)
\(654\) 18.6833 0.730575
\(655\) 9.25972 0.361807
\(656\) −18.0209 −0.703598
\(657\) −10.7424 −0.419099
\(658\) 12.3864 0.482874
\(659\) −16.8762 −0.657405 −0.328703 0.944433i \(-0.606611\pi\)
−0.328703 + 0.944433i \(0.606611\pi\)
\(660\) −0.812779 −0.0316374
\(661\) 12.4198 0.483073 0.241537 0.970392i \(-0.422349\pi\)
0.241537 + 0.970392i \(0.422349\pi\)
\(662\) 2.46009 0.0956139
\(663\) 0 0
\(664\) 10.9798 0.426099
\(665\) −25.8131 −1.00099
\(666\) −7.66186 −0.296891
\(667\) −51.7413 −2.00343
\(668\) 4.01771 0.155450
\(669\) −7.13542 −0.275871
\(670\) 7.76462 0.299974
\(671\) −2.10752 −0.0813600
\(672\) 15.1748 0.585379
\(673\) 1.62677 0.0627072 0.0313536 0.999508i \(-0.490018\pi\)
0.0313536 + 0.999508i \(0.490018\pi\)
\(674\) 25.6560 0.988232
\(675\) −21.2800 −0.819068
\(676\) 0 0
\(677\) −21.9960 −0.845377 −0.422688 0.906275i \(-0.638914\pi\)
−0.422688 + 0.906275i \(0.638914\pi\)
\(678\) −3.44801 −0.132420
\(679\) 66.6258 2.55687
\(680\) 15.1817 0.582193
\(681\) −4.59281 −0.175997
\(682\) −4.72536 −0.180943
\(683\) −15.2134 −0.582123 −0.291061 0.956704i \(-0.594008\pi\)
−0.291061 + 0.956704i \(0.594008\pi\)
\(684\) −6.04210 −0.231025
\(685\) 7.79916 0.297990
\(686\) 2.04759 0.0781772
\(687\) −22.7593 −0.868320
\(688\) −7.22876 −0.275594
\(689\) 0 0
\(690\) 10.6465 0.405307
\(691\) 31.9585 1.21576 0.607879 0.794029i \(-0.292020\pi\)
0.607879 + 0.794029i \(0.292020\pi\)
\(692\) −1.38140 −0.0525129
\(693\) 5.47597 0.208015
\(694\) −35.1177 −1.33305
\(695\) 13.1921 0.500407
\(696\) −28.4106 −1.07690
\(697\) 34.9110 1.32235
\(698\) −3.20721 −0.121395
\(699\) −18.7148 −0.707860
\(700\) −8.76950 −0.331456
\(701\) −40.6598 −1.53570 −0.767850 0.640630i \(-0.778673\pi\)
−0.767850 + 0.640630i \(0.778673\pi\)
\(702\) 0 0
\(703\) −28.7327 −1.08367
\(704\) 8.70765 0.328182
\(705\) −3.76637 −0.141850
\(706\) 39.0091 1.46813
\(707\) −48.4769 −1.82316
\(708\) 5.53820 0.208138
\(709\) 41.0918 1.54324 0.771618 0.636087i \(-0.219448\pi\)
0.771618 + 0.636087i \(0.219448\pi\)
\(710\) −12.5854 −0.472322
\(711\) 22.5608 0.846098
\(712\) −10.3529 −0.387990
\(713\) −27.6984 −1.03731
\(714\) 24.5136 0.917398
\(715\) 0 0
\(716\) −7.89613 −0.295092
\(717\) −29.8023 −1.11299
\(718\) 26.0066 0.970558
\(719\) 18.1968 0.678628 0.339314 0.940673i \(-0.389805\pi\)
0.339314 + 0.940673i \(0.389805\pi\)
\(720\) −3.79123 −0.141291
\(721\) −19.6822 −0.733003
\(722\) 28.3007 1.05324
\(723\) −17.9223 −0.666537
\(724\) −9.46071 −0.351605
\(725\) 28.9598 1.07554
\(726\) −1.44494 −0.0536269
\(727\) 20.6633 0.766360 0.383180 0.923674i \(-0.374829\pi\)
0.383180 + 0.923674i \(0.374829\pi\)
\(728\) 0 0
\(729\) 23.7983 0.881417
\(730\) −9.06914 −0.335664
\(731\) 14.0039 0.517953
\(732\) −1.60182 −0.0592050
\(733\) −19.0258 −0.702736 −0.351368 0.936237i \(-0.614283\pi\)
−0.351368 + 0.936237i \(0.614283\pi\)
\(734\) −31.6989 −1.17003
\(735\) 8.57918 0.316448
\(736\) 23.1267 0.852463
\(737\) −6.17708 −0.227536
\(738\) −13.2457 −0.487580
\(739\) −8.63479 −0.317636 −0.158818 0.987308i \(-0.550768\pi\)
−0.158818 + 0.987308i \(0.550768\pi\)
\(740\) 2.89458 0.106407
\(741\) 0 0
\(742\) −49.0594 −1.80103
\(743\) 11.9479 0.438326 0.219163 0.975688i \(-0.429667\pi\)
0.219163 + 0.975688i \(0.429667\pi\)
\(744\) −15.2089 −0.557586
\(745\) −0.148442 −0.00543851
\(746\) −22.9116 −0.838852
\(747\) 5.31177 0.194347
\(748\) −2.85209 −0.104283
\(749\) −30.9187 −1.12974
\(750\) −13.6849 −0.499701
\(751\) 15.8146 0.577084 0.288542 0.957467i \(-0.406830\pi\)
0.288542 + 0.957467i \(0.406830\pi\)
\(752\) 6.82227 0.248782
\(753\) 25.0481 0.912804
\(754\) 0 0
\(755\) 22.7548 0.828131
\(756\) 12.5480 0.456366
\(757\) 23.7363 0.862711 0.431356 0.902182i \(-0.358035\pi\)
0.431356 + 0.902182i \(0.358035\pi\)
\(758\) −42.1556 −1.53116
\(759\) −8.46977 −0.307433
\(760\) −21.6011 −0.783554
\(761\) −32.2561 −1.16928 −0.584641 0.811292i \(-0.698765\pi\)
−0.584641 + 0.811292i \(0.698765\pi\)
\(762\) −16.3335 −0.591700
\(763\) 47.5546 1.72159
\(764\) 6.18670 0.223827
\(765\) 7.34456 0.265543
\(766\) 35.4777 1.28186
\(767\) 0 0
\(768\) 16.3182 0.588831
\(769\) −7.48171 −0.269797 −0.134899 0.990859i \(-0.543071\pi\)
−0.134899 + 0.990859i \(0.543071\pi\)
\(770\) 4.62304 0.166603
\(771\) 2.83099 0.101956
\(772\) 6.73394 0.242360
\(773\) 10.9110 0.392442 0.196221 0.980560i \(-0.437133\pi\)
0.196221 + 0.980560i \(0.437133\pi\)
\(774\) −5.31327 −0.190982
\(775\) 15.5029 0.556882
\(776\) 55.7543 2.00146
\(777\) 19.7921 0.710037
\(778\) 29.1415 1.04477
\(779\) −49.6725 −1.77970
\(780\) 0 0
\(781\) 10.0122 0.358265
\(782\) 37.3594 1.33597
\(783\) −41.4377 −1.48086
\(784\) −15.5400 −0.555000
\(785\) −16.5736 −0.591537
\(786\) 12.5118 0.446280
\(787\) −7.03953 −0.250932 −0.125466 0.992098i \(-0.540043\pi\)
−0.125466 + 0.992098i \(0.540043\pi\)
\(788\) 1.49294 0.0531837
\(789\) 5.95848 0.212127
\(790\) 19.0468 0.677655
\(791\) −8.77622 −0.312046
\(792\) 4.58244 0.162830
\(793\) 0 0
\(794\) −31.1755 −1.10638
\(795\) 14.9176 0.529072
\(796\) −0.0316713 −0.00112256
\(797\) 48.7730 1.72763 0.863815 0.503810i \(-0.168069\pi\)
0.863815 + 0.503810i \(0.168069\pi\)
\(798\) −34.8787 −1.23469
\(799\) −13.2164 −0.467564
\(800\) −12.9441 −0.457645
\(801\) −5.00847 −0.176966
\(802\) 12.8622 0.454180
\(803\) 7.21487 0.254607
\(804\) −4.69489 −0.165576
\(805\) 27.0987 0.955103
\(806\) 0 0
\(807\) −30.9429 −1.08924
\(808\) −40.5668 −1.42713
\(809\) −1.73025 −0.0608323 −0.0304161 0.999537i \(-0.509683\pi\)
−0.0304161 + 0.999537i \(0.509683\pi\)
\(810\) 2.91169 0.102307
\(811\) −24.2221 −0.850555 −0.425277 0.905063i \(-0.639823\pi\)
−0.425277 + 0.905063i \(0.639823\pi\)
\(812\) −17.0765 −0.599267
\(813\) 10.9170 0.382877
\(814\) 5.14593 0.180365
\(815\) −1.41116 −0.0494307
\(816\) 13.5017 0.472654
\(817\) −19.9252 −0.697095
\(818\) 38.6575 1.35163
\(819\) 0 0
\(820\) 5.00409 0.174750
\(821\) 13.5810 0.473980 0.236990 0.971512i \(-0.423839\pi\)
0.236990 + 0.971512i \(0.423839\pi\)
\(822\) 10.5383 0.367564
\(823\) −27.9238 −0.973361 −0.486681 0.873580i \(-0.661792\pi\)
−0.486681 + 0.873580i \(0.661792\pi\)
\(824\) −16.4706 −0.573780
\(825\) 4.74057 0.165045
\(826\) −31.5010 −1.09606
\(827\) 40.2312 1.39897 0.699487 0.714645i \(-0.253412\pi\)
0.699487 + 0.714645i \(0.253412\pi\)
\(828\) 6.34302 0.220435
\(829\) 31.1538 1.08201 0.541007 0.841018i \(-0.318043\pi\)
0.541007 + 0.841018i \(0.318043\pi\)
\(830\) 4.48442 0.155656
\(831\) −23.5058 −0.815408
\(832\) 0 0
\(833\) 30.1048 1.04307
\(834\) 17.8253 0.617239
\(835\) 6.94882 0.240474
\(836\) 4.05805 0.140350
\(837\) −22.1826 −0.766744
\(838\) 12.2868 0.424439
\(839\) 29.6198 1.02259 0.511295 0.859405i \(-0.329166\pi\)
0.511295 + 0.859405i \(0.329166\pi\)
\(840\) 14.8796 0.513395
\(841\) 27.3922 0.944560
\(842\) 16.4141 0.565669
\(843\) 0.240487 0.00828282
\(844\) −15.8725 −0.546354
\(845\) 0 0
\(846\) 5.01449 0.172402
\(847\) −3.67782 −0.126371
\(848\) −27.0212 −0.927910
\(849\) 12.2206 0.419409
\(850\) −20.9102 −0.717214
\(851\) 30.1637 1.03400
\(852\) 7.60979 0.260707
\(853\) 15.9816 0.547201 0.273600 0.961843i \(-0.411785\pi\)
0.273600 + 0.961843i \(0.411785\pi\)
\(854\) 9.11108 0.311775
\(855\) −10.4501 −0.357385
\(856\) −25.8736 −0.884341
\(857\) −43.4613 −1.48461 −0.742304 0.670063i \(-0.766267\pi\)
−0.742304 + 0.670063i \(0.766267\pi\)
\(858\) 0 0
\(859\) −12.6283 −0.430873 −0.215436 0.976518i \(-0.569117\pi\)
−0.215436 + 0.976518i \(0.569117\pi\)
\(860\) 2.00730 0.0684484
\(861\) 34.2162 1.16608
\(862\) 13.3021 0.453071
\(863\) −1.60745 −0.0547183 −0.0273592 0.999626i \(-0.508710\pi\)
−0.0273592 + 0.999626i \(0.508710\pi\)
\(864\) 18.5214 0.630109
\(865\) −2.38919 −0.0812351
\(866\) −41.9262 −1.42471
\(867\) −5.25874 −0.178596
\(868\) −9.14147 −0.310282
\(869\) −15.1525 −0.514014
\(870\) −11.6036 −0.393397
\(871\) 0 0
\(872\) 39.7950 1.34763
\(873\) 26.9726 0.912884
\(874\) −53.1562 −1.79803
\(875\) −34.8321 −1.17754
\(876\) 5.48366 0.185276
\(877\) 29.9609 1.01171 0.505854 0.862619i \(-0.331177\pi\)
0.505854 + 0.862619i \(0.331177\pi\)
\(878\) 15.5925 0.526220
\(879\) 3.37184 0.113729
\(880\) 2.54630 0.0858358
\(881\) −21.5314 −0.725413 −0.362706 0.931903i \(-0.618147\pi\)
−0.362706 + 0.931903i \(0.618147\pi\)
\(882\) −11.4222 −0.384605
\(883\) −18.9850 −0.638897 −0.319449 0.947604i \(-0.603498\pi\)
−0.319449 + 0.947604i \(0.603498\pi\)
\(884\) 0 0
\(885\) 9.57857 0.321980
\(886\) 39.9470 1.34205
\(887\) 20.3848 0.684454 0.342227 0.939617i \(-0.388819\pi\)
0.342227 + 0.939617i \(0.388819\pi\)
\(888\) 16.5625 0.555803
\(889\) −41.5736 −1.39434
\(890\) −4.22836 −0.141735
\(891\) −2.31637 −0.0776014
\(892\) −3.58900 −0.120169
\(893\) 18.8048 0.629278
\(894\) −0.200576 −0.00670827
\(895\) −13.6567 −0.456494
\(896\) −12.9550 −0.432797
\(897\) 0 0
\(898\) −12.7203 −0.424481
\(899\) 30.1882 1.00683
\(900\) −3.55022 −0.118341
\(901\) 52.3467 1.74392
\(902\) 8.89618 0.296211
\(903\) 13.7252 0.456746
\(904\) −7.34418 −0.244264
\(905\) −16.3627 −0.543916
\(906\) 30.7464 1.02148
\(907\) −45.1311 −1.49855 −0.749277 0.662257i \(-0.769599\pi\)
−0.749277 + 0.662257i \(0.769599\pi\)
\(908\) −2.31011 −0.0766636
\(909\) −19.6252 −0.650928
\(910\) 0 0
\(911\) −48.3701 −1.60257 −0.801287 0.598281i \(-0.795851\pi\)
−0.801287 + 0.598281i \(0.795851\pi\)
\(912\) −19.2107 −0.636129
\(913\) −3.56754 −0.118068
\(914\) −32.6449 −1.07980
\(915\) −2.77043 −0.0915874
\(916\) −11.4475 −0.378237
\(917\) 31.8462 1.05166
\(918\) 29.9198 0.987499
\(919\) −13.2762 −0.437942 −0.218971 0.975731i \(-0.570270\pi\)
−0.218971 + 0.975731i \(0.570270\pi\)
\(920\) 22.6769 0.747636
\(921\) 36.5295 1.20369
\(922\) 3.86757 0.127372
\(923\) 0 0
\(924\) −2.79533 −0.0919595
\(925\) −16.8827 −0.555101
\(926\) −16.6161 −0.546040
\(927\) −7.96808 −0.261706
\(928\) −25.2056 −0.827414
\(929\) 7.34338 0.240929 0.120464 0.992718i \(-0.461562\pi\)
0.120464 + 0.992718i \(0.461562\pi\)
\(930\) −6.21168 −0.203689
\(931\) −42.8342 −1.40383
\(932\) −9.41325 −0.308341
\(933\) −15.1085 −0.494629
\(934\) 13.3054 0.435366
\(935\) −4.93282 −0.161320
\(936\) 0 0
\(937\) −0.746195 −0.0243771 −0.0121886 0.999926i \(-0.503880\pi\)
−0.0121886 + 0.999926i \(0.503880\pi\)
\(938\) 26.7043 0.871925
\(939\) 1.03108 0.0336481
\(940\) −1.89442 −0.0617893
\(941\) 9.19693 0.299811 0.149906 0.988700i \(-0.452103\pi\)
0.149906 + 0.988700i \(0.452103\pi\)
\(942\) −22.3943 −0.729646
\(943\) 52.1464 1.69812
\(944\) −17.3503 −0.564703
\(945\) 21.7023 0.705977
\(946\) 3.56855 0.116023
\(947\) 6.18127 0.200864 0.100432 0.994944i \(-0.467977\pi\)
0.100432 + 0.994944i \(0.467977\pi\)
\(948\) −11.5167 −0.374044
\(949\) 0 0
\(950\) 29.7517 0.965274
\(951\) −4.45061 −0.144321
\(952\) 52.2134 1.69225
\(953\) 9.60309 0.311074 0.155537 0.987830i \(-0.450289\pi\)
0.155537 + 0.987830i \(0.450289\pi\)
\(954\) −19.8610 −0.643025
\(955\) 10.7002 0.346250
\(956\) −14.9901 −0.484814
\(957\) 9.23111 0.298399
\(958\) 31.6254 1.02177
\(959\) 26.8230 0.866161
\(960\) 11.4466 0.369436
\(961\) −14.8395 −0.478693
\(962\) 0 0
\(963\) −12.5170 −0.403355
\(964\) −9.01462 −0.290341
\(965\) 11.6467 0.374919
\(966\) 36.6159 1.17810
\(967\) −1.44208 −0.0463741 −0.0231871 0.999731i \(-0.507381\pi\)
−0.0231871 + 0.999731i \(0.507381\pi\)
\(968\) −3.07770 −0.0989210
\(969\) 37.2159 1.19555
\(970\) 22.7714 0.731145
\(971\) −1.61534 −0.0518388 −0.0259194 0.999664i \(-0.508251\pi\)
−0.0259194 + 0.999664i \(0.508251\pi\)
\(972\) 8.47484 0.271831
\(973\) 45.3707 1.45452
\(974\) −46.8403 −1.50086
\(975\) 0 0
\(976\) 5.01824 0.160630
\(977\) −32.0531 −1.02547 −0.512734 0.858547i \(-0.671367\pi\)
−0.512734 + 0.858547i \(0.671367\pi\)
\(978\) −1.90676 −0.0609716
\(979\) 3.36383 0.107509
\(980\) 4.31519 0.137844
\(981\) 19.2519 0.614665
\(982\) −1.95962 −0.0625339
\(983\) 11.4865 0.366362 0.183181 0.983079i \(-0.441361\pi\)
0.183181 + 0.983079i \(0.441361\pi\)
\(984\) 28.6330 0.912787
\(985\) 2.58211 0.0822728
\(986\) −40.7176 −1.29671
\(987\) −12.9534 −0.412311
\(988\) 0 0
\(989\) 20.9176 0.665140
\(990\) 1.87158 0.0594827
\(991\) −8.32889 −0.264576 −0.132288 0.991211i \(-0.542232\pi\)
−0.132288 + 0.991211i \(0.542232\pi\)
\(992\) −13.4932 −0.428409
\(993\) −2.57269 −0.0816418
\(994\) −43.2841 −1.37289
\(995\) −0.0547770 −0.00173655
\(996\) −2.71151 −0.0859174
\(997\) 3.85545 0.122103 0.0610517 0.998135i \(-0.480555\pi\)
0.0610517 + 0.998135i \(0.480555\pi\)
\(998\) 29.5834 0.936446
\(999\) 24.1570 0.764293
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 1859.2.a.t.1.14 yes 21
13.12 even 2 1859.2.a.s.1.8 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.8 21 13.12 even 2
1859.2.a.t.1.14 yes 21 1.1 even 1 trivial