Properties

Label 637.2.a.n.1.1
Level $637$
Weight $2$
Character 637.1
Self dual yes
Analytic conductor $5.086$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.4507648.1
Defining polynomial: \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.66745\) of defining polynomial
Character \(\chi\) \(=\) 637.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.44785 q^{2} -0.667452 q^{3} +3.99195 q^{4} +0.910286 q^{5} +1.63382 q^{6} -4.87599 q^{8} -2.55451 q^{9} +O(q^{10})\) \(q-2.44785 q^{2} -0.667452 q^{3} +3.99195 q^{4} +0.910286 q^{5} +1.63382 q^{6} -4.87599 q^{8} -2.55451 q^{9} -2.22824 q^{10} +3.67837 q^{11} -2.66443 q^{12} +1.00000 q^{13} -0.607572 q^{15} +3.95177 q^{16} +7.18531 q^{17} +6.25304 q^{18} -1.97802 q^{19} +3.63382 q^{20} -9.00407 q^{22} -0.596700 q^{23} +3.25449 q^{24} -4.17138 q^{25} -2.44785 q^{26} +3.70737 q^{27} -3.64900 q^{29} +1.48724 q^{30} -7.08833 q^{31} +0.0786478 q^{32} -2.45513 q^{33} -17.5885 q^{34} -10.1975 q^{36} +0.710851 q^{37} +4.84189 q^{38} -0.667452 q^{39} -4.43855 q^{40} +5.27529 q^{41} +11.0790 q^{43} +14.6839 q^{44} -2.32533 q^{45} +1.46063 q^{46} +12.1135 q^{47} -2.63762 q^{48} +10.2109 q^{50} -4.79585 q^{51} +3.99195 q^{52} -11.4484 q^{53} -9.07506 q^{54} +3.34837 q^{55} +1.32023 q^{57} +8.93219 q^{58} +9.58986 q^{59} -2.42540 q^{60} +6.98536 q^{61} +17.3511 q^{62} -8.09606 q^{64} +0.910286 q^{65} +6.00978 q^{66} +1.22839 q^{67} +28.6834 q^{68} +0.398269 q^{69} +11.3635 q^{71} +12.4558 q^{72} +6.53419 q^{73} -1.74005 q^{74} +2.78419 q^{75} -7.89616 q^{76} +1.63382 q^{78} -11.5204 q^{79} +3.59725 q^{80} +5.18904 q^{81} -12.9131 q^{82} +7.16403 q^{83} +6.54069 q^{85} -27.1198 q^{86} +2.43553 q^{87} -17.9357 q^{88} +12.8490 q^{89} +5.69206 q^{90} -2.38200 q^{92} +4.73112 q^{93} -29.6520 q^{94} -1.80056 q^{95} -0.0524936 q^{96} +9.09062 q^{97} -9.39642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} + 6 q^{13} + 12 q^{15} + 16 q^{17} - 4 q^{18} + 2 q^{19} + 16 q^{20} - 12 q^{22} - 6 q^{23} + 12 q^{24} - 4 q^{25} + 20 q^{27} - 6 q^{29} + 6 q^{31} - 20 q^{32} + 4 q^{33} - 24 q^{36} + 8 q^{38} + 8 q^{39} + 4 q^{40} - 8 q^{41} + 2 q^{43} - 4 q^{44} + 14 q^{45} + 8 q^{46} + 30 q^{47} - 8 q^{48} + 8 q^{50} - 4 q^{51} + 4 q^{52} - 14 q^{53} - 48 q^{54} - 8 q^{55} + 4 q^{57} - 8 q^{58} + 24 q^{59} + 12 q^{60} + 28 q^{62} - 20 q^{64} + 6 q^{65} - 4 q^{66} + 16 q^{67} + 28 q^{68} - 20 q^{69} + 8 q^{71} + 28 q^{72} - 6 q^{73} - 12 q^{74} + 12 q^{75} - 16 q^{76} + 4 q^{78} - 22 q^{79} - 28 q^{80} + 46 q^{81} - 40 q^{82} + 50 q^{83} - 8 q^{85} - 16 q^{86} - 16 q^{87} - 44 q^{88} + 26 q^{89} - 40 q^{90} + 20 q^{92} + 16 q^{93} - 32 q^{94} - 6 q^{95} - 20 q^{96} - 14 q^{97} + 12 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44785 −1.73089 −0.865444 0.501005i \(-0.832964\pi\)
−0.865444 + 0.501005i \(0.832964\pi\)
\(3\) −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 \(-0.434753\pi\)
0.203546 + 0.979065i \(0.434753\pi\)
\(6\) 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 \(-0.312896\pi\)
0.554534 + 0.832161i \(0.312896\pi\)
\(12\) −2.66443 −0.769156
\(13\) 1.00000 0.277350
\(14\) 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 \(-0.572857\pi\)
−0.226894 + 0.973919i \(0.572857\pi\)
\(20\) 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
\(26\) −2.44785 −0.480062
\(27\) 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 \(-0.719639\pi\)
−0.636551 + 0.771235i \(0.719639\pi\)
\(32\) 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 \(-0.481390\pi\)
0.0584316 + 0.998291i \(0.481390\pi\)
\(38\) 4.84189 0.785458
\(39\) −0.667452 −0.106878
\(40\) −4.43855 −0.701796
\(41\) 5.27529 0.823863 0.411931 0.911215i \(-0.364854\pi\)
0.411931 + 0.911215i \(0.364854\pi\)
\(42\) 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 \(-0.155203\pi\)
0.883467 + 0.468494i \(0.155203\pi\)
\(48\) −2.63762 −0.380707
\(49\) 0 0
\(50\) 10.2109 1.44404
\(51\) −4.79585 −0.671553
\(52\) 3.99195 0.553584
\(53\) −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 \(-0.285406\pi\)
0.624247 + 0.781227i \(0.285406\pi\)
\(60\) −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
\(65\) 0.910286 0.112907
\(66\) 6.00978 0.739753
\(67\) 1.22839 0.150072 0.0750360 0.997181i \(-0.476093\pi\)
0.0750360 + 0.997181i \(0.476093\pi\)
\(68\) 28.6834 3.47837
\(69\) 0.398269 0.0479459
\(70\) 0 0
\(71\) 11.3635 1.34859 0.674297 0.738460i \(-0.264447\pi\)
0.674297 + 0.738460i \(0.264447\pi\)
\(72\) 12.4558 1.46793
\(73\) 6.53419 0.764769 0.382384 0.924003i \(-0.375103\pi\)
0.382384 + 0.924003i \(0.375103\pi\)
\(74\) −1.74005 −0.202277
\(75\) 2.78419 0.321491
\(76\) −7.89616 −0.905752
\(77\) 0 0
\(78\) 1.63382 0.184994
\(79\) −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 \(-0.371376\pi\)
0.393177 + 0.919463i \(0.371376\pi\)
\(84\) 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 \(-0.261547\pi\)
0.680997 + 0.732286i \(0.261547\pi\)
\(90\) 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 \(-0.347309\pi\)
0.461506 + 0.887137i \(0.347309\pi\)
\(98\) 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 \(0.281424\pi\)
\(104\) −4.87599 −0.478130
\(105\) 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 \(-0.486598\pi\)
0.0420915 + 0.999114i \(0.486598\pi\)
\(110\) −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
\(117\) −2.55451 −0.236164
\(118\) −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
\(130\) −2.22824 −0.195430
\(131\) −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 \(-0.420943\pi\)
0.245821 + 0.969315i \(0.420943\pi\)
\(138\) −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
\(143\) 3.67837 0.307600
\(144\) −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 \(-0.290483\pi\)
0.611707 + 0.791084i \(0.290483\pi\)
\(150\) −6.81528 −0.556465
\(151\) −7.90102 −0.642976 −0.321488 0.946914i \(-0.604183\pi\)
−0.321488 + 0.946914i \(0.604183\pi\)
\(152\) 9.64481 0.782297
\(153\) −18.3549 −1.48391
\(154\) 0 0
\(155\) −6.45241 −0.518270
\(156\) −2.66443 −0.213325
\(157\) 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 \(-0.411421\pi\)
0.274700 + 0.961530i \(0.411421\pi\)
\(164\) 21.0587 1.64441
\(165\) −2.23487 −0.173985
\(166\) −17.5365 −1.36109
\(167\) 4.82764 0.373574 0.186787 0.982400i \(-0.440193\pi\)
0.186787 + 0.982400i \(0.440193\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −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 \(-0.861807\pi\)
−0.907230 + 0.420635i \(0.861807\pi\)
\(194\) −22.2524 −1.59763
\(195\) −0.607572 −0.0435091
\(196\) 0 0
\(197\) −3.04497 −0.216945 −0.108473 0.994099i \(-0.534596\pi\)
−0.108473 + 0.994099i \(0.534596\pi\)
\(198\) 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
\(208\) 3.95177 0.274006
\(209\) −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
\(221\) 7.18531 0.483336
\(222\) 1.16140 0.0779482
\(223\) −16.1205 −1.07951 −0.539755 0.841822i \(-0.681483\pi\)
−0.539755 + 0.841822i \(0.681483\pi\)
\(224\) 0 0
\(225\) 10.6558 0.710388
\(226\) 13.1381 0.873936
\(227\) −8.67804 −0.575982 −0.287991 0.957633i \(-0.592987\pi\)
−0.287991 + 0.957633i \(0.592987\pi\)
\(228\) 5.27031 0.349034
\(229\) −20.7592 −1.37180 −0.685902 0.727694i \(-0.740592\pi\)
−0.685902 + 0.727694i \(0.740592\pi\)
\(230\) 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 \(0.604514\pi\)
\(234\) 6.25304 0.408774
\(235\) 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 \(-0.488309\pi\)
0.0367212 + 0.999326i \(0.488309\pi\)
\(240\) −2.40099 −0.154983
\(241\) −21.8208 −1.40560 −0.702802 0.711386i \(-0.748068\pi\)
−0.702802 + 0.711386i \(0.748068\pi\)
\(242\) −6.19396 −0.398163
\(243\) −14.5855 −0.935662
\(244\) 27.8852 1.78517
\(245\) 0 0
\(246\) 8.61888 0.549519
\(247\) −1.97802 −0.125858
\(248\) 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
\(260\) 3.63382 0.225360
\(261\) 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 \(-0.473890\pi\)
0.0819358 + 0.996638i \(0.473890\pi\)
\(272\) 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 \(-0.538582\pi\)
−0.120914 + 0.992663i \(0.538582\pi\)
\(282\) 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
\(286\) −9.00407 −0.532422
\(287\) 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 \(-0.741536\pi\)
−0.688057 + 0.725656i \(0.741536\pi\)
\(294\) 0 0
\(295\) 8.72952 0.508252
\(296\) −3.46610 −0.201463
\(297\) 13.6370 0.791302
\(298\) −36.5553 −2.11759
\(299\) −0.596700 −0.0345081
\(300\) 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 \(-0.307156\pi\)
0.569450 + 0.822026i \(0.307156\pi\)
\(308\) 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 \(0.441179\pi\)
\(312\) 3.25449 0.184249
\(313\) 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 \(-0.366208\pi\)
0.408053 + 0.912958i \(0.366208\pi\)
\(318\) −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
\(325\) −4.17138 −0.231386
\(326\) −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 \(-0.303158\pi\)
0.579730 + 0.814809i \(0.303158\pi\)
\(332\) 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 \(0.853004\pi\)
\(338\) −2.44785 −0.133145
\(339\) 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 \(-0.791420\pi\)
−0.792882 + 0.609375i \(0.791420\pi\)
\(350\) 0 0
\(351\) 3.70737 0.197885
\(352\) 0.289295 0.0154195
\(353\) −28.7078 −1.52796 −0.763980 0.645240i \(-0.776757\pi\)
−0.763980 + 0.645240i \(0.776757\pi\)
\(354\) 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 \(-0.244032\pi\)
0.720238 + 0.693727i \(0.244032\pi\)
\(360\) 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
\(377\) −3.64900 −0.187933
\(378\) 0 0
\(379\) −2.45019 −0.125858 −0.0629288 0.998018i \(-0.520044\pi\)
−0.0629288 + 0.998018i \(0.520044\pi\)
\(380\) −7.18777 −0.368725
\(381\) −4.41205 −0.226036
\(382\) −4.82818 −0.247031
\(383\) −10.7671 −0.550175 −0.275087 0.961419i \(-0.588707\pi\)
−0.275087 + 0.961419i \(0.588707\pi\)
\(384\) −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 \(0.384189\pi\)
\(390\) 1.48724 0.0753095
\(391\) −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 \(-0.268854\pi\)
0.664007 + 0.747726i \(0.268854\pi\)
\(398\) −9.93070 −0.497781
\(399\) 0 0
\(400\) −16.4843 −0.824217
\(401\) −19.0156 −0.949593 −0.474796 0.880096i \(-0.657478\pi\)
−0.474796 + 0.880096i \(0.657478\pi\)
\(402\) 2.00697 0.100099
\(403\) −7.08833 −0.353095
\(404\) −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 \(-0.397706\pi\)
0.315864 + 0.948804i \(0.397706\pi\)
\(410\) −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
\(416\) 0.0786478 0.00385603
\(417\) 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 \(-0.591818\pi\)
−0.284472 + 0.958684i \(0.591818\pi\)
\(422\) −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
\(429\) −2.45513 −0.118535
\(430\) −24.6868 −1.19050
\(431\) −0.467684 −0.0225275 −0.0112638 0.999937i \(-0.503585\pi\)
−0.0112638 + 0.999937i \(0.503585\pi\)
\(432\) 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
\(442\) −17.5885 −0.836601
\(443\) −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 \(-0.904623\pi\)
−0.955444 + 0.295171i \(0.904623\pi\)
\(450\) −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 \(-0.462541\pi\)
0.117410 + 0.993084i \(0.462541\pi\)
\(458\) 50.8153 2.37444
\(459\) 26.6386 1.24338
\(460\) −2.16830 −0.101098
\(461\) −17.3627 −0.808661 −0.404331 0.914613i \(-0.632495\pi\)
−0.404331 + 0.914613i \(0.632495\pi\)
\(462\) 0 0
\(463\) 35.4306 1.64660 0.823301 0.567606i \(-0.192130\pi\)
0.823301 + 0.567606i \(0.192130\pi\)
\(464\) −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 \(0.193263\pi\)
\(468\) −10.1975 −0.471378
\(469\) 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 \(-0.684958\pi\)
−0.548911 + 0.835881i \(0.684958\pi\)
\(480\) −0.0477842 −0.00218104
\(481\) 0.710851 0.0324120
\(482\) 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 \(-0.343734\pi\)
0.471440 + 0.881898i \(0.343734\pi\)
\(488\) −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
\(494\) 4.84189 0.217847
\(495\) −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 \(-0.856008\pi\)
−0.899416 + 0.437094i \(0.856008\pi\)
\(500\) −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
\(507\) −0.667452 −0.0296426
\(508\) 26.3879 1.17078
\(509\) 4.33977 0.192357 0.0961785 0.995364i \(-0.469338\pi\)
0.0961785 + 0.995364i \(0.469338\pi\)
\(510\) 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
\(520\) −4.43855 −0.194643
\(521\) 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
\(533\) 5.27529 0.228498
\(534\) 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 \(-0.333392\pi\)
0.499840 + 0.866118i \(0.333392\pi\)
\(542\) −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 \(-0.543485\pi\)
−0.136187 + 0.990683i \(0.543485\pi\)
\(558\) −44.3236 −1.87637
\(559\) 11.0790 0.468593
\(560\) 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 \(0.458195\pi\)
\(572\) 14.6839 0.613963
\(573\) −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 \(-0.499701\pi\)
0.000940708 1.00000i \(0.499701\pi\)
\(578\) −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
\(585\) −2.32533 −0.0961407
\(586\) 57.6597 2.38190
\(587\) 2.71409 0.112023 0.0560113 0.998430i \(-0.482162\pi\)
0.0560113 + 0.998430i \(0.482162\pi\)
\(588\) 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 \(-0.455503\pi\)
0.139337 + 0.990245i \(0.455503\pi\)
\(594\) −33.3814 −1.36965
\(595\) 0 0
\(596\) 59.6145 2.44190
\(597\) −2.70779 −0.110823
\(598\) 1.46063 0.0597296
\(599\) −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
\(611\) 12.1135 0.490059
\(612\) −73.2720 −2.96185
\(613\) 1.05026 0.0424198 0.0212099 0.999775i \(-0.493248\pi\)
0.0212099 + 0.999775i \(0.493248\pi\)
\(614\) −48.8471 −1.97131
\(615\) −3.20512 −0.129243
\(616\) 0 0
\(617\) 10.5872 0.426223 0.213111 0.977028i \(-0.431640\pi\)
0.213111 + 0.977028i \(0.431640\pi\)
\(618\) 21.0243 0.845723
\(619\) 1.23805 0.0497616 0.0248808 0.999690i \(-0.492079\pi\)
0.0248808 + 0.999690i \(0.492079\pi\)
\(620\) −25.7577 −1.03445
\(621\) −2.21219 −0.0887720
\(622\) −15.8637 −0.636078
\(623\) 0 0
\(624\) −2.63762 −0.105589
\(625\) 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 \(-0.639124\pi\)
−0.423289 + 0.905995i \(0.639124\pi\)
\(632\) 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 \(-0.459070\pi\)
0.128231 + 0.991744i \(0.459070\pi\)
\(644\) 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
\(650\) 10.2109 0.400504
\(651\) 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 \(-0.209957\pi\)
0.790237 + 0.612801i \(0.209957\pi\)
\(662\) −51.6361 −2.00690
\(663\) −4.79585 −0.186255
\(664\) −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
\(676\) 3.99195 0.153537
\(677\) −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 \(-0.538382\pi\)
−0.120289 + 0.992739i \(0.538382\pi\)
\(684\) 20.1708 0.771250
\(685\) 5.23826 0.200143
\(686\) 0 0
\(687\) 13.8557 0.528629
\(688\) 43.7818 1.66917
\(689\) −11.4484 −0.436151
\(690\) −0.887438 −0.0337842
\(691\) 17.1531 0.652533 0.326267 0.945278i \(-0.394209\pi\)
0.326267 + 0.945278i \(0.394209\pi\)
\(692\) −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 \(0.647455\pi\)
\(702\) −9.07506 −0.342516
\(703\) −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 \(-0.632304\pi\)
−0.403782 + 0.914855i \(0.632304\pi\)
\(710\) −25.3205 −0.950262
\(711\) 29.4290 1.10367
\(712\) −62.6517 −2.34797
\(713\) 4.22961 0.158400
\(714\) 0 0
\(715\) 3.34837 0.125222
\(716\) 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 \(-0.368606\pi\)
0.401164 + 0.916006i \(0.368606\pi\)
\(734\) 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 \(-0.490748\pi\)
0.0290609 + 0.999578i \(0.490748\pi\)
\(740\) 2.58310 0.0949568
\(741\) 1.32023 0.0485000
\(742\) 0 0
\(743\) 45.9718 1.68654 0.843271 0.537489i \(-0.180627\pi\)
0.843271 + 0.537489i \(0.180627\pi\)
\(744\) −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
\(754\) 8.93219 0.325291
\(755\) −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 \(-0.391802\pi\)
0.333406 + 0.942783i \(0.391802\pi\)
\(762\) 10.8000 0.391243
\(763\) 0 0
\(764\) 7.87380 0.284864
\(765\) −16.7082 −0.604088
\(766\) 26.3563 0.952291
\(767\) 9.58986 0.346270
\(768\) 21.3144 0.769119
\(769\) −24.1850 −0.872133 −0.436066 0.899914i \(-0.643629\pi\)
−0.436066 + 0.899914i \(0.643629\pi\)
\(770\) 0 0
\(771\) 2.42120 0.0871973
\(772\) −100.626 −3.62162
\(773\) −10.7601 −0.387014 −0.193507 0.981099i \(-0.561986\pi\)
−0.193507 + 0.981099i \(0.561986\pi\)
\(774\) 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
\(780\) −2.42540 −0.0868432
\(781\) 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 \(-0.584586\pi\)
−0.262619 + 0.964900i \(0.584586\pi\)
\(788\) −12.1554 −0.433018
\(789\) −4.40240 −0.156730
\(790\) 25.6703 0.913307
\(791\) 0 0
\(792\) 45.8168 1.62803
\(793\) 6.98536 0.248058
\(794\) −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
\(806\) 17.3511 0.611168
\(807\) −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 \(-0.202098\pi\)
0.805125 + 0.593105i \(0.202098\pi\)
\(812\) 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 \(-0.425489\pi\)
0.231953 + 0.972727i \(0.425489\pi\)
\(822\) 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 \(-0.525892\pi\)
−0.0812510 + 0.996694i \(0.525892\pi\)
\(828\) 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
\(832\) −8.09606 −0.280681
\(833\) 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 \(-0.585929\pi\)
−0.266687 + 0.963783i \(0.585929\pi\)
\(840\) 0 0
\(841\) −15.6848 −0.540855
\(842\) 28.5755 0.984777
\(843\) 2.70569 0.0931891
\(844\) 65.5143 2.25510
\(845\) 0.910286 0.0313148
\(846\) 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 \(-0.503284\pi\)
−0.0103159 + 0.999947i \(0.503284\pi\)
\(854\) 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 \(0.763865\pi\)
\(858\) 6.00978 0.205171
\(859\) 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 \(-0.304185\pi\)
0.577098 + 0.816675i \(0.304185\pi\)
\(864\) 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
\(871\) 1.22839 0.0416225
\(872\) −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 \(-0.464941\pi\)
0.109920 + 0.993940i \(0.464941\pi\)
\(878\) 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 \(0.660529\pi\)
\(884\) 28.6834 0.964727
\(885\) −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
\(897\) 0.398269 0.0132978
\(898\) 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
\(923\) 11.3635 0.374033
\(924\) 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 \(-0.627951\pi\)
−0.391233 + 0.920292i \(0.627951\pi\)
\(930\) −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
\(936\) 12.4558 0.407129
\(937\) −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 \(-0.429638\pi\)
0.219253 + 0.975668i \(0.429638\pi\)
\(942\) 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 \(-0.421451\pi\)
0.244271 + 0.969707i \(0.421451\pi\)
\(948\) 30.6954 0.996940
\(949\) 6.53419 0.212109
\(950\) −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
\(962\) −1.74005 −0.0561016
\(963\) −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 \(-0.816101\pi\)
−0.837701 + 0.546129i \(0.816101\pi\)
\(968\) −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
\(975\) 2.78419 0.0891655
\(976\) 27.6046 0.883601
\(977\) 34.6302 1.10792 0.553960 0.832544i \(-0.313116\pi\)
0.553960 + 0.832544i \(0.313116\pi\)
\(978\) 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 \(-0.887984\pi\)
−0.938717 + 0.344690i \(0.887984\pi\)
\(984\) 17.1684 0.547308
\(985\) −2.77180 −0.0883168
\(986\) 64.1806 2.04393
\(987\) 0 0
\(988\) −7.89616 −0.251210
\(989\) −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 637.2.a.n.1.1 yes 6
3.2 odd 2 5733.2.a.br.1.6 6
7.2 even 3 637.2.e.n.508.6 12
7.3 odd 6 637.2.e.o.79.6 12
7.4 even 3 637.2.e.n.79.6 12
7.5 odd 6 637.2.e.o.508.6 12
7.6 odd 2 637.2.a.m.1.1 6
13.12 even 2 8281.2.a.cd.1.6 6
21.20 even 2 5733.2.a.bu.1.6 6
91.90 odd 2 8281.2.a.cc.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.a.m.1.1 6 7.6 odd 2
637.2.a.n.1.1 yes 6 1.1 even 1 trivial
637.2.e.n.79.6 12 7.4 even 3
637.2.e.n.508.6 12 7.2 even 3
637.2.e.o.79.6 12 7.3 odd 6
637.2.e.o.508.6 12 7.5 odd 6
5733.2.a.br.1.6 6 3.2 odd 2
5733.2.a.bu.1.6 6 21.20 even 2
8281.2.a.cc.1.6 6 91.90 odd 2
8281.2.a.cd.1.6 6 13.12 even 2