Properties

Label 8281.2.a.cd.1.6
Level $8281$
Weight $2$
Character 8281.1
Self dual yes
Analytic conductor $66.124$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8281 = 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8281.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1241179138\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.4507648.1
Defining polynomial: \(x^{6} - 2 x^{5} - 5 x^{4} + 8 x^{3} + 7 x^{2} - 6 x - 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 637)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.66745\) of defining polynomial
Character \(\chi\) \(=\) 8281.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.44785 q^{2} -0.667452 q^{3} +3.99195 q^{4} -0.910286 q^{5} -1.63382 q^{6} +4.87599 q^{8} -2.55451 q^{9} +O(q^{10})\) \(q+2.44785 q^{2} -0.667452 q^{3} +3.99195 q^{4} -0.910286 q^{5} -1.63382 q^{6} +4.87599 q^{8} -2.55451 q^{9} -2.22824 q^{10} -3.67837 q^{11} -2.66443 q^{12} +0.607572 q^{15} +3.95177 q^{16} +7.18531 q^{17} -6.25304 q^{18} +1.97802 q^{19} -3.63382 q^{20} -9.00407 q^{22} -0.596700 q^{23} -3.25449 q^{24} -4.17138 q^{25} +3.70737 q^{27} -3.64900 q^{29} +1.48724 q^{30} +7.08833 q^{31} -0.0786478 q^{32} +2.45513 q^{33} +17.5885 q^{34} -10.1975 q^{36} -0.710851 q^{37} +4.84189 q^{38} -4.43855 q^{40} -5.27529 q^{41} +11.0790 q^{43} -14.6839 q^{44} +2.32533 q^{45} -1.46063 q^{46} -12.1135 q^{47} -2.63762 q^{48} -10.2109 q^{50} -4.79585 q^{51} -11.4484 q^{53} +9.07506 q^{54} +3.34837 q^{55} -1.32023 q^{57} -8.93219 q^{58} -9.58986 q^{59} +2.42540 q^{60} +6.98536 q^{61} +17.3511 q^{62} -8.09606 q^{64} +6.00978 q^{66} -1.22839 q^{67} +28.6834 q^{68} +0.398269 q^{69} -11.3635 q^{71} -12.4558 q^{72} -6.53419 q^{73} -1.74005 q^{74} +2.78419 q^{75} +7.89616 q^{76} -11.5204 q^{79} -3.59725 q^{80} +5.18904 q^{81} -12.9131 q^{82} -7.16403 q^{83} -6.54069 q^{85} +27.1198 q^{86} +2.43553 q^{87} -17.9357 q^{88} -12.8490 q^{89} +5.69206 q^{90} -2.38200 q^{92} -4.73112 q^{93} -29.6520 q^{94} -1.80056 q^{95} +0.0524936 q^{96} -9.09062 q^{97} +9.39642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 8 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{9} + O(q^{10}) \) \( 6 q + 8 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{15} + 16 q^{17} + 4 q^{18} - 2 q^{19} - 16 q^{20} - 12 q^{22} - 6 q^{23} - 12 q^{24} - 4 q^{25} + 20 q^{27} - 6 q^{29} - 6 q^{31} + 20 q^{32} - 4 q^{33} - 24 q^{36} + 8 q^{38} + 4 q^{40} + 8 q^{41} + 2 q^{43} + 4 q^{44} - 14 q^{45} - 8 q^{46} - 30 q^{47} - 8 q^{48} - 8 q^{50} - 4 q^{51} - 14 q^{53} + 48 q^{54} - 8 q^{55} - 4 q^{57} + 8 q^{58} - 24 q^{59} - 12 q^{60} + 28 q^{62} - 20 q^{64} - 4 q^{66} - 16 q^{67} + 28 q^{68} - 20 q^{69} - 8 q^{71} - 28 q^{72} + 6 q^{73} - 12 q^{74} + 12 q^{75} + 16 q^{76} - 22 q^{79} + 28 q^{80} + 46 q^{81} - 40 q^{82} - 50 q^{83} + 8 q^{85} + 16 q^{86} - 16 q^{87} - 44 q^{88} - 26 q^{89} - 40 q^{90} + 20 q^{92} - 16 q^{93} - 32 q^{94} - 6 q^{95} + 20 q^{96} + 14 q^{97} - 12 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.44785 1.73089 0.865444 0.501005i \(-0.167036\pi\)
0.865444 + 0.501005i \(0.167036\pi\)
\(3\) −0.667452 −0.385353 −0.192677 0.981262i \(-0.561717\pi\)
−0.192677 + 0.981262i \(0.561717\pi\)
\(4\) 3.99195 1.99598
\(5\) −0.910286 −0.407092 −0.203546 0.979065i \(-0.565247\pi\)
−0.203546 + 0.979065i \(0.565247\pi\)
\(6\) −1.63382 −0.667004
\(7\) 0 0
\(8\) 4.87599 1.72392
\(9\) −2.55451 −0.851503
\(10\) −2.22824 −0.704632
\(11\) −3.67837 −1.10907 −0.554534 0.832161i \(-0.687104\pi\)
−0.554534 + 0.832161i \(0.687104\pi\)
\(12\) −2.66443 −0.769156
\(13\) 0 0
\(14\) 0 0
\(15\) 0.607572 0.156874
\(16\) 3.95177 0.987943
\(17\) 7.18531 1.74269 0.871347 0.490668i \(-0.163247\pi\)
0.871347 + 0.490668i \(0.163247\pi\)
\(18\) −6.25304 −1.47386
\(19\) 1.97802 0.453789 0.226894 0.973919i \(-0.427143\pi\)
0.226894 + 0.973919i \(0.427143\pi\)
\(20\) −3.63382 −0.812547
\(21\) 0 0
\(22\) −9.00407 −1.91967
\(23\) −0.596700 −0.124421 −0.0622103 0.998063i \(-0.519815\pi\)
−0.0622103 + 0.998063i \(0.519815\pi\)
\(24\) −3.25449 −0.664320
\(25\) −4.17138 −0.834276
\(26\) 0 0
\(27\) 3.70737 0.713483
\(28\) 0 0
\(29\) −3.64900 −0.677602 −0.338801 0.940858i \(-0.610021\pi\)
−0.338801 + 0.940858i \(0.610021\pi\)
\(30\) 1.48724 0.271532
\(31\) 7.08833 1.27310 0.636551 0.771235i \(-0.280361\pi\)
0.636551 + 0.771235i \(0.280361\pi\)
\(32\) −0.0786478 −0.0139031
\(33\) 2.45513 0.427383
\(34\) 17.5885 3.01641
\(35\) 0 0
\(36\) −10.1975 −1.69958
\(37\) −0.710851 −0.116863 −0.0584316 0.998291i \(-0.518610\pi\)
−0.0584316 + 0.998291i \(0.518610\pi\)
\(38\) 4.84189 0.785458
\(39\) 0 0
\(40\) −4.43855 −0.701796
\(41\) −5.27529 −0.823863 −0.411931 0.911215i \(-0.635146\pi\)
−0.411931 + 0.911215i \(0.635146\pi\)
\(42\) 0 0
\(43\) 11.0790 1.68954 0.844768 0.535132i \(-0.179738\pi\)
0.844768 + 0.535132i \(0.179738\pi\)
\(44\) −14.6839 −2.21367
\(45\) 2.32533 0.346640
\(46\) −1.46063 −0.215358
\(47\) −12.1135 −1.76693 −0.883467 0.468494i \(-0.844797\pi\)
−0.883467 + 0.468494i \(0.844797\pi\)
\(48\) −2.63762 −0.380707
\(49\) 0 0
\(50\) −10.2109 −1.44404
\(51\) −4.79585 −0.671553
\(52\) 0 0
\(53\) −11.4484 −1.57256 −0.786282 0.617868i \(-0.787997\pi\)
−0.786282 + 0.617868i \(0.787997\pi\)
\(54\) 9.07506 1.23496
\(55\) 3.34837 0.451494
\(56\) 0 0
\(57\) −1.32023 −0.174869
\(58\) −8.93219 −1.17285
\(59\) −9.58986 −1.24849 −0.624247 0.781227i \(-0.714594\pi\)
−0.624247 + 0.781227i \(0.714594\pi\)
\(60\) 2.42540 0.313118
\(61\) 6.98536 0.894384 0.447192 0.894438i \(-0.352424\pi\)
0.447192 + 0.894438i \(0.352424\pi\)
\(62\) 17.3511 2.20360
\(63\) 0 0
\(64\) −8.09606 −1.01201
\(65\) 0 0
\(66\) 6.00978 0.739753
\(67\) −1.22839 −0.150072 −0.0750360 0.997181i \(-0.523907\pi\)
−0.0750360 + 0.997181i \(0.523907\pi\)
\(68\) 28.6834 3.47837
\(69\) 0.398269 0.0479459
\(70\) 0 0
\(71\) −11.3635 −1.34859 −0.674297 0.738460i \(-0.735553\pi\)
−0.674297 + 0.738460i \(0.735553\pi\)
\(72\) −12.4558 −1.46793
\(73\) −6.53419 −0.764769 −0.382384 0.924003i \(-0.624897\pi\)
−0.382384 + 0.924003i \(0.624897\pi\)
\(74\) −1.74005 −0.202277
\(75\) 2.78419 0.321491
\(76\) 7.89616 0.905752
\(77\) 0 0
\(78\) 0 0
\(79\) −11.5204 −1.29615 −0.648074 0.761577i \(-0.724425\pi\)
−0.648074 + 0.761577i \(0.724425\pi\)
\(80\) −3.59725 −0.402184
\(81\) 5.18904 0.576560
\(82\) −12.9131 −1.42601
\(83\) −7.16403 −0.786355 −0.393177 0.919463i \(-0.628624\pi\)
−0.393177 + 0.919463i \(0.628624\pi\)
\(84\) 0 0
\(85\) −6.54069 −0.709437
\(86\) 27.1198 2.92440
\(87\) 2.43553 0.261116
\(88\) −17.9357 −1.91195
\(89\) −12.8490 −1.36199 −0.680997 0.732286i \(-0.738453\pi\)
−0.680997 + 0.732286i \(0.738453\pi\)
\(90\) 5.69206 0.599996
\(91\) 0 0
\(92\) −2.38200 −0.248341
\(93\) −4.73112 −0.490594
\(94\) −29.6520 −3.05837
\(95\) −1.80056 −0.184734
\(96\) 0.0524936 0.00535761
\(97\) −9.09062 −0.923012 −0.461506 0.887137i \(-0.652691\pi\)
−0.461506 + 0.887137i \(0.652691\pi\)
\(98\) 0 0
\(99\) 9.39642 0.944375
\(100\) −16.6519 −1.66519
\(101\) −5.80645 −0.577763 −0.288882 0.957365i \(-0.593283\pi\)
−0.288882 + 0.957365i \(0.593283\pi\)
\(102\) −11.7395 −1.16238
\(103\) 12.8682 1.26794 0.633971 0.773357i \(-0.281424\pi\)
0.633971 + 0.773357i \(0.281424\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −28.0240 −2.72193
\(107\) 4.45747 0.430920 0.215460 0.976513i \(-0.430875\pi\)
0.215460 + 0.976513i \(0.430875\pi\)
\(108\) 14.7996 1.42409
\(109\) −0.878896 −0.0841830 −0.0420915 0.999114i \(-0.513402\pi\)
−0.0420915 + 0.999114i \(0.513402\pi\)
\(110\) 8.19628 0.781485
\(111\) 0.474459 0.0450336
\(112\) 0 0
\(113\) −5.36723 −0.504906 −0.252453 0.967609i \(-0.581237\pi\)
−0.252453 + 0.967609i \(0.581237\pi\)
\(114\) −3.23173 −0.302679
\(115\) 0.543168 0.0506507
\(116\) −14.5666 −1.35248
\(117\) 0 0
\(118\) −23.4745 −2.16100
\(119\) 0 0
\(120\) 2.96252 0.270439
\(121\) 2.53037 0.230034
\(122\) 17.0991 1.54808
\(123\) 3.52100 0.317478
\(124\) 28.2963 2.54108
\(125\) 8.34858 0.746720
\(126\) 0 0
\(127\) 6.61029 0.586568 0.293284 0.956025i \(-0.405252\pi\)
0.293284 + 0.956025i \(0.405252\pi\)
\(128\) −19.6606 −1.73777
\(129\) −7.39472 −0.651068
\(130\) 0 0
\(131\) −19.9665 −1.74448 −0.872240 0.489079i \(-0.837333\pi\)
−0.872240 + 0.489079i \(0.837333\pi\)
\(132\) 9.80076 0.853047
\(133\) 0 0
\(134\) −3.00692 −0.259758
\(135\) −3.37476 −0.290453
\(136\) 35.0355 3.00427
\(137\) −5.75451 −0.491641 −0.245821 0.969315i \(-0.579057\pi\)
−0.245821 + 0.969315i \(0.579057\pi\)
\(138\) 0.974900 0.0829890
\(139\) −1.55138 −0.131586 −0.0657931 0.997833i \(-0.520958\pi\)
−0.0657931 + 0.997833i \(0.520958\pi\)
\(140\) 0 0
\(141\) 8.08517 0.680894
\(142\) −27.8160 −2.33427
\(143\) 0 0
\(144\) −10.0948 −0.841237
\(145\) 3.32163 0.275847
\(146\) −15.9947 −1.32373
\(147\) 0 0
\(148\) −2.83768 −0.233256
\(149\) −14.9337 −1.22341 −0.611707 0.791084i \(-0.709517\pi\)
−0.611707 + 0.791084i \(0.709517\pi\)
\(150\) 6.81528 0.556465
\(151\) 7.90102 0.642976 0.321488 0.946914i \(-0.395817\pi\)
0.321488 + 0.946914i \(0.395817\pi\)
\(152\) 9.64481 0.782297
\(153\) −18.3549 −1.48391
\(154\) 0 0
\(155\) −6.45241 −0.518270
\(156\) 0 0
\(157\) 12.4948 0.997194 0.498597 0.866834i \(-0.333849\pi\)
0.498597 + 0.866834i \(0.333849\pi\)
\(158\) −28.2002 −2.24349
\(159\) 7.64127 0.605993
\(160\) 0.0715920 0.00565985
\(161\) 0 0
\(162\) 12.7020 0.997961
\(163\) −7.01427 −0.549400 −0.274700 0.961530i \(-0.588579\pi\)
−0.274700 + 0.961530i \(0.588579\pi\)
\(164\) −21.0587 −1.64441
\(165\) −2.23487 −0.173985
\(166\) −17.5365 −1.36109
\(167\) −4.82764 −0.373574 −0.186787 0.982400i \(-0.559807\pi\)
−0.186787 + 0.982400i \(0.559807\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −16.0106 −1.22796
\(171\) −5.05287 −0.386403
\(172\) 44.2270 3.37227
\(173\) −22.2124 −1.68878 −0.844388 0.535732i \(-0.820036\pi\)
−0.844388 + 0.535732i \(0.820036\pi\)
\(174\) 5.96180 0.451963
\(175\) 0 0
\(176\) −14.5361 −1.09570
\(177\) 6.40077 0.481111
\(178\) −31.4524 −2.35746
\(179\) 4.57505 0.341956 0.170978 0.985275i \(-0.445307\pi\)
0.170978 + 0.985275i \(0.445307\pi\)
\(180\) 9.28262 0.691886
\(181\) −7.23332 −0.537649 −0.268824 0.963189i \(-0.586635\pi\)
−0.268824 + 0.963189i \(0.586635\pi\)
\(182\) 0 0
\(183\) −4.66239 −0.344654
\(184\) −2.90951 −0.214492
\(185\) 0.647078 0.0475741
\(186\) −11.5810 −0.849163
\(187\) −26.4302 −1.93277
\(188\) −48.3565 −3.52676
\(189\) 0 0
\(190\) −4.40751 −0.319754
\(191\) 1.97242 0.142719 0.0713596 0.997451i \(-0.477266\pi\)
0.0713596 + 0.997451i \(0.477266\pi\)
\(192\) 5.40373 0.389981
\(193\) 25.2073 1.81446 0.907230 0.420635i \(-0.138193\pi\)
0.907230 + 0.420635i \(0.138193\pi\)
\(194\) −22.2524 −1.59763
\(195\) 0 0
\(196\) 0 0
\(197\) 3.04497 0.216945 0.108473 0.994099i \(-0.465404\pi\)
0.108473 + 0.994099i \(0.465404\pi\)
\(198\) 23.0010 1.63461
\(199\) 4.05691 0.287587 0.143794 0.989608i \(-0.454070\pi\)
0.143794 + 0.989608i \(0.454070\pi\)
\(200\) −20.3396 −1.43823
\(201\) 0.819893 0.0578308
\(202\) −14.2133 −1.00004
\(203\) 0 0
\(204\) −19.1448 −1.34040
\(205\) 4.80203 0.335388
\(206\) 31.4994 2.19467
\(207\) 1.52428 0.105944
\(208\) 0 0
\(209\) −7.27588 −0.503283
\(210\) 0 0
\(211\) 16.4116 1.12982 0.564910 0.825152i \(-0.308911\pi\)
0.564910 + 0.825152i \(0.308911\pi\)
\(212\) −45.7016 −3.13880
\(213\) 7.58456 0.519685
\(214\) 10.9112 0.745875
\(215\) −10.0851 −0.687797
\(216\) 18.0771 1.22999
\(217\) 0 0
\(218\) −2.15140 −0.145711
\(219\) 4.36125 0.294706
\(220\) 13.3665 0.901170
\(221\) 0 0
\(222\) 1.16140 0.0779482
\(223\) 16.1205 1.07951 0.539755 0.841822i \(-0.318517\pi\)
0.539755 + 0.841822i \(0.318517\pi\)
\(224\) 0 0
\(225\) 10.6558 0.710388
\(226\) −13.1381 −0.873936
\(227\) 8.67804 0.575982 0.287991 0.957633i \(-0.407013\pi\)
0.287991 + 0.957633i \(0.407013\pi\)
\(228\) −5.27031 −0.349034
\(229\) 20.7592 1.37180 0.685902 0.727694i \(-0.259408\pi\)
0.685902 + 0.727694i \(0.259408\pi\)
\(230\) 1.32959 0.0876707
\(231\) 0 0
\(232\) −17.7925 −1.16813
\(233\) −9.84468 −0.644946 −0.322473 0.946579i \(-0.604514\pi\)
−0.322473 + 0.946579i \(0.604514\pi\)
\(234\) 0 0
\(235\) 11.0267 0.719305
\(236\) −38.2823 −2.49196
\(237\) 7.68932 0.499475
\(238\) 0 0
\(239\) −1.13539 −0.0734424 −0.0367212 0.999326i \(-0.511691\pi\)
−0.0367212 + 0.999326i \(0.511691\pi\)
\(240\) 2.40099 0.154983
\(241\) 21.8208 1.40560 0.702802 0.711386i \(-0.251932\pi\)
0.702802 + 0.711386i \(0.251932\pi\)
\(242\) 6.19396 0.398163
\(243\) −14.5855 −0.935662
\(244\) 27.8852 1.78517
\(245\) 0 0
\(246\) 8.61888 0.549519
\(247\) 0 0
\(248\) 34.5626 2.19473
\(249\) 4.78165 0.303025
\(250\) 20.4360 1.29249
\(251\) 9.44377 0.596086 0.298043 0.954552i \(-0.403666\pi\)
0.298043 + 0.954552i \(0.403666\pi\)
\(252\) 0 0
\(253\) 2.19488 0.137991
\(254\) 16.1810 1.01528
\(255\) 4.36559 0.273384
\(256\) −31.9341 −1.99588
\(257\) −3.62752 −0.226279 −0.113139 0.993579i \(-0.536091\pi\)
−0.113139 + 0.993579i \(0.536091\pi\)
\(258\) −18.1011 −1.12693
\(259\) 0 0
\(260\) 0 0
\(261\) 9.32140 0.576980
\(262\) −48.8749 −3.01950
\(263\) 6.59584 0.406717 0.203359 0.979104i \(-0.434814\pi\)
0.203359 + 0.979104i \(0.434814\pi\)
\(264\) 11.9712 0.736776
\(265\) 10.4214 0.640179
\(266\) 0 0
\(267\) 8.57610 0.524849
\(268\) −4.90369 −0.299540
\(269\) 23.5313 1.43473 0.717365 0.696698i \(-0.245348\pi\)
0.717365 + 0.696698i \(0.245348\pi\)
\(270\) −8.26090 −0.502743
\(271\) −2.69767 −0.163872 −0.0819358 0.996638i \(-0.526110\pi\)
−0.0819358 + 0.996638i \(0.526110\pi\)
\(272\) 28.3947 1.72168
\(273\) 0 0
\(274\) −14.0862 −0.850976
\(275\) 15.3439 0.925269
\(276\) 1.58987 0.0956988
\(277\) −24.7549 −1.48738 −0.743690 0.668525i \(-0.766926\pi\)
−0.743690 + 0.668525i \(0.766926\pi\)
\(278\) −3.79754 −0.227761
\(279\) −18.1072 −1.08405
\(280\) 0 0
\(281\) 4.05377 0.241828 0.120914 0.992663i \(-0.461418\pi\)
0.120914 + 0.992663i \(0.461418\pi\)
\(282\) 19.7912 1.17855
\(283\) 12.9237 0.768235 0.384118 0.923284i \(-0.374506\pi\)
0.384118 + 0.923284i \(0.374506\pi\)
\(284\) −45.3624 −2.69176
\(285\) 1.20179 0.0711879
\(286\) 0 0
\(287\) 0 0
\(288\) 0.200906 0.0118385
\(289\) 34.6287 2.03698
\(290\) 8.13085 0.477460
\(291\) 6.06755 0.355686
\(292\) −26.0842 −1.52646
\(293\) 23.5553 1.37611 0.688057 0.725656i \(-0.258464\pi\)
0.688057 + 0.725656i \(0.258464\pi\)
\(294\) 0 0
\(295\) 8.72952 0.508252
\(296\) −3.46610 −0.201463
\(297\) −13.6370 −0.791302
\(298\) −36.5553 −2.11759
\(299\) 0 0
\(300\) 11.1144 0.641688
\(301\) 0 0
\(302\) 19.3405 1.11292
\(303\) 3.87552 0.222643
\(304\) 7.81669 0.448318
\(305\) −6.35868 −0.364097
\(306\) −44.9301 −2.56848
\(307\) −19.9551 −1.13890 −0.569450 0.822026i \(-0.692844\pi\)
−0.569450 + 0.822026i \(0.692844\pi\)
\(308\) 0 0
\(309\) −8.58891 −0.488606
\(310\) −15.7945 −0.897068
\(311\) 6.48069 0.367486 0.183743 0.982974i \(-0.441179\pi\)
0.183743 + 0.982974i \(0.441179\pi\)
\(312\) 0 0
\(313\) 16.1154 0.910897 0.455449 0.890262i \(-0.349479\pi\)
0.455449 + 0.890262i \(0.349479\pi\)
\(314\) 30.5854 1.72603
\(315\) 0 0
\(316\) −45.9889 −2.58708
\(317\) −14.5303 −0.816106 −0.408053 0.912958i \(-0.633792\pi\)
−0.408053 + 0.912958i \(0.633792\pi\)
\(318\) 18.7047 1.04891
\(319\) 13.4224 0.751508
\(320\) 7.36974 0.411981
\(321\) −2.97515 −0.166057
\(322\) 0 0
\(323\) 14.2127 0.790815
\(324\) 20.7144 1.15080
\(325\) 0 0
\(326\) −17.1699 −0.950951
\(327\) 0.586621 0.0324402
\(328\) −25.7223 −1.42028
\(329\) 0 0
\(330\) −5.47062 −0.301148
\(331\) −21.0945 −1.15946 −0.579730 0.814809i \(-0.696842\pi\)
−0.579730 + 0.814809i \(0.696842\pi\)
\(332\) −28.5985 −1.56955
\(333\) 1.81588 0.0995094
\(334\) −11.8173 −0.646615
\(335\) 1.11819 0.0610932
\(336\) 0 0
\(337\) −32.8693 −1.79050 −0.895251 0.445562i \(-0.853004\pi\)
−0.895251 + 0.445562i \(0.853004\pi\)
\(338\) 0 0
\(339\) 3.58236 0.194567
\(340\) −26.1101 −1.41602
\(341\) −26.0735 −1.41196
\(342\) −12.3686 −0.668820
\(343\) 0 0
\(344\) 54.0213 2.91263
\(345\) −0.362538 −0.0195184
\(346\) −54.3725 −2.92308
\(347\) 15.9160 0.854418 0.427209 0.904153i \(-0.359497\pi\)
0.427209 + 0.904153i \(0.359497\pi\)
\(348\) 9.72252 0.521182
\(349\) 29.6245 1.58576 0.792882 0.609375i \(-0.208580\pi\)
0.792882 + 0.609375i \(0.208580\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.289295 0.0154195
\(353\) 28.7078 1.52796 0.763980 0.645240i \(-0.223243\pi\)
0.763980 + 0.645240i \(0.223243\pi\)
\(354\) 15.6681 0.832750
\(355\) 10.3440 0.549002
\(356\) −51.2927 −2.71851
\(357\) 0 0
\(358\) 11.1990 0.591887
\(359\) −27.2931 −1.44048 −0.720238 0.693727i \(-0.755968\pi\)
−0.720238 + 0.693727i \(0.755968\pi\)
\(360\) 11.3383 0.597581
\(361\) −15.0874 −0.794076
\(362\) −17.7061 −0.930610
\(363\) −1.68890 −0.0886443
\(364\) 0 0
\(365\) 5.94798 0.311332
\(366\) −11.4128 −0.596558
\(367\) −9.98326 −0.521122 −0.260561 0.965457i \(-0.583907\pi\)
−0.260561 + 0.965457i \(0.583907\pi\)
\(368\) −2.35802 −0.122921
\(369\) 13.4758 0.701521
\(370\) 1.58395 0.0823455
\(371\) 0 0
\(372\) −18.8864 −0.979214
\(373\) 4.68608 0.242636 0.121318 0.992614i \(-0.461288\pi\)
0.121318 + 0.992614i \(0.461288\pi\)
\(374\) −64.6971 −3.34541
\(375\) −5.57227 −0.287751
\(376\) −59.0653 −3.04606
\(377\) 0 0
\(378\) 0 0
\(379\) 2.45019 0.125858 0.0629288 0.998018i \(-0.479956\pi\)
0.0629288 + 0.998018i \(0.479956\pi\)
\(380\) −7.18777 −0.368725
\(381\) −4.41205 −0.226036
\(382\) 4.82818 0.247031
\(383\) 10.7671 0.550175 0.275087 0.961419i \(-0.411293\pi\)
0.275087 + 0.961419i \(0.411293\pi\)
\(384\) 13.1225 0.669656
\(385\) 0 0
\(386\) 61.7035 3.14063
\(387\) −28.3015 −1.43864
\(388\) −36.2893 −1.84231
\(389\) 14.0372 0.711714 0.355857 0.934540i \(-0.384189\pi\)
0.355857 + 0.934540i \(0.384189\pi\)
\(390\) 0 0
\(391\) −4.28748 −0.216827
\(392\) 0 0
\(393\) 13.3267 0.672241
\(394\) 7.45363 0.375508
\(395\) 10.4869 0.527652
\(396\) 37.5100 1.88495
\(397\) −26.4605 −1.32801 −0.664007 0.747726i \(-0.731146\pi\)
−0.664007 + 0.747726i \(0.731146\pi\)
\(398\) 9.93070 0.497781
\(399\) 0 0
\(400\) −16.4843 −0.824217
\(401\) 19.0156 0.949593 0.474796 0.880096i \(-0.342522\pi\)
0.474796 + 0.880096i \(0.342522\pi\)
\(402\) 2.00697 0.100099
\(403\) 0 0
\(404\) −23.1791 −1.15320
\(405\) −4.72351 −0.234713
\(406\) 0 0
\(407\) 2.61477 0.129609
\(408\) −23.3845 −1.15771
\(409\) −12.7759 −0.631728 −0.315864 0.948804i \(-0.602294\pi\)
−0.315864 + 0.948804i \(0.602294\pi\)
\(410\) 11.7546 0.580520
\(411\) 3.84086 0.189456
\(412\) 51.3693 2.53078
\(413\) 0 0
\(414\) 3.73119 0.183378
\(415\) 6.52132 0.320119
\(416\) 0 0
\(417\) 1.03547 0.0507072
\(418\) −17.8102 −0.871127
\(419\) 12.9811 0.634170 0.317085 0.948397i \(-0.397296\pi\)
0.317085 + 0.948397i \(0.397296\pi\)
\(420\) 0 0
\(421\) 11.6737 0.568943 0.284472 0.958684i \(-0.408182\pi\)
0.284472 + 0.958684i \(0.408182\pi\)
\(422\) 40.1731 1.95559
\(423\) 30.9440 1.50455
\(424\) −55.8225 −2.71098
\(425\) −29.9726 −1.45389
\(426\) 18.5658 0.899517
\(427\) 0 0
\(428\) 17.7940 0.860107
\(429\) 0 0
\(430\) −24.6868 −1.19050
\(431\) 0.467684 0.0225275 0.0112638 0.999937i \(-0.496415\pi\)
0.0112638 + 0.999937i \(0.496415\pi\)
\(432\) 14.6507 0.704881
\(433\) −9.27593 −0.445773 −0.222886 0.974844i \(-0.571548\pi\)
−0.222886 + 0.974844i \(0.571548\pi\)
\(434\) 0 0
\(435\) −2.21703 −0.106298
\(436\) −3.50851 −0.168027
\(437\) −1.18029 −0.0564607
\(438\) 10.6757 0.510104
\(439\) −35.7077 −1.70424 −0.852119 0.523348i \(-0.824683\pi\)
−0.852119 + 0.523348i \(0.824683\pi\)
\(440\) 16.3266 0.778340
\(441\) 0 0
\(442\) 0 0
\(443\) −36.3458 −1.72684 −0.863421 0.504484i \(-0.831683\pi\)
−0.863421 + 0.504484i \(0.831683\pi\)
\(444\) 1.89402 0.0898860
\(445\) 11.6963 0.554457
\(446\) 39.4605 1.86851
\(447\) 9.96750 0.471447
\(448\) 0 0
\(449\) 40.4910 1.91089 0.955444 0.295171i \(-0.0953767\pi\)
0.955444 + 0.295171i \(0.0953767\pi\)
\(450\) 26.0838 1.22960
\(451\) 19.4045 0.913720
\(452\) −21.4257 −1.00778
\(453\) −5.27355 −0.247773
\(454\) 21.2425 0.996960
\(455\) 0 0
\(456\) −6.43744 −0.301461
\(457\) −5.01988 −0.234820 −0.117410 0.993084i \(-0.537459\pi\)
−0.117410 + 0.993084i \(0.537459\pi\)
\(458\) 50.8153 2.37444
\(459\) 26.6386 1.24338
\(460\) 2.16830 0.101098
\(461\) 17.3627 0.808661 0.404331 0.914613i \(-0.367505\pi\)
0.404331 + 0.914613i \(0.367505\pi\)
\(462\) 0 0
\(463\) −35.4306 −1.64660 −0.823301 0.567606i \(-0.807870\pi\)
−0.823301 + 0.567606i \(0.807870\pi\)
\(464\) −14.4200 −0.669433
\(465\) 4.30667 0.199717
\(466\) −24.0983 −1.11633
\(467\) 35.4958 1.64255 0.821275 0.570533i \(-0.193263\pi\)
0.821275 + 0.570533i \(0.193263\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 26.9918 1.24504
\(471\) −8.33967 −0.384272
\(472\) −46.7601 −2.15231
\(473\) −40.7527 −1.87381
\(474\) 18.8223 0.864536
\(475\) −8.25107 −0.378585
\(476\) 0 0
\(477\) 29.2451 1.33904
\(478\) −2.77926 −0.127121
\(479\) 24.0270 1.09782 0.548911 0.835881i \(-0.315042\pi\)
0.548911 + 0.835881i \(0.315042\pi\)
\(480\) −0.0477842 −0.00218104
\(481\) 0 0
\(482\) 53.4140 2.43294
\(483\) 0 0
\(484\) 10.1011 0.459142
\(485\) 8.27506 0.375751
\(486\) −35.7031 −1.61953
\(487\) −20.8076 −0.942880 −0.471440 0.881898i \(-0.656266\pi\)
−0.471440 + 0.881898i \(0.656266\pi\)
\(488\) 34.0606 1.54185
\(489\) 4.68169 0.211713
\(490\) 0 0
\(491\) −36.2195 −1.63456 −0.817281 0.576240i \(-0.804519\pi\)
−0.817281 + 0.576240i \(0.804519\pi\)
\(492\) 14.0557 0.633679
\(493\) −26.2192 −1.18085
\(494\) 0 0
\(495\) −8.55343 −0.384448
\(496\) 28.0115 1.25775
\(497\) 0 0
\(498\) 11.7047 0.524502
\(499\) 40.1828 1.79883 0.899416 0.437094i \(-0.143992\pi\)
0.899416 + 0.437094i \(0.143992\pi\)
\(500\) 33.3271 1.49043
\(501\) 3.22222 0.143958
\(502\) 23.1169 1.03176
\(503\) 38.5636 1.71946 0.859732 0.510745i \(-0.170630\pi\)
0.859732 + 0.510745i \(0.170630\pi\)
\(504\) 0 0
\(505\) 5.28553 0.235203
\(506\) 5.37273 0.238847
\(507\) 0 0
\(508\) 26.3879 1.17078
\(509\) −4.33977 −0.192357 −0.0961785 0.995364i \(-0.530662\pi\)
−0.0961785 + 0.995364i \(0.530662\pi\)
\(510\) 10.6863 0.473197
\(511\) 0 0
\(512\) −38.8484 −1.71687
\(513\) 7.33324 0.323771
\(514\) −8.87962 −0.391663
\(515\) −11.7138 −0.516170
\(516\) −29.5193 −1.29952
\(517\) 44.5578 1.95965
\(518\) 0 0
\(519\) 14.8257 0.650776
\(520\) 0 0
\(521\) 13.7844 0.603905 0.301952 0.953323i \(-0.402362\pi\)
0.301952 + 0.953323i \(0.402362\pi\)
\(522\) 22.8174 0.998689
\(523\) −29.4834 −1.28922 −0.644609 0.764512i \(-0.722980\pi\)
−0.644609 + 0.764512i \(0.722980\pi\)
\(524\) −79.7052 −3.48194
\(525\) 0 0
\(526\) 16.1456 0.703982
\(527\) 50.9318 2.21863
\(528\) 9.70212 0.422231
\(529\) −22.6439 −0.984520
\(530\) 25.5099 1.10808
\(531\) 24.4974 1.06310
\(532\) 0 0
\(533\) 0 0
\(534\) 20.9930 0.908455
\(535\) −4.05758 −0.175424
\(536\) −5.98963 −0.258713
\(537\) −3.05363 −0.131774
\(538\) 57.6011 2.48336
\(539\) 0 0
\(540\) −13.4719 −0.579738
\(541\) −23.2519 −0.999679 −0.499840 0.866118i \(-0.666608\pi\)
−0.499840 + 0.866118i \(0.666608\pi\)
\(542\) −6.60348 −0.283644
\(543\) 4.82789 0.207185
\(544\) −0.565109 −0.0242288
\(545\) 0.800047 0.0342703
\(546\) 0 0
\(547\) 1.18365 0.0506093 0.0253046 0.999680i \(-0.491944\pi\)
0.0253046 + 0.999680i \(0.491944\pi\)
\(548\) −22.9717 −0.981304
\(549\) −17.8442 −0.761571
\(550\) 37.5594 1.60154
\(551\) −7.21780 −0.307488
\(552\) 1.94195 0.0826550
\(553\) 0 0
\(554\) −60.5962 −2.57449
\(555\) −0.431893 −0.0183328
\(556\) −6.19303 −0.262643
\(557\) 6.42824 0.272373 0.136187 0.990683i \(-0.456515\pi\)
0.136187 + 0.990683i \(0.456515\pi\)
\(558\) −44.3236 −1.87637
\(559\) 0 0
\(560\) 0 0
\(561\) 17.6409 0.744798
\(562\) 9.92300 0.418577
\(563\) 11.4563 0.482824 0.241412 0.970423i \(-0.422390\pi\)
0.241412 + 0.970423i \(0.422390\pi\)
\(564\) 32.2756 1.35905
\(565\) 4.88571 0.205543
\(566\) 31.6353 1.32973
\(567\) 0 0
\(568\) −55.4081 −2.32487
\(569\) 38.3335 1.60702 0.803512 0.595288i \(-0.202962\pi\)
0.803512 + 0.595288i \(0.202962\pi\)
\(570\) 2.94180 0.123218
\(571\) 6.25857 0.261913 0.130956 0.991388i \(-0.458195\pi\)
0.130956 + 0.991388i \(0.458195\pi\)
\(572\) 0 0
\(573\) −1.31649 −0.0549973
\(574\) 0 0
\(575\) 2.48906 0.103801
\(576\) 20.6815 0.861728
\(577\) −0.0451932 −0.00188142 −0.000940708 1.00000i \(-0.500299\pi\)
−0.000940708 1.00000i \(0.500299\pi\)
\(578\) 84.7657 3.52579
\(579\) −16.8246 −0.699208
\(580\) 13.2598 0.550583
\(581\) 0 0
\(582\) 14.8524 0.615653
\(583\) 42.1115 1.74408
\(584\) −31.8606 −1.31840
\(585\) 0 0
\(586\) 57.6597 2.38190
\(587\) −2.71409 −0.112023 −0.0560113 0.998430i \(-0.517838\pi\)
−0.0560113 + 0.998430i \(0.517838\pi\)
\(588\) 0 0
\(589\) 14.0209 0.577719
\(590\) 21.3685 0.879728
\(591\) −2.03237 −0.0836006
\(592\) −2.80912 −0.115454
\(593\) −6.78615 −0.278674 −0.139337 0.990245i \(-0.544497\pi\)
−0.139337 + 0.990245i \(0.544497\pi\)
\(594\) −33.3814 −1.36965
\(595\) 0 0
\(596\) −59.6145 −2.44190
\(597\) −2.70779 −0.110823
\(598\) 0 0
\(599\) −26.8337 −1.09640 −0.548198 0.836348i \(-0.684686\pi\)
−0.548198 + 0.836348i \(0.684686\pi\)
\(600\) 13.5757 0.554226
\(601\) 12.3356 0.503178 0.251589 0.967834i \(-0.419047\pi\)
0.251589 + 0.967834i \(0.419047\pi\)
\(602\) 0 0
\(603\) 3.13794 0.127787
\(604\) 31.5405 1.28336
\(605\) −2.30336 −0.0936450
\(606\) 9.48668 0.385370
\(607\) −17.4596 −0.708665 −0.354332 0.935120i \(-0.615292\pi\)
−0.354332 + 0.935120i \(0.615292\pi\)
\(608\) −0.155567 −0.00630907
\(609\) 0 0
\(610\) −15.5651 −0.630211
\(611\) 0 0
\(612\) −73.2720 −2.96185
\(613\) −1.05026 −0.0424198 −0.0212099 0.999775i \(-0.506752\pi\)
−0.0212099 + 0.999775i \(0.506752\pi\)
\(614\) −48.8471 −1.97131
\(615\) −3.20512 −0.129243
\(616\) 0 0
\(617\) −10.5872 −0.426223 −0.213111 0.977028i \(-0.568360\pi\)
−0.213111 + 0.977028i \(0.568360\pi\)
\(618\) −21.0243 −0.845723
\(619\) −1.23805 −0.0497616 −0.0248808 0.999690i \(-0.507921\pi\)
−0.0248808 + 0.999690i \(0.507921\pi\)
\(620\) −25.7577 −1.03445
\(621\) −2.21219 −0.0887720
\(622\) 15.8637 0.636078
\(623\) 0 0
\(624\) 0 0
\(625\) 13.2573 0.530292
\(626\) 39.4481 1.57666
\(627\) 4.85630 0.193942
\(628\) 49.8786 1.99037
\(629\) −5.10769 −0.203657
\(630\) 0 0
\(631\) 21.2658 0.846577 0.423289 0.905995i \(-0.360876\pi\)
0.423289 + 0.905995i \(0.360876\pi\)
\(632\) −56.1735 −2.23446
\(633\) −10.9539 −0.435380
\(634\) −35.5681 −1.41259
\(635\) −6.01725 −0.238787
\(636\) 30.5036 1.20955
\(637\) 0 0
\(638\) 32.8559 1.30078
\(639\) 29.0280 1.14833
\(640\) 17.8968 0.707433
\(641\) 11.0506 0.436474 0.218237 0.975896i \(-0.429969\pi\)
0.218237 + 0.975896i \(0.429969\pi\)
\(642\) −7.28271 −0.287425
\(643\) −6.50321 −0.256461 −0.128231 0.991744i \(-0.540930\pi\)
−0.128231 + 0.991744i \(0.540930\pi\)
\(644\) 0 0
\(645\) 6.73131 0.265045
\(646\) 34.7905 1.36881
\(647\) −0.893941 −0.0351444 −0.0175722 0.999846i \(-0.505594\pi\)
−0.0175722 + 0.999846i \(0.505594\pi\)
\(648\) 25.3017 0.993945
\(649\) 35.2750 1.38467
\(650\) 0 0
\(651\) 0 0
\(652\) −28.0006 −1.09659
\(653\) −38.5477 −1.50849 −0.754244 0.656594i \(-0.771997\pi\)
−0.754244 + 0.656594i \(0.771997\pi\)
\(654\) 1.43596 0.0561504
\(655\) 18.1752 0.710164
\(656\) −20.8468 −0.813930
\(657\) 16.6916 0.651203
\(658\) 0 0
\(659\) −10.8013 −0.420759 −0.210380 0.977620i \(-0.567470\pi\)
−0.210380 + 0.977620i \(0.567470\pi\)
\(660\) −8.92150 −0.347269
\(661\) −40.6339 −1.58047 −0.790237 0.612801i \(-0.790043\pi\)
−0.790237 + 0.612801i \(0.790043\pi\)
\(662\) −51.6361 −2.00690
\(663\) 0 0
\(664\) −34.9318 −1.35562
\(665\) 0 0
\(666\) 4.44498 0.172240
\(667\) 2.17736 0.0843077
\(668\) −19.2717 −0.745645
\(669\) −10.7597 −0.415992
\(670\) 2.73716 0.105746
\(671\) −25.6947 −0.991934
\(672\) 0 0
\(673\) 32.3136 1.24560 0.622799 0.782382i \(-0.285995\pi\)
0.622799 + 0.782382i \(0.285995\pi\)
\(674\) −80.4589 −3.09916
\(675\) −15.4648 −0.595241
\(676\) 0 0
\(677\) −25.2158 −0.969123 −0.484562 0.874757i \(-0.661021\pi\)
−0.484562 + 0.874757i \(0.661021\pi\)
\(678\) 8.76908 0.336774
\(679\) 0 0
\(680\) −31.8923 −1.22302
\(681\) −5.79217 −0.221956
\(682\) −63.8238 −2.44394
\(683\) 6.28731 0.240577 0.120289 0.992739i \(-0.461618\pi\)
0.120289 + 0.992739i \(0.461618\pi\)
\(684\) −20.1708 −0.771250
\(685\) 5.23826 0.200143
\(686\) 0 0
\(687\) −13.8557 −0.528629
\(688\) 43.7818 1.66917
\(689\) 0 0
\(690\) −0.887438 −0.0337842
\(691\) −17.1531 −0.652533 −0.326267 0.945278i \(-0.605791\pi\)
−0.326267 + 0.945278i \(0.605791\pi\)
\(692\) −88.6707 −3.37076
\(693\) 0 0
\(694\) 38.9600 1.47890
\(695\) 1.41220 0.0535678
\(696\) 11.8756 0.450144
\(697\) −37.9046 −1.43574
\(698\) 72.5162 2.74478
\(699\) 6.57085 0.248532
\(700\) 0 0
\(701\) −23.6620 −0.893702 −0.446851 0.894609i \(-0.647455\pi\)
−0.446851 + 0.894609i \(0.647455\pi\)
\(702\) 0 0
\(703\) −1.40608 −0.0530312
\(704\) 29.7803 1.12239
\(705\) −7.35982 −0.277187
\(706\) 70.2722 2.64473
\(707\) 0 0
\(708\) 25.5516 0.960286
\(709\) 21.5030 0.807563 0.403782 0.914855i \(-0.367696\pi\)
0.403782 + 0.914855i \(0.367696\pi\)
\(710\) 25.3205 0.950262
\(711\) 29.4290 1.10367
\(712\) −62.6517 −2.34797
\(713\) −4.22961 −0.158400
\(714\) 0 0
\(715\) 0 0
\(716\) 18.2634 0.682535
\(717\) 0.757819 0.0283013
\(718\) −66.8094 −2.49330
\(719\) −12.8693 −0.479943 −0.239971 0.970780i \(-0.577138\pi\)
−0.239971 + 0.970780i \(0.577138\pi\)
\(720\) 9.18919 0.342461
\(721\) 0 0
\(722\) −36.9317 −1.37446
\(723\) −14.5643 −0.541654
\(724\) −28.8751 −1.07313
\(725\) 15.2214 0.565307
\(726\) −4.13417 −0.153433
\(727\) −16.4329 −0.609463 −0.304732 0.952438i \(-0.598567\pi\)
−0.304732 + 0.952438i \(0.598567\pi\)
\(728\) 0 0
\(729\) −5.83198 −0.215999
\(730\) 14.5597 0.538880
\(731\) 79.6063 2.94434
\(732\) −18.6120 −0.687921
\(733\) −21.7222 −0.802328 −0.401164 0.916006i \(-0.631394\pi\)
−0.401164 + 0.916006i \(0.631394\pi\)
\(734\) −24.4375 −0.902004
\(735\) 0 0
\(736\) 0.0469292 0.00172983
\(737\) 4.51848 0.166440
\(738\) 32.9866 1.21426
\(739\) −1.58001 −0.0581218 −0.0290609 0.999578i \(-0.509252\pi\)
−0.0290609 + 0.999578i \(0.509252\pi\)
\(740\) 2.58310 0.0949568
\(741\) 0 0
\(742\) 0 0
\(743\) −45.9718 −1.68654 −0.843271 0.537489i \(-0.819373\pi\)
−0.843271 + 0.537489i \(0.819373\pi\)
\(744\) −23.0689 −0.845746
\(745\) 13.5939 0.498043
\(746\) 11.4708 0.419976
\(747\) 18.3006 0.669583
\(748\) −105.508 −3.85776
\(749\) 0 0
\(750\) −13.6401 −0.498065
\(751\) −6.42286 −0.234373 −0.117187 0.993110i \(-0.537388\pi\)
−0.117187 + 0.993110i \(0.537388\pi\)
\(752\) −47.8698 −1.74563
\(753\) −6.30326 −0.229704
\(754\) 0 0
\(755\) −7.19219 −0.261750
\(756\) 0 0
\(757\) −6.10016 −0.221714 −0.110857 0.993836i \(-0.535360\pi\)
−0.110857 + 0.993836i \(0.535360\pi\)
\(758\) 5.99768 0.217846
\(759\) −1.46498 −0.0531753
\(760\) −8.77954 −0.318467
\(761\) −18.3948 −0.666812 −0.333406 0.942783i \(-0.608198\pi\)
−0.333406 + 0.942783i \(0.608198\pi\)
\(762\) −10.8000 −0.391243
\(763\) 0 0
\(764\) 7.87380 0.284864
\(765\) 16.7082 0.604088
\(766\) 26.3563 0.952291
\(767\) 0 0
\(768\) 21.3144 0.769119
\(769\) 24.1850 0.872133 0.436066 0.899914i \(-0.356371\pi\)
0.436066 + 0.899914i \(0.356371\pi\)
\(770\) 0 0
\(771\) 2.42120 0.0871973
\(772\) 100.626 3.62162
\(773\) 10.7601 0.387014 0.193507 0.981099i \(-0.438014\pi\)
0.193507 + 0.981099i \(0.438014\pi\)
\(774\) −69.2777 −2.49013
\(775\) −29.5681 −1.06212
\(776\) −44.3258 −1.59120
\(777\) 0 0
\(778\) 34.3609 1.23190
\(779\) −10.4346 −0.373860
\(780\) 0 0
\(781\) 41.7989 1.49568
\(782\) −10.4951 −0.375303
\(783\) −13.5282 −0.483458
\(784\) 0 0
\(785\) −11.3738 −0.405950
\(786\) 32.6216 1.16357
\(787\) 14.7348 0.525238 0.262619 0.964900i \(-0.415414\pi\)
0.262619 + 0.964900i \(0.415414\pi\)
\(788\) 12.1554 0.433018
\(789\) −4.40240 −0.156730
\(790\) 25.6703 0.913307
\(791\) 0 0
\(792\) 45.8168 1.62803
\(793\) 0 0
\(794\) −64.7713 −2.29865
\(795\) −6.95575 −0.246695
\(796\) 16.1950 0.574017
\(797\) 32.5732 1.15380 0.576901 0.816814i \(-0.304262\pi\)
0.576901 + 0.816814i \(0.304262\pi\)
\(798\) 0 0
\(799\) −87.0392 −3.07922
\(800\) 0.328070 0.0115990
\(801\) 32.8229 1.15974
\(802\) 46.5472 1.64364
\(803\) 24.0351 0.848181
\(804\) 3.27297 0.115429
\(805\) 0 0
\(806\) 0 0
\(807\) −15.7060 −0.552878
\(808\) −28.3122 −0.996019
\(809\) −23.6926 −0.832987 −0.416493 0.909139i \(-0.636741\pi\)
−0.416493 + 0.909139i \(0.636741\pi\)
\(810\) −11.5624 −0.406262
\(811\) −45.8568 −1.61025 −0.805125 0.593105i \(-0.797902\pi\)
−0.805125 + 0.593105i \(0.797902\pi\)
\(812\) 0 0
\(813\) 1.80056 0.0631485
\(814\) 6.40056 0.224339
\(815\) 6.38500 0.223657
\(816\) −18.9521 −0.663456
\(817\) 21.9145 0.766693
\(818\) −31.2735 −1.09345
\(819\) 0 0
\(820\) 19.1695 0.669427
\(821\) −13.2923 −0.463905 −0.231953 0.972727i \(-0.574511\pi\)
−0.231953 + 0.972727i \(0.574511\pi\)
\(822\) 9.40183 0.327927
\(823\) −4.13033 −0.143974 −0.0719871 0.997406i \(-0.522934\pi\)
−0.0719871 + 0.997406i \(0.522934\pi\)
\(824\) 62.7453 2.18584
\(825\) −10.2413 −0.356556
\(826\) 0 0
\(827\) 4.67317 0.162502 0.0812510 0.996694i \(-0.474108\pi\)
0.0812510 + 0.996694i \(0.474108\pi\)
\(828\) 6.08484 0.211463
\(829\) 1.74971 0.0607700 0.0303850 0.999538i \(-0.490327\pi\)
0.0303850 + 0.999538i \(0.490327\pi\)
\(830\) 15.9632 0.554091
\(831\) 16.5227 0.573167
\(832\) 0 0
\(833\) 0 0
\(834\) 2.53467 0.0877685
\(835\) 4.39454 0.152079
\(836\) −29.0450 −1.00454
\(837\) 26.2790 0.908336
\(838\) 31.7758 1.09768
\(839\) 15.4495 0.533374 0.266687 0.963783i \(-0.414071\pi\)
0.266687 + 0.963783i \(0.414071\pi\)
\(840\) 0 0
\(841\) −15.6848 −0.540855
\(842\) 28.5755 0.984777
\(843\) −2.70569 −0.0931891
\(844\) 65.5143 2.25510
\(845\) 0 0
\(846\) 75.7462 2.60421
\(847\) 0 0
\(848\) −45.2416 −1.55360
\(849\) −8.62595 −0.296042
\(850\) −73.3684 −2.51652
\(851\) 0.424165 0.0145402
\(852\) 30.2772 1.03728
\(853\) 0.602575 0.0206318 0.0103159 0.999947i \(-0.496716\pi\)
0.0103159 + 0.999947i \(0.496716\pi\)
\(854\) 0 0
\(855\) 4.59956 0.157302
\(856\) 21.7346 0.742874
\(857\) −43.1639 −1.47445 −0.737226 0.675647i \(-0.763865\pi\)
−0.737226 + 0.675647i \(0.763865\pi\)
\(858\) 0 0
\(859\) 37.9408 1.29452 0.647261 0.762269i \(-0.275914\pi\)
0.647261 + 0.762269i \(0.275914\pi\)
\(860\) −40.2592 −1.37283
\(861\) 0 0
\(862\) 1.14482 0.0389927
\(863\) −33.9067 −1.15420 −0.577098 0.816675i \(-0.695815\pi\)
−0.577098 + 0.816675i \(0.695815\pi\)
\(864\) −0.291576 −0.00991962
\(865\) 20.2196 0.687488
\(866\) −22.7061 −0.771583
\(867\) −23.1130 −0.784957
\(868\) 0 0
\(869\) 42.3763 1.43752
\(870\) −5.42695 −0.183991
\(871\) 0 0
\(872\) −4.28549 −0.145125
\(873\) 23.2221 0.785948
\(874\) −2.88916 −0.0977272
\(875\) 0 0
\(876\) 17.4099 0.588226
\(877\) −6.51036 −0.219839 −0.109920 0.993940i \(-0.535059\pi\)
−0.109920 + 0.993940i \(0.535059\pi\)
\(878\) −87.4071 −2.94985
\(879\) −15.7220 −0.530290
\(880\) 13.2320 0.446050
\(881\) −24.5160 −0.825966 −0.412983 0.910739i \(-0.635513\pi\)
−0.412983 + 0.910739i \(0.635513\pi\)
\(882\) 0 0
\(883\) −28.7175 −0.966419 −0.483210 0.875505i \(-0.660529\pi\)
−0.483210 + 0.875505i \(0.660529\pi\)
\(884\) 0 0
\(885\) −5.82653 −0.195857
\(886\) −88.9690 −2.98897
\(887\) 6.94442 0.233171 0.116585 0.993181i \(-0.462805\pi\)
0.116585 + 0.993181i \(0.462805\pi\)
\(888\) 2.31346 0.0776345
\(889\) 0 0
\(890\) 28.6307 0.959704
\(891\) −19.0872 −0.639445
\(892\) 64.3523 2.15467
\(893\) −23.9607 −0.801815
\(894\) 24.3989 0.816022
\(895\) −4.16461 −0.139208
\(896\) 0 0
\(897\) 0 0
\(898\) 99.1158 3.30754
\(899\) −25.8653 −0.862656
\(900\) 42.5375 1.41792
\(901\) −82.2605 −2.74050
\(902\) 47.4991 1.58155
\(903\) 0 0
\(904\) −26.1705 −0.870419
\(905\) 6.58439 0.218873
\(906\) −12.9088 −0.428867
\(907\) 0.229549 0.00762204 0.00381102 0.999993i \(-0.498787\pi\)
0.00381102 + 0.999993i \(0.498787\pi\)
\(908\) 34.6423 1.14965
\(909\) 14.8326 0.491967
\(910\) 0 0
\(911\) −26.6727 −0.883706 −0.441853 0.897087i \(-0.645679\pi\)
−0.441853 + 0.897087i \(0.645679\pi\)
\(912\) −5.21726 −0.172761
\(913\) 26.3519 0.872122
\(914\) −12.2879 −0.406447
\(915\) 4.24411 0.140306
\(916\) 82.8696 2.73809
\(917\) 0 0
\(918\) 65.2071 2.15216
\(919\) −43.2331 −1.42613 −0.713064 0.701099i \(-0.752693\pi\)
−0.713064 + 0.701099i \(0.752693\pi\)
\(920\) 2.64848 0.0873179
\(921\) 13.3191 0.438879
\(922\) 42.5012 1.39970
\(923\) 0 0
\(924\) 0 0
\(925\) 2.96523 0.0974961
\(926\) −86.7287 −2.85008
\(927\) −32.8720 −1.07966
\(928\) 0.286986 0.00942077
\(929\) 23.8491 0.782465 0.391233 0.920292i \(-0.372049\pi\)
0.391233 + 0.920292i \(0.372049\pi\)
\(930\) 10.5421 0.345688
\(931\) 0 0
\(932\) −39.2995 −1.28730
\(933\) −4.32555 −0.141612
\(934\) 86.8883 2.84307
\(935\) 24.0590 0.786815
\(936\) 0 0
\(937\) −27.2033 −0.888694 −0.444347 0.895855i \(-0.646564\pi\)
−0.444347 + 0.895855i \(0.646564\pi\)
\(938\) 0 0
\(939\) −10.7563 −0.351017
\(940\) 44.0182 1.43572
\(941\) −13.4515 −0.438505 −0.219253 0.975668i \(-0.570362\pi\)
−0.219253 + 0.975668i \(0.570362\pi\)
\(942\) −20.4142 −0.665132
\(943\) 3.14777 0.102505
\(944\) −37.8970 −1.23344
\(945\) 0 0
\(946\) −99.7564 −3.24336
\(947\) −15.0341 −0.488543 −0.244271 0.969707i \(-0.578549\pi\)
−0.244271 + 0.969707i \(0.578549\pi\)
\(948\) 30.6954 0.996940
\(949\) 0 0
\(950\) −20.1974 −0.655289
\(951\) 9.69830 0.314489
\(952\) 0 0
\(953\) 28.3775 0.919237 0.459618 0.888116i \(-0.347986\pi\)
0.459618 + 0.888116i \(0.347986\pi\)
\(954\) 71.5876 2.31773
\(955\) −1.79546 −0.0580999
\(956\) −4.53243 −0.146589
\(957\) −8.95877 −0.289596
\(958\) 58.8144 1.90021
\(959\) 0 0
\(960\) −4.91894 −0.158758
\(961\) 19.2444 0.620787
\(962\) 0 0
\(963\) −11.3867 −0.366930
\(964\) 87.1077 2.80555
\(965\) −22.9458 −0.738653
\(966\) 0 0
\(967\) 52.0994 1.67540 0.837701 0.546129i \(-0.183899\pi\)
0.837701 + 0.546129i \(0.183899\pi\)
\(968\) 12.3381 0.396561
\(969\) −9.48628 −0.304743
\(970\) 20.2561 0.650384
\(971\) −20.8418 −0.668845 −0.334423 0.942423i \(-0.608541\pi\)
−0.334423 + 0.942423i \(0.608541\pi\)
\(972\) −58.2247 −1.86756
\(973\) 0 0
\(974\) −50.9337 −1.63202
\(975\) 0 0
\(976\) 27.6046 0.883601
\(977\) −34.6302 −1.10792 −0.553960 0.832544i \(-0.686884\pi\)
−0.553960 + 0.832544i \(0.686884\pi\)
\(978\) 11.4600 0.366452
\(979\) 47.2634 1.51054
\(980\) 0 0
\(981\) 2.24515 0.0716820
\(982\) −88.6597 −2.82924
\(983\) 58.8628 1.87743 0.938717 0.344690i \(-0.112016\pi\)
0.938717 + 0.344690i \(0.112016\pi\)
\(984\) 17.1684 0.547308
\(985\) −2.77180 −0.0883168
\(986\) −64.1806 −2.04393
\(987\) 0 0
\(988\) 0 0
\(989\) −6.61086 −0.210213
\(990\) −20.9375 −0.665437
\(991\) −29.3747 −0.933118 −0.466559 0.884490i \(-0.654507\pi\)
−0.466559 + 0.884490i \(0.654507\pi\)
\(992\) −0.557482 −0.0177001
\(993\) 14.0796 0.446802
\(994\) 0 0
\(995\) −3.69295 −0.117075
\(996\) 19.0881 0.604830
\(997\) −7.50606 −0.237719 −0.118860 0.992911i \(-0.537924\pi\)
−0.118860 + 0.992911i \(0.537924\pi\)
\(998\) 98.3614 3.11358
\(999\) −2.63539 −0.0833799
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 8281.2.a.cd.1.6 6
7.6 odd 2 8281.2.a.cc.1.6 6
13.12 even 2 637.2.a.n.1.1 yes 6
39.38 odd 2 5733.2.a.br.1.6 6
91.12 odd 6 637.2.e.o.508.6 12
91.25 even 6 637.2.e.n.79.6 12
91.38 odd 6 637.2.e.o.79.6 12
91.51 even 6 637.2.e.n.508.6 12
91.90 odd 2 637.2.a.m.1.1 6
273.272 even 2 5733.2.a.bu.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.a.m.1.1 6 91.90 odd 2
637.2.a.n.1.1 yes 6 13.12 even 2
637.2.e.n.79.6 12 91.25 even 6
637.2.e.n.508.6 12 91.51 even 6
637.2.e.o.79.6 12 91.38 odd 6
637.2.e.o.508.6 12 91.12 odd 6
5733.2.a.br.1.6 6 39.38 odd 2
5733.2.a.bu.1.6 6 273.272 even 2
8281.2.a.cc.1.6 6 7.6 odd 2
8281.2.a.cd.1.6 6 1.1 even 1 trivial