Properties

Label 105.4.a.d.1.1
Level 105
Weight 4
Character 105.1
Self dual yes
Analytic conductor 6.195
Analytic rank 1
Dimension 2
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.19520055060\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of \(x^{2} - x - 1\)
Character \(\chi\) \(=\) 105.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.23607 q^{2} +3.00000 q^{3} +9.94427 q^{4} -5.00000 q^{5} -12.7082 q^{6} -7.00000 q^{7} -8.23607 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-4.23607 q^{2} +3.00000 q^{3} +9.94427 q^{4} -5.00000 q^{5} -12.7082 q^{6} -7.00000 q^{7} -8.23607 q^{8} +9.00000 q^{9} +21.1803 q^{10} -41.5279 q^{11} +29.8328 q^{12} +88.9706 q^{13} +29.6525 q^{14} -15.0000 q^{15} -44.6656 q^{16} -120.387 q^{17} -38.1246 q^{18} -112.138 q^{19} -49.7214 q^{20} -21.0000 q^{21} +175.915 q^{22} -115.279 q^{23} -24.7082 q^{24} +25.0000 q^{25} -376.885 q^{26} +27.0000 q^{27} -69.6099 q^{28} -144.833 q^{29} +63.5410 q^{30} -258.079 q^{31} +255.095 q^{32} -124.584 q^{33} +509.967 q^{34} +35.0000 q^{35} +89.4984 q^{36} +48.3344 q^{37} +475.023 q^{38} +266.912 q^{39} +41.1803 q^{40} +200.885 q^{41} +88.9574 q^{42} -218.217 q^{43} -412.964 q^{44} -45.0000 q^{45} +488.328 q^{46} +575.659 q^{47} -133.997 q^{48} +49.0000 q^{49} -105.902 q^{50} -361.161 q^{51} +884.748 q^{52} -184.302 q^{53} -114.374 q^{54} +207.639 q^{55} +57.6525 q^{56} -336.413 q^{57} +613.522 q^{58} -151.502 q^{59} -149.164 q^{60} -529.830 q^{61} +1093.24 q^{62} -63.0000 q^{63} -723.276 q^{64} -444.853 q^{65} +527.745 q^{66} +1.28485 q^{67} -1197.16 q^{68} -345.836 q^{69} -148.262 q^{70} -61.4226 q^{71} -74.1246 q^{72} +484.800 q^{73} -204.748 q^{74} +75.0000 q^{75} -1115.13 q^{76} +290.695 q^{77} -1130.66 q^{78} +878.257 q^{79} +223.328 q^{80} +81.0000 q^{81} -850.964 q^{82} +491.830 q^{83} -208.830 q^{84} +601.935 q^{85} +924.381 q^{86} -434.498 q^{87} +342.026 q^{88} -415.560 q^{89} +190.623 q^{90} -622.794 q^{91} -1146.36 q^{92} -774.237 q^{93} -2438.53 q^{94} +560.689 q^{95} +765.286 q^{96} -1031.70 q^{97} -207.567 q^{98} -373.751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{2} + 6q^{3} + 2q^{4} - 10q^{5} - 12q^{6} - 14q^{7} - 12q^{8} + 18q^{9} + O(q^{10}) \) \( 2q - 4q^{2} + 6q^{3} + 2q^{4} - 10q^{5} - 12q^{6} - 14q^{7} - 12q^{8} + 18q^{9} + 20q^{10} - 92q^{11} + 6q^{12} + 8q^{13} + 28q^{14} - 30q^{15} + 18q^{16} - 44q^{17} - 36q^{18} - 108q^{19} - 10q^{20} - 42q^{21} + 164q^{22} - 320q^{23} - 36q^{24} + 50q^{25} - 396q^{26} + 54q^{27} - 14q^{28} - 236q^{29} + 60q^{30} - 60q^{31} + 300q^{32} - 276q^{33} + 528q^{34} + 70q^{35} + 18q^{36} + 204q^{37} + 476q^{38} + 24q^{39} + 60q^{40} + 44q^{41} + 84q^{42} + 136q^{43} - 12q^{44} - 90q^{45} + 440q^{46} + 400q^{47} + 54q^{48} + 98q^{49} - 100q^{50} - 132q^{51} + 1528q^{52} + 16q^{53} - 108q^{54} + 460q^{55} + 84q^{56} - 324q^{57} + 592q^{58} - 464q^{59} - 30q^{60} - 684q^{61} + 1140q^{62} - 126q^{63} - 1214q^{64} - 40q^{65} + 492q^{66} + 736q^{67} - 1804q^{68} - 960q^{69} - 140q^{70} - 740q^{71} - 108q^{72} + 424q^{73} - 168q^{74} + 150q^{75} - 1148q^{76} + 644q^{77} - 1188q^{78} - 408q^{79} - 90q^{80} + 162q^{81} - 888q^{82} + 608q^{83} - 42q^{84} + 220q^{85} + 1008q^{86} - 708q^{87} + 532q^{88} - 1332q^{89} + 180q^{90} - 56q^{91} + 480q^{92} - 180q^{93} - 2480q^{94} + 540q^{95} + 900q^{96} - 2448q^{97} - 196q^{98} - 828q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.23607 −1.49768 −0.748838 0.662753i \(-0.769388\pi\)
−0.748838 + 0.662753i \(0.769388\pi\)
\(3\) 3.00000 0.577350
\(4\) 9.94427 1.24303
\(5\) −5.00000 −0.447214
\(6\) −12.7082 −0.864684
\(7\) −7.00000 −0.377964
\(8\) −8.23607 −0.363986
\(9\) 9.00000 0.333333
\(10\) 21.1803 0.669781
\(11\) −41.5279 −1.13828 −0.569142 0.822239i \(-0.692725\pi\)
−0.569142 + 0.822239i \(0.692725\pi\)
\(12\) 29.8328 0.717666
\(13\) 88.9706 1.89815 0.949077 0.315044i \(-0.102019\pi\)
0.949077 + 0.315044i \(0.102019\pi\)
\(14\) 29.6525 0.566068
\(15\) −15.0000 −0.258199
\(16\) −44.6656 −0.697900
\(17\) −120.387 −1.71754 −0.858769 0.512364i \(-0.828770\pi\)
−0.858769 + 0.512364i \(0.828770\pi\)
\(18\) −38.1246 −0.499225
\(19\) −112.138 −1.35401 −0.677004 0.735979i \(-0.736722\pi\)
−0.677004 + 0.735979i \(0.736722\pi\)
\(20\) −49.7214 −0.555902
\(21\) −21.0000 −0.218218
\(22\) 175.915 1.70478
\(23\) −115.279 −1.04510 −0.522549 0.852609i \(-0.675019\pi\)
−0.522549 + 0.852609i \(0.675019\pi\)
\(24\) −24.7082 −0.210148
\(25\) 25.0000 0.200000
\(26\) −376.885 −2.84282
\(27\) 27.0000 0.192450
\(28\) −69.6099 −0.469823
\(29\) −144.833 −0.927406 −0.463703 0.885991i \(-0.653480\pi\)
−0.463703 + 0.885991i \(0.653480\pi\)
\(30\) 63.5410 0.386698
\(31\) −258.079 −1.49524 −0.747618 0.664128i \(-0.768803\pi\)
−0.747618 + 0.664128i \(0.768803\pi\)
\(32\) 255.095 1.40922
\(33\) −124.584 −0.657188
\(34\) 509.967 2.57231
\(35\) 35.0000 0.169031
\(36\) 89.4984 0.414345
\(37\) 48.3344 0.214760 0.107380 0.994218i \(-0.465754\pi\)
0.107380 + 0.994218i \(0.465754\pi\)
\(38\) 475.023 2.02787
\(39\) 266.912 1.09590
\(40\) 41.1803 0.162780
\(41\) 200.885 0.765196 0.382598 0.923915i \(-0.375029\pi\)
0.382598 + 0.923915i \(0.375029\pi\)
\(42\) 88.9574 0.326820
\(43\) −218.217 −0.773901 −0.386950 0.922101i \(-0.626472\pi\)
−0.386950 + 0.922101i \(0.626472\pi\)
\(44\) −412.964 −1.41493
\(45\) −45.0000 −0.149071
\(46\) 488.328 1.56522
\(47\) 575.659 1.78657 0.893283 0.449496i \(-0.148396\pi\)
0.893283 + 0.449496i \(0.148396\pi\)
\(48\) −133.997 −0.402933
\(49\) 49.0000 0.142857
\(50\) −105.902 −0.299535
\(51\) −361.161 −0.991621
\(52\) 884.748 2.35947
\(53\) −184.302 −0.477657 −0.238828 0.971062i \(-0.576763\pi\)
−0.238828 + 0.971062i \(0.576763\pi\)
\(54\) −114.374 −0.288228
\(55\) 207.639 0.509056
\(56\) 57.6525 0.137574
\(57\) −336.413 −0.781737
\(58\) 613.522 1.38895
\(59\) −151.502 −0.334302 −0.167151 0.985931i \(-0.553457\pi\)
−0.167151 + 0.985931i \(0.553457\pi\)
\(60\) −149.164 −0.320950
\(61\) −529.830 −1.11209 −0.556047 0.831151i \(-0.687683\pi\)
−0.556047 + 0.831151i \(0.687683\pi\)
\(62\) 1093.24 2.23938
\(63\) −63.0000 −0.125988
\(64\) −723.276 −1.41265
\(65\) −444.853 −0.848880
\(66\) 527.745 0.984256
\(67\) 1.28485 0.00234283 0.00117142 0.999999i \(-0.499627\pi\)
0.00117142 + 0.999999i \(0.499627\pi\)
\(68\) −1197.16 −2.13496
\(69\) −345.836 −0.603388
\(70\) −148.262 −0.253153
\(71\) −61.4226 −0.102669 −0.0513347 0.998682i \(-0.516348\pi\)
−0.0513347 + 0.998682i \(0.516348\pi\)
\(72\) −74.1246 −0.121329
\(73\) 484.800 0.777282 0.388641 0.921389i \(-0.372945\pi\)
0.388641 + 0.921389i \(0.372945\pi\)
\(74\) −204.748 −0.321641
\(75\) 75.0000 0.115470
\(76\) −1115.13 −1.68308
\(77\) 290.695 0.430231
\(78\) −1130.66 −1.64130
\(79\) 878.257 1.25078 0.625390 0.780312i \(-0.284940\pi\)
0.625390 + 0.780312i \(0.284940\pi\)
\(80\) 223.328 0.312111
\(81\) 81.0000 0.111111
\(82\) −850.964 −1.14602
\(83\) 491.830 0.650426 0.325213 0.945641i \(-0.394564\pi\)
0.325213 + 0.945641i \(0.394564\pi\)
\(84\) −208.830 −0.271252
\(85\) 601.935 0.768106
\(86\) 924.381 1.15905
\(87\) −434.498 −0.535438
\(88\) 342.026 0.414320
\(89\) −415.560 −0.494936 −0.247468 0.968896i \(-0.579599\pi\)
−0.247468 + 0.968896i \(0.579599\pi\)
\(90\) 190.623 0.223260
\(91\) −622.794 −0.717435
\(92\) −1146.36 −1.29909
\(93\) −774.237 −0.863275
\(94\) −2438.53 −2.67570
\(95\) 560.689 0.605531
\(96\) 765.286 0.813611
\(97\) −1031.70 −1.07993 −0.539964 0.841688i \(-0.681562\pi\)
−0.539964 + 0.841688i \(0.681562\pi\)
\(98\) −207.567 −0.213954
\(99\) −373.751 −0.379428
\(100\) 248.607 0.248607
\(101\) 1447.19 1.42576 0.712878 0.701288i \(-0.247391\pi\)
0.712878 + 0.701288i \(0.247391\pi\)
\(102\) 1529.90 1.48513
\(103\) −163.567 −0.156473 −0.0782364 0.996935i \(-0.524929\pi\)
−0.0782364 + 0.996935i \(0.524929\pi\)
\(104\) −732.768 −0.690902
\(105\) 105.000 0.0975900
\(106\) 780.715 0.715375
\(107\) −129.653 −0.117141 −0.0585703 0.998283i \(-0.518654\pi\)
−0.0585703 + 0.998283i \(0.518654\pi\)
\(108\) 268.495 0.239222
\(109\) 566.681 0.497965 0.248983 0.968508i \(-0.419904\pi\)
0.248983 + 0.968508i \(0.419904\pi\)
\(110\) −879.574 −0.762401
\(111\) 145.003 0.123992
\(112\) 312.659 0.263782
\(113\) 809.890 0.674230 0.337115 0.941463i \(-0.390549\pi\)
0.337115 + 0.941463i \(0.390549\pi\)
\(114\) 1425.07 1.17079
\(115\) 576.393 0.467382
\(116\) −1440.26 −1.15280
\(117\) 800.735 0.632718
\(118\) 641.771 0.500676
\(119\) 842.709 0.649168
\(120\) 123.541 0.0939808
\(121\) 393.563 0.295690
\(122\) 2244.39 1.66556
\(123\) 602.656 0.441786
\(124\) −2566.41 −1.85863
\(125\) −125.000 −0.0894427
\(126\) 266.872 0.188689
\(127\) −2584.25 −1.80563 −0.902816 0.430028i \(-0.858504\pi\)
−0.902816 + 0.430028i \(0.858504\pi\)
\(128\) 1023.08 0.706473
\(129\) −654.650 −0.446812
\(130\) 1884.43 1.27135
\(131\) −1421.10 −0.947804 −0.473902 0.880578i \(-0.657155\pi\)
−0.473902 + 0.880578i \(0.657155\pi\)
\(132\) −1238.89 −0.816908
\(133\) 784.964 0.511767
\(134\) −5.44272 −0.00350880
\(135\) −135.000 −0.0860663
\(136\) 991.515 0.625160
\(137\) 104.878 0.0654037 0.0327019 0.999465i \(-0.489589\pi\)
0.0327019 + 0.999465i \(0.489589\pi\)
\(138\) 1464.98 0.903679
\(139\) −913.160 −0.557217 −0.278609 0.960405i \(-0.589873\pi\)
−0.278609 + 0.960405i \(0.589873\pi\)
\(140\) 348.050 0.210111
\(141\) 1726.98 1.03147
\(142\) 260.190 0.153765
\(143\) −3694.76 −2.16064
\(144\) −401.991 −0.232633
\(145\) 724.164 0.414749
\(146\) −2053.65 −1.16412
\(147\) 147.000 0.0824786
\(148\) 480.650 0.266954
\(149\) 1781.45 0.979476 0.489738 0.871870i \(-0.337092\pi\)
0.489738 + 0.871870i \(0.337092\pi\)
\(150\) −317.705 −0.172937
\(151\) 1407.53 0.758564 0.379282 0.925281i \(-0.376171\pi\)
0.379282 + 0.925281i \(0.376171\pi\)
\(152\) 923.574 0.492841
\(153\) −1083.48 −0.572512
\(154\) −1231.40 −0.644346
\(155\) 1290.39 0.668690
\(156\) 2654.24 1.36224
\(157\) −1598.94 −0.812798 −0.406399 0.913696i \(-0.633216\pi\)
−0.406399 + 0.913696i \(0.633216\pi\)
\(158\) −3720.36 −1.87326
\(159\) −552.906 −0.275775
\(160\) −1275.48 −0.630220
\(161\) 806.950 0.395010
\(162\) −343.122 −0.166408
\(163\) −204.892 −0.0984562 −0.0492281 0.998788i \(-0.515676\pi\)
−0.0492281 + 0.998788i \(0.515676\pi\)
\(164\) 1997.66 0.951165
\(165\) 622.918 0.293904
\(166\) −2083.42 −0.974127
\(167\) −1165.94 −0.540259 −0.270129 0.962824i \(-0.587067\pi\)
−0.270129 + 0.962824i \(0.587067\pi\)
\(168\) 172.957 0.0794283
\(169\) 5718.76 2.60299
\(170\) −2549.84 −1.15037
\(171\) −1009.24 −0.451336
\(172\) −2170.01 −0.961985
\(173\) −2538.00 −1.11538 −0.557690 0.830049i \(-0.688312\pi\)
−0.557690 + 0.830049i \(0.688312\pi\)
\(174\) 1840.56 0.801913
\(175\) −175.000 −0.0755929
\(176\) 1854.87 0.794409
\(177\) −454.505 −0.193009
\(178\) 1760.34 0.741254
\(179\) 392.255 0.163791 0.0818954 0.996641i \(-0.473903\pi\)
0.0818954 + 0.996641i \(0.473903\pi\)
\(180\) −447.492 −0.185301
\(181\) −2978.08 −1.22298 −0.611489 0.791253i \(-0.709429\pi\)
−0.611489 + 0.791253i \(0.709429\pi\)
\(182\) 2638.20 1.07448
\(183\) −1589.49 −0.642068
\(184\) 949.443 0.380401
\(185\) −241.672 −0.0960436
\(186\) 3279.72 1.29291
\(187\) 4999.41 1.95504
\(188\) 5724.51 2.22076
\(189\) −189.000 −0.0727393
\(190\) −2375.12 −0.906890
\(191\) −1097.37 −0.415722 −0.207861 0.978158i \(-0.566650\pi\)
−0.207861 + 0.978158i \(0.566650\pi\)
\(192\) −2169.83 −0.815592
\(193\) 3500.31 1.30548 0.652740 0.757582i \(-0.273619\pi\)
0.652740 + 0.757582i \(0.273619\pi\)
\(194\) 4370.34 1.61738
\(195\) −1334.56 −0.490101
\(196\) 487.269 0.177576
\(197\) 1573.96 0.569237 0.284618 0.958641i \(-0.408133\pi\)
0.284618 + 0.958641i \(0.408133\pi\)
\(198\) 1583.23 0.568260
\(199\) −3396.62 −1.20995 −0.604976 0.796244i \(-0.706817\pi\)
−0.604976 + 0.796244i \(0.706817\pi\)
\(200\) −205.902 −0.0727972
\(201\) 3.85456 0.00135263
\(202\) −6130.42 −2.13532
\(203\) 1013.83 0.350527
\(204\) −3591.48 −1.23262
\(205\) −1004.43 −0.342206
\(206\) 692.879 0.234346
\(207\) −1037.51 −0.348366
\(208\) −3973.93 −1.32472
\(209\) 4656.84 1.54125
\(210\) −444.787 −0.146158
\(211\) 3337.81 1.08903 0.544513 0.838753i \(-0.316715\pi\)
0.544513 + 0.838753i \(0.316715\pi\)
\(212\) −1832.75 −0.593744
\(213\) −184.268 −0.0592762
\(214\) 549.220 0.175439
\(215\) 1091.08 0.346099
\(216\) −222.374 −0.0700492
\(217\) 1806.55 0.565146
\(218\) −2400.50 −0.745791
\(219\) 1454.40 0.448764
\(220\) 2064.82 0.632774
\(221\) −10710.9 −3.26015
\(222\) −614.243 −0.185700
\(223\) 127.328 0.0382356 0.0191178 0.999817i \(-0.493914\pi\)
0.0191178 + 0.999817i \(0.493914\pi\)
\(224\) −1785.67 −0.532633
\(225\) 225.000 0.0666667
\(226\) −3430.75 −1.00978
\(227\) 3844.12 1.12398 0.561990 0.827144i \(-0.310036\pi\)
0.561990 + 0.827144i \(0.310036\pi\)
\(228\) −3345.39 −0.971726
\(229\) 2536.95 0.732080 0.366040 0.930599i \(-0.380713\pi\)
0.366040 + 0.930599i \(0.380713\pi\)
\(230\) −2441.64 −0.699987
\(231\) 872.085 0.248394
\(232\) 1192.85 0.337563
\(233\) 3987.44 1.12114 0.560570 0.828107i \(-0.310582\pi\)
0.560570 + 0.828107i \(0.310582\pi\)
\(234\) −3391.97 −0.947607
\(235\) −2878.30 −0.798976
\(236\) −1506.57 −0.415549
\(237\) 2634.77 0.722138
\(238\) −3569.77 −0.972244
\(239\) −3367.18 −0.911317 −0.455659 0.890155i \(-0.650596\pi\)
−0.455659 + 0.890155i \(0.650596\pi\)
\(240\) 669.984 0.180197
\(241\) −939.551 −0.251128 −0.125564 0.992086i \(-0.540074\pi\)
−0.125564 + 0.992086i \(0.540074\pi\)
\(242\) −1667.16 −0.442848
\(243\) 243.000 0.0641500
\(244\) −5268.77 −1.38237
\(245\) −245.000 −0.0638877
\(246\) −2552.89 −0.661653
\(247\) −9976.96 −2.57012
\(248\) 2125.56 0.544246
\(249\) 1475.49 0.375523
\(250\) 529.508 0.133956
\(251\) −1403.96 −0.353056 −0.176528 0.984296i \(-0.556487\pi\)
−0.176528 + 0.984296i \(0.556487\pi\)
\(252\) −626.489 −0.156608
\(253\) 4787.28 1.18962
\(254\) 10947.1 2.70425
\(255\) 1805.80 0.443466
\(256\) 1452.36 0.354579
\(257\) −1964.86 −0.476905 −0.238453 0.971154i \(-0.576640\pi\)
−0.238453 + 0.971154i \(0.576640\pi\)
\(258\) 2773.14 0.669179
\(259\) −338.341 −0.0811717
\(260\) −4423.74 −1.05519
\(261\) −1303.50 −0.309135
\(262\) 6019.89 1.41950
\(263\) −393.821 −0.0923347 −0.0461673 0.998934i \(-0.514701\pi\)
−0.0461673 + 0.998934i \(0.514701\pi\)
\(264\) 1026.08 0.239208
\(265\) 921.509 0.213615
\(266\) −3325.16 −0.766462
\(267\) −1246.68 −0.285751
\(268\) 12.7769 0.00291222
\(269\) −1877.03 −0.425444 −0.212722 0.977113i \(-0.568233\pi\)
−0.212722 + 0.977113i \(0.568233\pi\)
\(270\) 571.869 0.128899
\(271\) −689.909 −0.154646 −0.0773228 0.997006i \(-0.524637\pi\)
−0.0773228 + 0.997006i \(0.524637\pi\)
\(272\) 5377.16 1.19867
\(273\) −1868.38 −0.414211
\(274\) −444.269 −0.0979536
\(275\) −1038.20 −0.227657
\(276\) −3439.09 −0.750031
\(277\) 6289.13 1.36418 0.682088 0.731270i \(-0.261072\pi\)
0.682088 + 0.731270i \(0.261072\pi\)
\(278\) 3868.21 0.834531
\(279\) −2322.71 −0.498412
\(280\) −288.262 −0.0615249
\(281\) −1954.87 −0.415010 −0.207505 0.978234i \(-0.566534\pi\)
−0.207505 + 0.978234i \(0.566534\pi\)
\(282\) −7315.60 −1.54481
\(283\) 5033.96 1.05738 0.528688 0.848816i \(-0.322684\pi\)
0.528688 + 0.848816i \(0.322684\pi\)
\(284\) −610.803 −0.127621
\(285\) 1682.07 0.349604
\(286\) 15651.2 3.23594
\(287\) −1406.20 −0.289217
\(288\) 2295.86 0.469738
\(289\) 9580.03 1.94993
\(290\) −3067.61 −0.621159
\(291\) −3095.09 −0.623497
\(292\) 4820.99 0.966188
\(293\) 6369.12 1.26993 0.634963 0.772543i \(-0.281015\pi\)
0.634963 + 0.772543i \(0.281015\pi\)
\(294\) −622.702 −0.123526
\(295\) 757.508 0.149504
\(296\) −398.085 −0.0781697
\(297\) −1121.25 −0.219063
\(298\) −7546.34 −1.46694
\(299\) −10256.4 −1.98376
\(300\) 745.820 0.143533
\(301\) 1527.52 0.292507
\(302\) −5962.39 −1.13608
\(303\) 4341.58 0.823160
\(304\) 5008.70 0.944963
\(305\) 2649.15 0.497344
\(306\) 4589.71 0.857438
\(307\) −6619.83 −1.23066 −0.615332 0.788268i \(-0.710978\pi\)
−0.615332 + 0.788268i \(0.710978\pi\)
\(308\) 2890.75 0.534792
\(309\) −490.700 −0.0903396
\(310\) −5466.20 −1.00148
\(311\) −9909.22 −1.80675 −0.903377 0.428848i \(-0.858920\pi\)
−0.903377 + 0.428848i \(0.858920\pi\)
\(312\) −2198.30 −0.398892
\(313\) −422.336 −0.0762678 −0.0381339 0.999273i \(-0.512141\pi\)
−0.0381339 + 0.999273i \(0.512141\pi\)
\(314\) 6773.22 1.21731
\(315\) 315.000 0.0563436
\(316\) 8733.63 1.55476
\(317\) −4902.78 −0.868668 −0.434334 0.900752i \(-0.643016\pi\)
−0.434334 + 0.900752i \(0.643016\pi\)
\(318\) 2342.15 0.413022
\(319\) 6014.60 1.05565
\(320\) 3616.38 0.631755
\(321\) −388.960 −0.0676312
\(322\) −3418.30 −0.591597
\(323\) 13499.9 2.32556
\(324\) 805.486 0.138115
\(325\) 2224.26 0.379631
\(326\) 867.935 0.147455
\(327\) 1700.04 0.287500
\(328\) −1654.51 −0.278521
\(329\) −4029.62 −0.675258
\(330\) −2638.72 −0.440172
\(331\) −5281.74 −0.877071 −0.438535 0.898714i \(-0.644503\pi\)
−0.438535 + 0.898714i \(0.644503\pi\)
\(332\) 4890.89 0.808501
\(333\) 435.009 0.0715867
\(334\) 4939.01 0.809133
\(335\) −6.42426 −0.00104775
\(336\) 937.978 0.152294
\(337\) 4459.60 0.720860 0.360430 0.932786i \(-0.382630\pi\)
0.360430 + 0.932786i \(0.382630\pi\)
\(338\) −24225.1 −3.89843
\(339\) 2429.67 0.389267
\(340\) 5985.80 0.954782
\(341\) 10717.5 1.70200
\(342\) 4275.21 0.675956
\(343\) −343.000 −0.0539949
\(344\) 1797.25 0.281689
\(345\) 1729.18 0.269843
\(346\) 10751.2 1.67048
\(347\) 5261.97 0.814056 0.407028 0.913416i \(-0.366565\pi\)
0.407028 + 0.913416i \(0.366565\pi\)
\(348\) −4320.77 −0.665568
\(349\) 960.325 0.147292 0.0736461 0.997284i \(-0.476536\pi\)
0.0736461 + 0.997284i \(0.476536\pi\)
\(350\) 741.312 0.113214
\(351\) 2402.21 0.365300
\(352\) −10593.6 −1.60409
\(353\) −8925.80 −1.34581 −0.672907 0.739727i \(-0.734955\pi\)
−0.672907 + 0.739727i \(0.734955\pi\)
\(354\) 1925.31 0.289066
\(355\) 307.113 0.0459151
\(356\) −4132.45 −0.615222
\(357\) 2528.13 0.374797
\(358\) −1661.62 −0.245306
\(359\) −3056.27 −0.449314 −0.224657 0.974438i \(-0.572126\pi\)
−0.224657 + 0.974438i \(0.572126\pi\)
\(360\) 370.623 0.0542599
\(361\) 5715.88 0.833340
\(362\) 12615.4 1.83162
\(363\) 1180.69 0.170717
\(364\) −6193.23 −0.891796
\(365\) −2424.00 −0.347611
\(366\) 6733.18 0.961610
\(367\) −1813.52 −0.257943 −0.128971 0.991648i \(-0.541168\pi\)
−0.128971 + 0.991648i \(0.541168\pi\)
\(368\) 5148.99 0.729375
\(369\) 1807.97 0.255065
\(370\) 1023.74 0.143842
\(371\) 1290.11 0.180537
\(372\) −7699.22 −1.07308
\(373\) −4517.48 −0.627094 −0.313547 0.949573i \(-0.601517\pi\)
−0.313547 + 0.949573i \(0.601517\pi\)
\(374\) −21177.9 −2.92802
\(375\) −375.000 −0.0516398
\(376\) −4741.17 −0.650285
\(377\) −12885.9 −1.76036
\(378\) 800.617 0.108940
\(379\) −4931.24 −0.668340 −0.334170 0.942513i \(-0.608456\pi\)
−0.334170 + 0.942513i \(0.608456\pi\)
\(380\) 5575.64 0.752696
\(381\) −7752.75 −1.04248
\(382\) 4648.53 0.622617
\(383\) −1482.37 −0.197770 −0.0988849 0.995099i \(-0.531528\pi\)
−0.0988849 + 0.995099i \(0.531528\pi\)
\(384\) 3069.25 0.407883
\(385\) −1453.48 −0.192405
\(386\) −14827.5 −1.95519
\(387\) −1963.95 −0.257967
\(388\) −10259.5 −1.34239
\(389\) −5448.98 −0.710217 −0.355109 0.934825i \(-0.615556\pi\)
−0.355109 + 0.934825i \(0.615556\pi\)
\(390\) 5653.28 0.734013
\(391\) 13878.0 1.79500
\(392\) −403.567 −0.0519980
\(393\) −4263.31 −0.547215
\(394\) −6667.38 −0.852532
\(395\) −4391.28 −0.559366
\(396\) −3716.68 −0.471642
\(397\) −13675.9 −1.72891 −0.864453 0.502713i \(-0.832335\pi\)
−0.864453 + 0.502713i \(0.832335\pi\)
\(398\) 14388.3 1.81212
\(399\) 2354.89 0.295469
\(400\) −1116.64 −0.139580
\(401\) 14109.9 1.75714 0.878570 0.477613i \(-0.158498\pi\)
0.878570 + 0.477613i \(0.158498\pi\)
\(402\) −16.3282 −0.00202581
\(403\) −22961.4 −2.83819
\(404\) 14391.3 1.77226
\(405\) −405.000 −0.0496904
\(406\) −4294.65 −0.524975
\(407\) −2007.22 −0.244458
\(408\) 2974.55 0.360936
\(409\) −13995.6 −1.69203 −0.846015 0.533159i \(-0.821005\pi\)
−0.846015 + 0.533159i \(0.821005\pi\)
\(410\) 4254.82 0.512514
\(411\) 314.633 0.0377609
\(412\) −1626.55 −0.194501
\(413\) 1060.51 0.126354
\(414\) 4394.95 0.521740
\(415\) −2459.15 −0.290879
\(416\) 22696.0 2.67491
\(417\) −2739.48 −0.321709
\(418\) −19726.7 −2.30829
\(419\) −9840.61 −1.14736 −0.573682 0.819078i \(-0.694485\pi\)
−0.573682 + 0.819078i \(0.694485\pi\)
\(420\) 1044.15 0.121308
\(421\) −12660.5 −1.46564 −0.732822 0.680420i \(-0.761797\pi\)
−0.732822 + 0.680420i \(0.761797\pi\)
\(422\) −14139.2 −1.63101
\(423\) 5180.93 0.595522
\(424\) 1517.92 0.173860
\(425\) −3009.67 −0.343507
\(426\) 780.571 0.0887765
\(427\) 3708.81 0.420332
\(428\) −1289.31 −0.145610
\(429\) −11084.3 −1.24744
\(430\) −4621.90 −0.518344
\(431\) −4578.91 −0.511736 −0.255868 0.966712i \(-0.582361\pi\)
−0.255868 + 0.966712i \(0.582361\pi\)
\(432\) −1205.97 −0.134311
\(433\) −3279.88 −0.364020 −0.182010 0.983297i \(-0.558260\pi\)
−0.182010 + 0.983297i \(0.558260\pi\)
\(434\) −7652.68 −0.846406
\(435\) 2172.49 0.239455
\(436\) 5635.23 0.618988
\(437\) 12927.1 1.41507
\(438\) −6160.94 −0.672103
\(439\) −427.807 −0.0465105 −0.0232552 0.999730i \(-0.507403\pi\)
−0.0232552 + 0.999730i \(0.507403\pi\)
\(440\) −1710.13 −0.185289
\(441\) 441.000 0.0476190
\(442\) 45372.1 4.88265
\(443\) 15441.2 1.65605 0.828027 0.560688i \(-0.189463\pi\)
0.828027 + 0.560688i \(0.189463\pi\)
\(444\) 1441.95 0.154126
\(445\) 2077.80 0.221342
\(446\) −539.371 −0.0572645
\(447\) 5344.35 0.565501
\(448\) 5062.93 0.533931
\(449\) 9382.02 0.986113 0.493057 0.869997i \(-0.335880\pi\)
0.493057 + 0.869997i \(0.335880\pi\)
\(450\) −953.115 −0.0998451
\(451\) −8342.34 −0.871010
\(452\) 8053.77 0.838091
\(453\) 4222.59 0.437957
\(454\) −16284.0 −1.68336
\(455\) 3113.97 0.320847
\(456\) 2770.72 0.284542
\(457\) 13570.4 1.38905 0.694524 0.719469i \(-0.255615\pi\)
0.694524 + 0.719469i \(0.255615\pi\)
\(458\) −10746.7 −1.09642
\(459\) −3250.45 −0.330540
\(460\) 5731.81 0.580972
\(461\) 1251.88 0.126477 0.0632386 0.997998i \(-0.479857\pi\)
0.0632386 + 0.997998i \(0.479857\pi\)
\(462\) −3694.21 −0.372014
\(463\) 7934.36 0.796417 0.398209 0.917295i \(-0.369632\pi\)
0.398209 + 0.917295i \(0.369632\pi\)
\(464\) 6469.05 0.647237
\(465\) 3871.18 0.386069
\(466\) −16891.1 −1.67911
\(467\) 7583.76 0.751466 0.375733 0.926728i \(-0.377391\pi\)
0.375733 + 0.926728i \(0.377391\pi\)
\(468\) 7962.73 0.786490
\(469\) −8.99396 −0.000885507 0
\(470\) 12192.7 1.19661
\(471\) −4796.82 −0.469269
\(472\) 1247.78 0.121681
\(473\) 9062.07 0.880919
\(474\) −11161.1 −1.08153
\(475\) −2803.44 −0.270802
\(476\) 8380.13 0.806938
\(477\) −1658.72 −0.159219
\(478\) 14263.6 1.36486
\(479\) −5829.34 −0.556053 −0.278027 0.960573i \(-0.589680\pi\)
−0.278027 + 0.960573i \(0.589680\pi\)
\(480\) −3826.43 −0.363858
\(481\) 4300.34 0.407648
\(482\) 3980.00 0.376108
\(483\) 2420.85 0.228059
\(484\) 3913.70 0.367553
\(485\) 5158.49 0.482959
\(486\) −1029.36 −0.0960760
\(487\) −19902.1 −1.85185 −0.925925 0.377708i \(-0.876712\pi\)
−0.925925 + 0.377708i \(0.876712\pi\)
\(488\) 4363.71 0.404787
\(489\) −614.675 −0.0568437
\(490\) 1037.84 0.0956830
\(491\) −16821.6 −1.54613 −0.773065 0.634327i \(-0.781277\pi\)
−0.773065 + 0.634327i \(0.781277\pi\)
\(492\) 5992.98 0.549155
\(493\) 17436.0 1.59285
\(494\) 42263.1 3.84920
\(495\) 1868.75 0.169685
\(496\) 11527.3 1.04353
\(497\) 429.958 0.0388054
\(498\) −6250.27 −0.562412
\(499\) 6031.83 0.541126 0.270563 0.962702i \(-0.412790\pi\)
0.270563 + 0.962702i \(0.412790\pi\)
\(500\) −1243.03 −0.111180
\(501\) −3497.82 −0.311919
\(502\) 5947.27 0.528764
\(503\) −17176.4 −1.52258 −0.761290 0.648412i \(-0.775434\pi\)
−0.761290 + 0.648412i \(0.775434\pi\)
\(504\) 518.872 0.0458580
\(505\) −7235.97 −0.637617
\(506\) −20279.2 −1.78166
\(507\) 17156.3 1.50284
\(508\) −25698.5 −2.24446
\(509\) 4706.59 0.409854 0.204927 0.978777i \(-0.434304\pi\)
0.204927 + 0.978777i \(0.434304\pi\)
\(510\) −7649.51 −0.664169
\(511\) −3393.60 −0.293785
\(512\) −14336.9 −1.23752
\(513\) −3027.72 −0.260579
\(514\) 8323.28 0.714250
\(515\) 817.833 0.0699768
\(516\) −6510.02 −0.555402
\(517\) −23905.9 −2.03362
\(518\) 1433.23 0.121569
\(519\) −7614.01 −0.643965
\(520\) 3663.84 0.308981
\(521\) −8557.18 −0.719572 −0.359786 0.933035i \(-0.617150\pi\)
−0.359786 + 0.933035i \(0.617150\pi\)
\(522\) 5521.69 0.462985
\(523\) 18248.5 1.52572 0.762858 0.646566i \(-0.223796\pi\)
0.762858 + 0.646566i \(0.223796\pi\)
\(524\) −14131.8 −1.17815
\(525\) −525.000 −0.0436436
\(526\) 1668.25 0.138287
\(527\) 31069.3 2.56813
\(528\) 5564.60 0.458652
\(529\) 1122.16 0.0922302
\(530\) −3903.58 −0.319925
\(531\) −1363.51 −0.111434
\(532\) 7805.90 0.636144
\(533\) 17872.9 1.45246
\(534\) 5281.03 0.427963
\(535\) 648.266 0.0523869
\(536\) −10.5821 −0.000852758 0
\(537\) 1176.77 0.0945646
\(538\) 7951.22 0.637177
\(539\) −2034.87 −0.162612
\(540\) −1342.48 −0.106983
\(541\) −5734.17 −0.455696 −0.227848 0.973697i \(-0.573169\pi\)
−0.227848 + 0.973697i \(0.573169\pi\)
\(542\) 2922.50 0.231609
\(543\) −8934.24 −0.706087
\(544\) −30710.1 −2.42038
\(545\) −2833.41 −0.222697
\(546\) 7914.59 0.620354
\(547\) −8002.52 −0.625527 −0.312763 0.949831i \(-0.601255\pi\)
−0.312763 + 0.949831i \(0.601255\pi\)
\(548\) 1042.93 0.0812991
\(549\) −4768.47 −0.370698
\(550\) 4397.87 0.340956
\(551\) 16241.2 1.25572
\(552\) 2848.33 0.219625
\(553\) −6147.80 −0.472750
\(554\) −26641.2 −2.04310
\(555\) −725.016 −0.0554508
\(556\) −9080.71 −0.692640
\(557\) 1276.82 0.0971289 0.0485644 0.998820i \(-0.484535\pi\)
0.0485644 + 0.998820i \(0.484535\pi\)
\(558\) 9839.16 0.746460
\(559\) −19414.9 −1.46898
\(560\) −1563.30 −0.117967
\(561\) 14998.2 1.12875
\(562\) 8280.96 0.621550
\(563\) 11027.7 0.825507 0.412753 0.910843i \(-0.364567\pi\)
0.412753 + 0.910843i \(0.364567\pi\)
\(564\) 17173.5 1.28216
\(565\) −4049.45 −0.301525
\(566\) −21324.2 −1.58361
\(567\) −567.000 −0.0419961
\(568\) 505.881 0.0373702
\(569\) −4519.03 −0.332948 −0.166474 0.986046i \(-0.553238\pi\)
−0.166474 + 0.986046i \(0.553238\pi\)
\(570\) −7125.35 −0.523593
\(571\) 3598.81 0.263758 0.131879 0.991266i \(-0.457899\pi\)
0.131879 + 0.991266i \(0.457899\pi\)
\(572\) −36741.7 −2.68575
\(573\) −3292.11 −0.240017
\(574\) 5956.75 0.433153
\(575\) −2881.97 −0.209020
\(576\) −6509.48 −0.470883
\(577\) −3439.23 −0.248140 −0.124070 0.992273i \(-0.539595\pi\)
−0.124070 + 0.992273i \(0.539595\pi\)
\(578\) −40581.6 −2.92037
\(579\) 10500.9 0.753720
\(580\) 7201.28 0.515547
\(581\) −3442.81 −0.245838
\(582\) 13111.0 0.933797
\(583\) 7653.66 0.543709
\(584\) −3992.85 −0.282920
\(585\) −4003.68 −0.282960
\(586\) −26980.0 −1.90194
\(587\) 21285.2 1.49665 0.748327 0.663330i \(-0.230857\pi\)
0.748327 + 0.663330i \(0.230857\pi\)
\(588\) 1461.81 0.102524
\(589\) 28940.4 2.02456
\(590\) −3208.85 −0.223909
\(591\) 4721.87 0.328649
\(592\) −2158.89 −0.149881
\(593\) −14200.8 −0.983404 −0.491702 0.870764i \(-0.663625\pi\)
−0.491702 + 0.870764i \(0.663625\pi\)
\(594\) 4749.70 0.328085
\(595\) −4213.54 −0.290317
\(596\) 17715.2 1.21752
\(597\) −10189.9 −0.698566
\(598\) 43446.8 2.97103
\(599\) −8885.05 −0.606065 −0.303033 0.952980i \(-0.597999\pi\)
−0.303033 + 0.952980i \(0.597999\pi\)
\(600\) −617.705 −0.0420295
\(601\) −2052.89 −0.139333 −0.0696664 0.997570i \(-0.522193\pi\)
−0.0696664 + 0.997570i \(0.522193\pi\)
\(602\) −6470.67 −0.438081
\(603\) 11.5637 0.000780943 0
\(604\) 13996.9 0.942920
\(605\) −1967.82 −0.132237
\(606\) −18391.2 −1.23283
\(607\) 10280.0 0.687404 0.343702 0.939079i \(-0.388319\pi\)
0.343702 + 0.939079i \(0.388319\pi\)
\(608\) −28605.8 −1.90809
\(609\) 3041.49 0.202377
\(610\) −11222.0 −0.744860
\(611\) 51216.8 3.39118
\(612\) −10774.4 −0.711652
\(613\) 23409.5 1.54242 0.771208 0.636584i \(-0.219653\pi\)
0.771208 + 0.636584i \(0.219653\pi\)
\(614\) 28042.0 1.84314
\(615\) −3013.28 −0.197573
\(616\) −2394.18 −0.156598
\(617\) −6632.75 −0.432779 −0.216389 0.976307i \(-0.569428\pi\)
−0.216389 + 0.976307i \(0.569428\pi\)
\(618\) 2078.64 0.135299
\(619\) 10734.0 0.696990 0.348495 0.937311i \(-0.386693\pi\)
0.348495 + 0.937311i \(0.386693\pi\)
\(620\) 12832.0 0.831205
\(621\) −3112.52 −0.201129
\(622\) 41976.1 2.70593
\(623\) 2908.92 0.187068
\(624\) −11921.8 −0.764829
\(625\) 625.000 0.0400000
\(626\) 1789.04 0.114225
\(627\) 13970.5 0.889839
\(628\) −15900.3 −1.01034
\(629\) −5818.83 −0.368858
\(630\) −1334.36 −0.0843845
\(631\) −17071.0 −1.07700 −0.538499 0.842626i \(-0.681008\pi\)
−0.538499 + 0.842626i \(0.681008\pi\)
\(632\) −7233.38 −0.455267
\(633\) 10013.4 0.628749
\(634\) 20768.5 1.30098
\(635\) 12921.3 0.807503
\(636\) −5498.24 −0.342798
\(637\) 4359.56 0.271165
\(638\) −25478.2 −1.58102
\(639\) −552.804 −0.0342231
\(640\) −5115.41 −0.315945
\(641\) −19389.7 −1.19477 −0.597386 0.801954i \(-0.703794\pi\)
−0.597386 + 0.801954i \(0.703794\pi\)
\(642\) 1647.66 0.101290
\(643\) −25409.3 −1.55839 −0.779196 0.626780i \(-0.784372\pi\)
−0.779196 + 0.626780i \(0.784372\pi\)
\(644\) 8024.54 0.491011
\(645\) 3273.25 0.199820
\(646\) −57186.6 −3.48294
\(647\) −6039.08 −0.366956 −0.183478 0.983024i \(-0.558736\pi\)
−0.183478 + 0.983024i \(0.558736\pi\)
\(648\) −667.122 −0.0404429
\(649\) 6291.54 0.380531
\(650\) −9422.14 −0.568564
\(651\) 5419.66 0.326287
\(652\) −2037.50 −0.122384
\(653\) −30666.2 −1.83776 −0.918882 0.394532i \(-0.870907\pi\)
−0.918882 + 0.394532i \(0.870907\pi\)
\(654\) −7201.50 −0.430582
\(655\) 7105.51 0.423871
\(656\) −8972.67 −0.534031
\(657\) 4363.20 0.259094
\(658\) 17069.7 1.01132
\(659\) −2765.96 −0.163500 −0.0817500 0.996653i \(-0.526051\pi\)
−0.0817500 + 0.996653i \(0.526051\pi\)
\(660\) 6194.47 0.365332
\(661\) 27261.8 1.60418 0.802089 0.597204i \(-0.203722\pi\)
0.802089 + 0.597204i \(0.203722\pi\)
\(662\) 22373.8 1.31357
\(663\) −32132.7 −1.88225
\(664\) −4050.74 −0.236746
\(665\) −3924.82 −0.228869
\(666\) −1842.73 −0.107214
\(667\) 16696.1 0.969230
\(668\) −11594.4 −0.671560
\(669\) 381.985 0.0220753
\(670\) 27.2136 0.00156918
\(671\) 22002.7 1.26588
\(672\) −5357.00 −0.307516
\(673\) −1048.17 −0.0600356 −0.0300178 0.999549i \(-0.509556\pi\)
−0.0300178 + 0.999549i \(0.509556\pi\)
\(674\) −18891.2 −1.07961
\(675\) 675.000 0.0384900
\(676\) 56869.0 3.23560
\(677\) −34554.7 −1.96166 −0.980831 0.194860i \(-0.937575\pi\)
−0.980831 + 0.194860i \(0.937575\pi\)
\(678\) −10292.2 −0.582996
\(679\) 7221.89 0.408175
\(680\) −4957.58 −0.279580
\(681\) 11532.4 0.648930
\(682\) −45399.9 −2.54905
\(683\) 14711.6 0.824192 0.412096 0.911140i \(-0.364797\pi\)
0.412096 + 0.911140i \(0.364797\pi\)
\(684\) −10036.2 −0.561026
\(685\) −524.389 −0.0292494
\(686\) 1452.97 0.0808669
\(687\) 7610.85 0.422667
\(688\) 9746.79 0.540106
\(689\) −16397.4 −0.906666
\(690\) −7324.92 −0.404138
\(691\) −24522.6 −1.35005 −0.675024 0.737796i \(-0.735867\pi\)
−0.675024 + 0.737796i \(0.735867\pi\)
\(692\) −25238.6 −1.38646
\(693\) 2616.26 0.143410
\(694\) −22290.1 −1.21919
\(695\) 4565.80 0.249195
\(696\) 3578.56 0.194892
\(697\) −24184.0 −1.31425
\(698\) −4068.00 −0.220596
\(699\) 11962.3 0.647291
\(700\) −1740.25 −0.0939645
\(701\) 19912.2 1.07286 0.536429 0.843946i \(-0.319773\pi\)
0.536429 + 0.843946i \(0.319773\pi\)
\(702\) −10175.9 −0.547101
\(703\) −5420.11 −0.290787
\(704\) 30036.1 1.60799
\(705\) −8634.89 −0.461289
\(706\) 37810.3 2.01559
\(707\) −10130.4 −0.538885
\(708\) −4519.72 −0.239917
\(709\) 6208.79 0.328880 0.164440 0.986387i \(-0.447418\pi\)
0.164440 + 0.986387i \(0.447418\pi\)
\(710\) −1300.95 −0.0687660
\(711\) 7904.31 0.416927
\(712\) 3422.58 0.180150
\(713\) 29751.0 1.56267
\(714\) −10709.3 −0.561325
\(715\) 18473.8 0.966267
\(716\) 3900.69 0.203597
\(717\) −10101.5 −0.526149
\(718\) 12946.6 0.672927
\(719\) 13063.6 0.677593 0.338797 0.940860i \(-0.389980\pi\)
0.338797 + 0.940860i \(0.389980\pi\)
\(720\) 2009.95 0.104037
\(721\) 1144.97 0.0591411
\(722\) −24212.9 −1.24807
\(723\) −2818.65 −0.144989
\(724\) −29614.8 −1.52020
\(725\) −3620.82 −0.185481
\(726\) −5001.49 −0.255678
\(727\) −12897.0 −0.657940 −0.328970 0.944340i \(-0.606702\pi\)
−0.328970 + 0.944340i \(0.606702\pi\)
\(728\) 5129.37 0.261136
\(729\) 729.000 0.0370370
\(730\) 10268.2 0.520609
\(731\) 26270.5 1.32920
\(732\) −15806.3 −0.798112
\(733\) 11699.6 0.589540 0.294770 0.955568i \(-0.404757\pi\)
0.294770 + 0.955568i \(0.404757\pi\)
\(734\) 7682.19 0.386315
\(735\) −735.000 −0.0368856
\(736\) −29407.0 −1.47277
\(737\) −53.3571 −0.00266681
\(738\) −7658.68 −0.382005
\(739\) 14974.0 0.745368 0.372684 0.927958i \(-0.378438\pi\)
0.372684 + 0.927958i \(0.378438\pi\)
\(740\) −2403.25 −0.119385
\(741\) −29930.9 −1.48386
\(742\) −5465.01 −0.270386
\(743\) 18500.7 0.913492 0.456746 0.889597i \(-0.349015\pi\)
0.456746 + 0.889597i \(0.349015\pi\)
\(744\) 6376.67 0.314220
\(745\) −8907.24 −0.438035
\(746\) 19136.3 0.939184
\(747\) 4426.47 0.216809
\(748\) 49715.5 2.43019
\(749\) 907.572 0.0442750
\(750\) 1588.53 0.0773397
\(751\) −26348.4 −1.28025 −0.640125 0.768271i \(-0.721117\pi\)
−0.640125 + 0.768271i \(0.721117\pi\)
\(752\) −25712.2 −1.24684
\(753\) −4211.88 −0.203837
\(754\) 54585.4 2.63645
\(755\) −7037.65 −0.339240
\(756\) −1879.47 −0.0904174
\(757\) −28061.7 −1.34732 −0.673659 0.739042i \(-0.735278\pi\)
−0.673659 + 0.739042i \(0.735278\pi\)
\(758\) 20889.1 1.00096
\(759\) 14361.8 0.686826
\(760\) −4617.87 −0.220405
\(761\) −3579.22 −0.170495 −0.0852476 0.996360i \(-0.527168\pi\)
−0.0852476 + 0.996360i \(0.527168\pi\)
\(762\) 32841.2 1.56130
\(763\) −3966.77 −0.188213
\(764\) −10912.5 −0.516757
\(765\) 5417.41 0.256035
\(766\) 6279.44 0.296195
\(767\) −13479.2 −0.634557
\(768\) 4357.07 0.204716
\(769\) 4339.61 0.203499 0.101749 0.994810i \(-0.467556\pi\)
0.101749 + 0.994810i \(0.467556\pi\)
\(770\) 6157.02 0.288161
\(771\) −5894.58 −0.275341
\(772\) 34808.0 1.62276
\(773\) 10005.1 0.465537 0.232769 0.972532i \(-0.425222\pi\)
0.232769 + 0.972532i \(0.425222\pi\)
\(774\) 8319.43 0.386351
\(775\) −6451.97 −0.299047
\(776\) 8497.14 0.393079
\(777\) −1015.02 −0.0468645
\(778\) 23082.3 1.06368
\(779\) −22526.8 −1.03608
\(780\) −13271.2 −0.609212
\(781\) 2550.75 0.116867
\(782\) −58788.4 −2.68832
\(783\) −3910.49 −0.178479
\(784\) −2188.62 −0.0997001
\(785\) 7994.70 0.363494
\(786\) 18059.7 0.819550
\(787\) 17826.8 0.807443 0.403721 0.914882i \(-0.367716\pi\)
0.403721 + 0.914882i \(0.367716\pi\)
\(788\) 15651.8 0.707581
\(789\) −1181.46 −0.0533094
\(790\) 18601.8 0.837749
\(791\) −5669.23 −0.254835
\(792\) 3078.24 0.138107
\(793\) −47139.3 −2.11093
\(794\) 57932.2 2.58934
\(795\) 2764.53 0.123330
\(796\) −33777.0 −1.50401
\(797\) 36723.0 1.63211 0.816057 0.577971i \(-0.196155\pi\)
0.816057 + 0.577971i \(0.196155\pi\)
\(798\) −9975.49 −0.442517
\(799\) −69301.9 −3.06849
\(800\) 6377.38 0.281843
\(801\) −3740.04 −0.164979
\(802\) −59770.4 −2.63163
\(803\) −20132.7 −0.884767
\(804\) 38.3307 0.00168137
\(805\) −4034.75 −0.176654
\(806\) 97266.2 4.25069
\(807\) −5631.08 −0.245630
\(808\) −11919.2 −0.518955
\(809\) 5657.55 0.245870 0.122935 0.992415i \(-0.460769\pi\)
0.122935 + 0.992415i \(0.460769\pi\)
\(810\) 1715.61 0.0744201
\(811\) 7532.41 0.326139 0.163070 0.986615i \(-0.447861\pi\)
0.163070 + 0.986615i \(0.447861\pi\)
\(812\) 10081.8 0.435716
\(813\) −2069.73 −0.0892847
\(814\) 8502.73 0.366119
\(815\) 1024.46 0.0440309
\(816\) 16131.5 0.692053
\(817\) 24470.3 1.04787
\(818\) 59286.5 2.53411
\(819\) −5605.15 −0.239145
\(820\) −9988.30 −0.425374
\(821\) −6489.25 −0.275854 −0.137927 0.990442i \(-0.544044\pi\)
−0.137927 + 0.990442i \(0.544044\pi\)
\(822\) −1332.81 −0.0565535
\(823\) 7901.57 0.334668 0.167334 0.985900i \(-0.446484\pi\)
0.167334 + 0.985900i \(0.446484\pi\)
\(824\) 1347.15 0.0569539
\(825\) −3114.59 −0.131438
\(826\) −4492.40 −0.189238
\(827\) −37815.8 −1.59007 −0.795033 0.606566i \(-0.792547\pi\)
−0.795033 + 0.606566i \(0.792547\pi\)
\(828\) −10317.3 −0.433031
\(829\) 26073.5 1.09236 0.546182 0.837667i \(-0.316081\pi\)
0.546182 + 0.837667i \(0.316081\pi\)
\(830\) 10417.1 0.435643
\(831\) 18867.4 0.787608
\(832\) −64350.2 −2.68142
\(833\) −5898.96 −0.245362
\(834\) 11604.6 0.481817
\(835\) 5829.71 0.241611
\(836\) 46308.9 1.91582
\(837\) −6968.13 −0.287758
\(838\) 41685.5 1.71838
\(839\) −15590.3 −0.641523 −0.320762 0.947160i \(-0.603939\pi\)
−0.320762 + 0.947160i \(0.603939\pi\)
\(840\) −864.787 −0.0355214
\(841\) −3412.46 −0.139918
\(842\) 53630.8 2.19506
\(843\) −5864.61 −0.239606
\(844\) 33192.1 1.35370
\(845\) −28593.8 −1.16409
\(846\) −21946.8 −0.891899
\(847\) −2754.94 −0.111760
\(848\) 8231.96 0.333357
\(849\) 15101.9 0.610477
\(850\) 12749.2 0.514463
\(851\) −5571.92 −0.224445
\(852\) −1832.41 −0.0736823
\(853\) −17476.1 −0.701488 −0.350744 0.936471i \(-0.614071\pi\)
−0.350744 + 0.936471i \(0.614071\pi\)
\(854\) −15710.8 −0.629521
\(855\) 5046.20 0.201844
\(856\) 1067.83 0.0426376
\(857\) −5694.54 −0.226980 −0.113490 0.993539i \(-0.536203\pi\)
−0.113490 + 0.993539i \(0.536203\pi\)
\(858\) 46953.7 1.86827
\(859\) 27313.6 1.08490 0.542448 0.840089i \(-0.317497\pi\)
0.542448 + 0.840089i \(0.317497\pi\)
\(860\) 10850.0 0.430213
\(861\) −4218.59 −0.166979
\(862\) 19396.6 0.766415
\(863\) −9046.07 −0.356815 −0.178408 0.983957i \(-0.557095\pi\)
−0.178408 + 0.983957i \(0.557095\pi\)
\(864\) 6887.57 0.271204
\(865\) 12690.0 0.498813
\(866\) 13893.8 0.545185
\(867\) 28740.1 1.12580
\(868\) 17964.8 0.702496
\(869\) −36472.1 −1.42374
\(870\) −9202.82 −0.358626
\(871\) 114.314 0.00444705
\(872\) −4667.22 −0.181252
\(873\) −9285.28 −0.359976
\(874\) −54760.0 −2.11932
\(875\) 875.000 0.0338062
\(876\) 14463.0 0.557829
\(877\) −2104.29 −0.0810224 −0.0405112 0.999179i \(-0.512899\pi\)
−0.0405112 + 0.999179i \(0.512899\pi\)
\(878\) 1812.22 0.0696576
\(879\) 19107.4 0.733192
\(880\) −9274.34 −0.355270
\(881\) −22589.6 −0.863861 −0.431931 0.901907i \(-0.642167\pi\)
−0.431931 + 0.901907i \(0.642167\pi\)
\(882\) −1868.11 −0.0713179
\(883\) −2419.71 −0.0922193 −0.0461096 0.998936i \(-0.514682\pi\)
−0.0461096 + 0.998936i \(0.514682\pi\)
\(884\) −106512. −4.05248
\(885\) 2272.52 0.0863164
\(886\) −65409.8 −2.48023
\(887\) 13177.0 0.498806 0.249403 0.968400i \(-0.419766\pi\)
0.249403 + 0.968400i \(0.419766\pi\)
\(888\) −1194.26 −0.0451313
\(889\) 18089.8 0.682464
\(890\) −8801.71 −0.331499
\(891\) −3363.76 −0.126476
\(892\) 1266.19 0.0475281
\(893\) −64553.2 −2.41902
\(894\) −22639.0 −0.846937
\(895\) −1961.28 −0.0732495
\(896\) −7161.58 −0.267022
\(897\) −30769.2 −1.14532
\(898\) −39742.9 −1.47688
\(899\) 37378.3 1.38669
\(900\) 2237.46 0.0828689
\(901\) 22187.5 0.820393
\(902\) 35338.7 1.30449
\(903\) 4582.55 0.168879
\(904\) −6670.31 −0.245411
\(905\) 14890.4 0.546932
\(906\) −17887.2 −0.655918
\(907\) 9189.14 0.336406 0.168203 0.985752i \(-0.446204\pi\)
0.168203 + 0.985752i \(0.446204\pi\)
\(908\) 38227.0 1.39714
\(909\) 13024.8 0.475252
\(910\) −13191.0 −0.480524
\(911\) −17045.8 −0.619928 −0.309964 0.950748i \(-0.600317\pi\)
−0.309964 + 0.950748i \(0.600317\pi\)
\(912\) 15026.1 0.545575
\(913\) −20424.6 −0.740369
\(914\) −57485.0 −2.08034
\(915\) 7947.45 0.287141
\(916\) 25228.1 0.910001
\(917\) 9947.71 0.358236
\(918\) 13769.1 0.495042
\(919\) −30825.0 −1.10645 −0.553223 0.833033i \(-0.686602\pi\)
−0.553223 + 0.833033i \(0.686602\pi\)
\(920\) −4747.21 −0.170121
\(921\) −19859.5 −0.710524
\(922\) −5303.06 −0.189422
\(923\) −5464.81 −0.194882
\(924\) 8672.25 0.308762
\(925\) 1208.36 0.0429520
\(926\) −33610.5 −1.19277
\(927\) −1472.10 −0.0521576
\(928\) −36946.2 −1.30691
\(929\) −5785.88 −0.204336 −0.102168 0.994767i \(-0.532578\pi\)
−0.102168 + 0.994767i \(0.532578\pi\)
\(930\) −16398.6 −0.578206
\(931\) −5494.75 −0.193430
\(932\) 39652.2 1.39362
\(933\) −29727.7 −1.04313
\(934\) −32125.3 −1.12545
\(935\) −24997.1 −0.874323
\(936\) −6594.91 −0.230301
\(937\) −13680.9 −0.476986 −0.238493 0.971144i \(-0.576653\pi\)
−0.238493 + 0.971144i \(0.576653\pi\)
\(938\) 38.0990 0.00132620
\(939\) −1267.01 −0.0440333
\(940\) −28622.6 −0.993155
\(941\) −45448.8 −1.57448 −0.787242 0.616644i \(-0.788492\pi\)
−0.787242 + 0.616644i \(0.788492\pi\)
\(942\) 20319.6 0.702813
\(943\) −23157.8 −0.799705
\(944\) 6766.91 0.233310
\(945\) 945.000 0.0325300
\(946\) −38387.6 −1.31933
\(947\) −7788.45 −0.267255 −0.133628 0.991032i \(-0.542663\pi\)
−0.133628 + 0.991032i \(0.542663\pi\)
\(948\) 26200.9 0.897642
\(949\) 43133.0 1.47540
\(950\) 11875.6 0.405573
\(951\) −14708.4 −0.501526
\(952\) −6940.61 −0.236288
\(953\) 6149.43 0.209024 0.104512 0.994524i \(-0.466672\pi\)
0.104512 + 0.994524i \(0.466672\pi\)
\(954\) 7026.44 0.238458
\(955\) 5486.85 0.185917
\(956\) −33484.2 −1.13280
\(957\) 18043.8 0.609481
\(958\) 24693.5 0.832788
\(959\) −734.144 −0.0247203
\(960\) 10849.1 0.364744
\(961\) 36813.7 1.23573
\(962\) −18216.5 −0.610524
\(963\) −1166.88 −0.0390469
\(964\) −9343.15 −0.312160
\(965\) −17501.5 −0.583829
\(966\) −10254.9 −0.341559
\(967\) 23902.9 0.794896 0.397448 0.917625i \(-0.369896\pi\)
0.397448 + 0.917625i \(0.369896\pi\)
\(968\) −3241.42 −0.107627
\(969\) 40499.8 1.34266
\(970\) −21851.7 −0.723316
\(971\) −8015.06 −0.264898 −0.132449 0.991190i \(-0.542284\pi\)
−0.132449 + 0.991190i \(0.542284\pi\)
\(972\) 2416.46 0.0797407
\(973\) 6392.12 0.210608
\(974\) 84306.7 2.77347
\(975\) 6672.79 0.219180
\(976\) 23665.2 0.776131
\(977\) −34861.1 −1.14156 −0.570780 0.821103i \(-0.693359\pi\)
−0.570780 + 0.821103i \(0.693359\pi\)
\(978\) 2603.80 0.0851334
\(979\) 17257.3 0.563378
\(980\) −2436.35 −0.0794145
\(981\) 5100.13 0.165988
\(982\) 71257.6 2.31560
\(983\) 6620.83 0.214824 0.107412 0.994215i \(-0.465744\pi\)
0.107412 + 0.994215i \(0.465744\pi\)
\(984\) −4963.52 −0.160804
\(985\) −7869.78 −0.254570
\(986\) −73860.0 −2.38558
\(987\) −12088.8 −0.389860
\(988\) −99213.6 −3.19474
\(989\) 25155.7 0.808802
\(990\) −7916.17 −0.254134
\(991\) 10360.1 0.332089 0.166045 0.986118i \(-0.446900\pi\)
0.166045 + 0.986118i \(0.446900\pi\)
\(992\) −65834.7 −2.10711
\(993\) −15845.2 −0.506377
\(994\) −1821.33 −0.0581179
\(995\) 16983.1 0.541107
\(996\) 14672.7 0.466788
\(997\) −40309.3 −1.28045 −0.640225 0.768188i \(-0.721159\pi\)
−0.640225 + 0.768188i \(0.721159\pi\)
\(998\) −25551.3 −0.810432
\(999\) 1305.03 0.0413306
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 105.4.a.d.1.1 2
3.2 odd 2 315.4.a.l.1.2 2
4.3 odd 2 1680.4.a.bd.1.1 2
5.2 odd 4 525.4.d.k.274.1 4
5.3 odd 4 525.4.d.k.274.4 4
5.4 even 2 525.4.a.o.1.2 2
7.6 odd 2 735.4.a.m.1.1 2
15.14 odd 2 1575.4.a.n.1.1 2
21.20 even 2 2205.4.a.be.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.a.d.1.1 2 1.1 even 1 trivial
315.4.a.l.1.2 2 3.2 odd 2
525.4.a.o.1.2 2 5.4 even 2
525.4.d.k.274.1 4 5.2 odd 4
525.4.d.k.274.4 4 5.3 odd 4
735.4.a.m.1.1 2 7.6 odd 2
1575.4.a.n.1.1 2 15.14 odd 2
1680.4.a.bd.1.1 2 4.3 odd 2
2205.4.a.be.1.2 2 21.20 even 2