Properties

Label 1849.4.a.j.1.24
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(50\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.24
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0180033 q^{2} -4.14959 q^{3} -7.99968 q^{4} +13.3506 q^{5} +0.0747066 q^{6} +5.69523 q^{7} +0.288048 q^{8} -9.78088 q^{9} +O(q^{10})\) \(q-0.0180033 q^{2} -4.14959 q^{3} -7.99968 q^{4} +13.3506 q^{5} +0.0747066 q^{6} +5.69523 q^{7} +0.288048 q^{8} -9.78088 q^{9} -0.240356 q^{10} -47.5373 q^{11} +33.1954 q^{12} +76.9850 q^{13} -0.102533 q^{14} -55.3996 q^{15} +63.9922 q^{16} +7.02247 q^{17} +0.176089 q^{18} -132.370 q^{19} -106.800 q^{20} -23.6329 q^{21} +0.855831 q^{22} +93.7845 q^{23} -1.19528 q^{24} +53.2386 q^{25} -1.38599 q^{26} +152.626 q^{27} -45.5600 q^{28} +100.339 q^{29} +0.997377 q^{30} -169.100 q^{31} -3.45646 q^{32} +197.260 q^{33} -0.126428 q^{34} +76.0348 q^{35} +78.2439 q^{36} -268.545 q^{37} +2.38311 q^{38} -319.456 q^{39} +3.84561 q^{40} +157.369 q^{41} +0.425471 q^{42} +380.283 q^{44} -130.581 q^{45} -1.68843 q^{46} +394.707 q^{47} -265.542 q^{48} -310.564 q^{49} -0.958472 q^{50} -29.1404 q^{51} -615.855 q^{52} +447.422 q^{53} -2.74777 q^{54} -634.652 q^{55} +1.64050 q^{56} +549.282 q^{57} -1.80643 q^{58} -653.194 q^{59} +443.178 q^{60} -168.494 q^{61} +3.04437 q^{62} -55.7044 q^{63} -511.876 q^{64} +1027.80 q^{65} -3.55135 q^{66} +646.419 q^{67} -56.1775 q^{68} -389.167 q^{69} -1.36888 q^{70} -61.1604 q^{71} -2.81736 q^{72} +336.572 q^{73} +4.83471 q^{74} -220.918 q^{75} +1058.92 q^{76} -270.736 q^{77} +5.75129 q^{78} +664.672 q^{79} +854.335 q^{80} -369.250 q^{81} -2.83318 q^{82} -242.758 q^{83} +189.055 q^{84} +93.7542 q^{85} -416.364 q^{87} -13.6930 q^{88} +1437.09 q^{89} +2.35089 q^{90} +438.448 q^{91} -750.245 q^{92} +701.698 q^{93} -7.10606 q^{94} -1767.22 q^{95} +14.3429 q^{96} -1444.16 q^{97} +5.59120 q^{98} +464.957 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0180033 −0.00636515 −0.00318257 0.999995i \(-0.501013\pi\)
−0.00318257 + 0.999995i \(0.501013\pi\)
\(3\) −4.14959 −0.798589 −0.399295 0.916823i \(-0.630745\pi\)
−0.399295 + 0.916823i \(0.630745\pi\)
\(4\) −7.99968 −0.999959
\(5\) 13.3506 1.19411 0.597057 0.802199i \(-0.296337\pi\)
0.597057 + 0.802199i \(0.296337\pi\)
\(6\) 0.0747066 0.00508314
\(7\) 5.69523 0.307514 0.153757 0.988109i \(-0.450863\pi\)
0.153757 + 0.988109i \(0.450863\pi\)
\(8\) 0.288048 0.0127300
\(9\) −9.78088 −0.362255
\(10\) −0.240356 −0.00760071
\(11\) −47.5373 −1.30300 −0.651502 0.758647i \(-0.725861\pi\)
−0.651502 + 0.758647i \(0.725861\pi\)
\(12\) 33.1954 0.798557
\(13\) 76.9850 1.64245 0.821223 0.570607i \(-0.193292\pi\)
0.821223 + 0.570607i \(0.193292\pi\)
\(14\) −0.102533 −0.00195737
\(15\) −55.3996 −0.953607
\(16\) 63.9922 0.999878
\(17\) 7.02247 0.100188 0.0500941 0.998745i \(-0.484048\pi\)
0.0500941 + 0.998745i \(0.484048\pi\)
\(18\) 0.176089 0.00230581
\(19\) −132.370 −1.59830 −0.799152 0.601128i \(-0.794718\pi\)
−0.799152 + 0.601128i \(0.794718\pi\)
\(20\) −106.800 −1.19407
\(21\) −23.6329 −0.245577
\(22\) 0.855831 0.00829381
\(23\) 93.7845 0.850235 0.425118 0.905138i \(-0.360233\pi\)
0.425118 + 0.905138i \(0.360233\pi\)
\(24\) −1.19528 −0.0101661
\(25\) 53.2386 0.425908
\(26\) −1.38599 −0.0104544
\(27\) 152.626 1.08788
\(28\) −45.5600 −0.307501
\(29\) 100.339 0.642497 0.321249 0.946995i \(-0.395898\pi\)
0.321249 + 0.946995i \(0.395898\pi\)
\(30\) 0.997377 0.00606985
\(31\) −169.100 −0.979720 −0.489860 0.871801i \(-0.662952\pi\)
−0.489860 + 0.871801i \(0.662952\pi\)
\(32\) −3.45646 −0.0190944
\(33\) 197.260 1.04056
\(34\) −0.126428 −0.000637712 0
\(35\) 76.0348 0.367206
\(36\) 78.2439 0.362240
\(37\) −268.545 −1.19320 −0.596601 0.802538i \(-0.703483\pi\)
−0.596601 + 0.802538i \(0.703483\pi\)
\(38\) 2.38311 0.0101734
\(39\) −319.456 −1.31164
\(40\) 3.84561 0.0152011
\(41\) 157.369 0.599438 0.299719 0.954027i \(-0.403107\pi\)
0.299719 + 0.954027i \(0.403107\pi\)
\(42\) 0.425471 0.00156313
\(43\) 0 0
\(44\) 380.283 1.30295
\(45\) −130.581 −0.432574
\(46\) −1.68843 −0.00541187
\(47\) 394.707 1.22498 0.612489 0.790479i \(-0.290168\pi\)
0.612489 + 0.790479i \(0.290168\pi\)
\(48\) −265.542 −0.798492
\(49\) −310.564 −0.905435
\(50\) −0.958472 −0.00271097
\(51\) −29.1404 −0.0800092
\(52\) −615.855 −1.64238
\(53\) 447.422 1.15959 0.579794 0.814763i \(-0.303133\pi\)
0.579794 + 0.814763i \(0.303133\pi\)
\(54\) −2.74777 −0.00692453
\(55\) −634.652 −1.55594
\(56\) 1.64050 0.00391466
\(57\) 549.282 1.27639
\(58\) −1.80643 −0.00408959
\(59\) −653.194 −1.44133 −0.720666 0.693283i \(-0.756164\pi\)
−0.720666 + 0.693283i \(0.756164\pi\)
\(60\) 443.178 0.953568
\(61\) −168.494 −0.353664 −0.176832 0.984241i \(-0.556585\pi\)
−0.176832 + 0.984241i \(0.556585\pi\)
\(62\) 3.04437 0.00623606
\(63\) −55.7044 −0.111398
\(64\) −511.876 −0.999757
\(65\) 1027.80 1.96127
\(66\) −3.55135 −0.00662335
\(67\) 646.419 1.17870 0.589348 0.807879i \(-0.299385\pi\)
0.589348 + 0.807879i \(0.299385\pi\)
\(68\) −56.1775 −0.100184
\(69\) −389.167 −0.678989
\(70\) −1.36888 −0.00233732
\(71\) −61.1604 −0.102231 −0.0511155 0.998693i \(-0.516278\pi\)
−0.0511155 + 0.998693i \(0.516278\pi\)
\(72\) −2.81736 −0.00461152
\(73\) 336.572 0.539627 0.269814 0.962913i \(-0.413038\pi\)
0.269814 + 0.962913i \(0.413038\pi\)
\(74\) 4.83471 0.00759491
\(75\) −220.918 −0.340126
\(76\) 1058.92 1.59824
\(77\) −270.736 −0.400691
\(78\) 5.75129 0.00834878
\(79\) 664.672 0.946601 0.473301 0.880901i \(-0.343062\pi\)
0.473301 + 0.880901i \(0.343062\pi\)
\(80\) 854.335 1.19397
\(81\) −369.250 −0.506516
\(82\) −2.83318 −0.00381551
\(83\) −242.758 −0.321037 −0.160519 0.987033i \(-0.551317\pi\)
−0.160519 + 0.987033i \(0.551317\pi\)
\(84\) 189.055 0.245567
\(85\) 93.7542 0.119636
\(86\) 0 0
\(87\) −416.364 −0.513091
\(88\) −13.6930 −0.0165873
\(89\) 1437.09 1.71158 0.855792 0.517320i \(-0.173070\pi\)
0.855792 + 0.517320i \(0.173070\pi\)
\(90\) 2.35089 0.00275339
\(91\) 438.448 0.505075
\(92\) −750.245 −0.850201
\(93\) 701.698 0.782394
\(94\) −7.10606 −0.00779717
\(95\) −1767.22 −1.90856
\(96\) 14.3429 0.0152486
\(97\) −1444.16 −1.51168 −0.755839 0.654758i \(-0.772771\pi\)
−0.755839 + 0.654758i \(0.772771\pi\)
\(98\) 5.59120 0.00576323
\(99\) 464.957 0.472020
\(100\) −425.891 −0.425891
\(101\) 120.466 0.118681 0.0593404 0.998238i \(-0.481100\pi\)
0.0593404 + 0.998238i \(0.481100\pi\)
\(102\) 0.524624 0.000509270 0
\(103\) −224.367 −0.214636 −0.107318 0.994225i \(-0.534226\pi\)
−0.107318 + 0.994225i \(0.534226\pi\)
\(104\) 22.1754 0.0209084
\(105\) −315.513 −0.293247
\(106\) −8.05510 −0.00738094
\(107\) 290.938 0.262860 0.131430 0.991325i \(-0.458043\pi\)
0.131430 + 0.991325i \(0.458043\pi\)
\(108\) −1220.96 −1.08784
\(109\) 873.020 0.767158 0.383579 0.923508i \(-0.374691\pi\)
0.383579 + 0.923508i \(0.374691\pi\)
\(110\) 11.4259 0.00990375
\(111\) 1114.35 0.952879
\(112\) 364.451 0.307476
\(113\) 1726.96 1.43769 0.718843 0.695173i \(-0.244672\pi\)
0.718843 + 0.695173i \(0.244672\pi\)
\(114\) −9.88892 −0.00812440
\(115\) 1252.08 1.01528
\(116\) −802.676 −0.642471
\(117\) −752.982 −0.594984
\(118\) 11.7597 0.00917428
\(119\) 39.9946 0.0308092
\(120\) −15.9577 −0.0121394
\(121\) 928.796 0.697819
\(122\) 3.03346 0.00225112
\(123\) −653.019 −0.478705
\(124\) 1352.75 0.979681
\(125\) −958.058 −0.685531
\(126\) 1.00287 0.000709067 0
\(127\) −496.351 −0.346804 −0.173402 0.984851i \(-0.555476\pi\)
−0.173402 + 0.984851i \(0.555476\pi\)
\(128\) 36.8671 0.0254580
\(129\) 0 0
\(130\) −18.5038 −0.0124838
\(131\) −187.413 −0.124995 −0.0624975 0.998045i \(-0.519907\pi\)
−0.0624975 + 0.998045i \(0.519907\pi\)
\(132\) −1578.02 −1.04052
\(133\) −753.879 −0.491500
\(134\) −11.6377 −0.00750257
\(135\) 2037.64 1.29906
\(136\) 2.02281 0.00127540
\(137\) −2099.47 −1.30927 −0.654633 0.755947i \(-0.727177\pi\)
−0.654633 + 0.755947i \(0.727177\pi\)
\(138\) 7.00631 0.00432186
\(139\) −2945.77 −1.79753 −0.898767 0.438426i \(-0.855536\pi\)
−0.898767 + 0.438426i \(0.855536\pi\)
\(140\) −608.253 −0.367191
\(141\) −1637.87 −0.978255
\(142\) 1.10109 0.000650715 0
\(143\) −3659.66 −2.14011
\(144\) −625.901 −0.362211
\(145\) 1339.58 0.767215
\(146\) −6.05943 −0.00343481
\(147\) 1288.72 0.723071
\(148\) 2148.27 1.19315
\(149\) 3106.95 1.70827 0.854133 0.520055i \(-0.174088\pi\)
0.854133 + 0.520055i \(0.174088\pi\)
\(150\) 3.97727 0.00216495
\(151\) −1846.66 −0.995226 −0.497613 0.867399i \(-0.665790\pi\)
−0.497613 + 0.867399i \(0.665790\pi\)
\(152\) −38.1289 −0.0203465
\(153\) −68.6859 −0.0362937
\(154\) 4.87416 0.00255046
\(155\) −2257.59 −1.16990
\(156\) 2555.55 1.31159
\(157\) −1270.26 −0.645719 −0.322860 0.946447i \(-0.604644\pi\)
−0.322860 + 0.946447i \(0.604644\pi\)
\(158\) −11.9663 −0.00602525
\(159\) −1856.62 −0.926034
\(160\) −46.1458 −0.0228009
\(161\) 534.124 0.261459
\(162\) 6.64774 0.00322405
\(163\) 1810.04 0.869773 0.434886 0.900485i \(-0.356789\pi\)
0.434886 + 0.900485i \(0.356789\pi\)
\(164\) −1258.90 −0.599414
\(165\) 2633.55 1.24255
\(166\) 4.37045 0.00204345
\(167\) −4200.89 −1.94656 −0.973278 0.229630i \(-0.926248\pi\)
−0.973278 + 0.229630i \(0.926248\pi\)
\(168\) −6.80740 −0.00312620
\(169\) 3729.69 1.69763
\(170\) −1.68789 −0.000761501 0
\(171\) 1294.70 0.578994
\(172\) 0 0
\(173\) −1786.31 −0.785031 −0.392516 0.919745i \(-0.628395\pi\)
−0.392516 + 0.919745i \(0.628395\pi\)
\(174\) 7.49595 0.00326590
\(175\) 303.206 0.130973
\(176\) −3042.02 −1.30285
\(177\) 2710.49 1.15103
\(178\) −25.8724 −0.0108945
\(179\) 2188.39 0.913787 0.456894 0.889521i \(-0.348962\pi\)
0.456894 + 0.889521i \(0.348962\pi\)
\(180\) 1044.60 0.432556
\(181\) 1287.39 0.528680 0.264340 0.964430i \(-0.414846\pi\)
0.264340 + 0.964430i \(0.414846\pi\)
\(182\) −7.89352 −0.00321487
\(183\) 699.183 0.282432
\(184\) 27.0144 0.0108235
\(185\) −3585.23 −1.42482
\(186\) −12.6329 −0.00498005
\(187\) −333.829 −0.130546
\(188\) −3157.53 −1.22493
\(189\) 869.239 0.334539
\(190\) 31.8159 0.0121483
\(191\) 2171.05 0.822468 0.411234 0.911530i \(-0.365098\pi\)
0.411234 + 0.911530i \(0.365098\pi\)
\(192\) 2124.07 0.798395
\(193\) 1864.44 0.695365 0.347683 0.937612i \(-0.386969\pi\)
0.347683 + 0.937612i \(0.386969\pi\)
\(194\) 25.9998 0.00962205
\(195\) −4264.94 −1.56625
\(196\) 2484.41 0.905399
\(197\) −1865.97 −0.674848 −0.337424 0.941353i \(-0.609556\pi\)
−0.337424 + 0.941353i \(0.609556\pi\)
\(198\) −8.37078 −0.00300447
\(199\) −2313.58 −0.824147 −0.412073 0.911151i \(-0.635195\pi\)
−0.412073 + 0.911151i \(0.635195\pi\)
\(200\) 15.3352 0.00542183
\(201\) −2682.37 −0.941294
\(202\) −2.16878 −0.000755421 0
\(203\) 571.452 0.197577
\(204\) 233.114 0.0800059
\(205\) 2100.98 0.715798
\(206\) 4.03936 0.00136619
\(207\) −917.295 −0.308002
\(208\) 4926.44 1.64225
\(209\) 6292.52 2.08260
\(210\) 5.68030 0.00186656
\(211\) −741.102 −0.241799 −0.120899 0.992665i \(-0.538578\pi\)
−0.120899 + 0.992665i \(0.538578\pi\)
\(212\) −3579.23 −1.15954
\(213\) 253.791 0.0816406
\(214\) −5.23786 −0.00167314
\(215\) 0 0
\(216\) 43.9635 0.0138488
\(217\) −963.066 −0.301277
\(218\) −15.7173 −0.00488307
\(219\) −1396.64 −0.430941
\(220\) 5077.01 1.55587
\(221\) 540.625 0.164554
\(222\) −20.0621 −0.00606521
\(223\) −2820.00 −0.846822 −0.423411 0.905938i \(-0.639167\pi\)
−0.423411 + 0.905938i \(0.639167\pi\)
\(224\) −19.6853 −0.00587179
\(225\) −520.720 −0.154287
\(226\) −31.0910 −0.00915107
\(227\) 2015.04 0.589176 0.294588 0.955624i \(-0.404818\pi\)
0.294588 + 0.955624i \(0.404818\pi\)
\(228\) −4394.08 −1.27634
\(229\) −5723.24 −1.65154 −0.825769 0.564009i \(-0.809258\pi\)
−0.825769 + 0.564009i \(0.809258\pi\)
\(230\) −22.5416 −0.00646239
\(231\) 1123.44 0.319988
\(232\) 28.9023 0.00817901
\(233\) −6380.23 −1.79392 −0.896959 0.442114i \(-0.854229\pi\)
−0.896959 + 0.442114i \(0.854229\pi\)
\(234\) 13.5562 0.00378716
\(235\) 5269.58 1.46276
\(236\) 5225.34 1.44127
\(237\) −2758.12 −0.755946
\(238\) −0.720036 −0.000196105 0
\(239\) 1828.53 0.494887 0.247443 0.968902i \(-0.420410\pi\)
0.247443 + 0.968902i \(0.420410\pi\)
\(240\) −3545.14 −0.953491
\(241\) −5943.97 −1.58873 −0.794367 0.607439i \(-0.792197\pi\)
−0.794367 + 0.607439i \(0.792197\pi\)
\(242\) −16.7214 −0.00444172
\(243\) −2588.65 −0.683384
\(244\) 1347.90 0.353649
\(245\) −4146.22 −1.08119
\(246\) 11.7565 0.00304703
\(247\) −10190.5 −2.62513
\(248\) −48.7090 −0.0124719
\(249\) 1007.34 0.256377
\(250\) 17.2483 0.00436350
\(251\) −5413.50 −1.36134 −0.680671 0.732589i \(-0.738312\pi\)
−0.680671 + 0.732589i \(0.738312\pi\)
\(252\) 445.617 0.111394
\(253\) −4458.26 −1.10786
\(254\) 8.93599 0.00220746
\(255\) −389.041 −0.0955401
\(256\) 4094.34 0.999595
\(257\) −886.594 −0.215191 −0.107596 0.994195i \(-0.534315\pi\)
−0.107596 + 0.994195i \(0.534315\pi\)
\(258\) 0 0
\(259\) −1529.42 −0.366926
\(260\) −8222.04 −1.96119
\(261\) −981.401 −0.232748
\(262\) 3.37406 0.000795611 0
\(263\) −5738.13 −1.34535 −0.672677 0.739936i \(-0.734856\pi\)
−0.672677 + 0.739936i \(0.734856\pi\)
\(264\) 56.8204 0.0132464
\(265\) 5973.35 1.38468
\(266\) 13.5723 0.00312847
\(267\) −5963.33 −1.36685
\(268\) −5171.14 −1.17865
\(269\) −6018.64 −1.36418 −0.682088 0.731270i \(-0.738928\pi\)
−0.682088 + 0.731270i \(0.738928\pi\)
\(270\) −36.6844 −0.00826868
\(271\) −5924.82 −1.32807 −0.664035 0.747701i \(-0.731158\pi\)
−0.664035 + 0.747701i \(0.731158\pi\)
\(272\) 449.383 0.100176
\(273\) −1819.38 −0.403347
\(274\) 37.7974 0.00833367
\(275\) −2530.82 −0.554960
\(276\) 3113.21 0.678961
\(277\) −4026.86 −0.873467 −0.436733 0.899591i \(-0.643865\pi\)
−0.436733 + 0.899591i \(0.643865\pi\)
\(278\) 53.0338 0.0114416
\(279\) 1653.95 0.354909
\(280\) 21.9016 0.00467455
\(281\) −2988.01 −0.634340 −0.317170 0.948369i \(-0.602733\pi\)
−0.317170 + 0.948369i \(0.602733\pi\)
\(282\) 29.4872 0.00622673
\(283\) −715.323 −0.150253 −0.0751264 0.997174i \(-0.523936\pi\)
−0.0751264 + 0.997174i \(0.523936\pi\)
\(284\) 489.263 0.102227
\(285\) 7333.25 1.52415
\(286\) 65.8862 0.0136221
\(287\) 896.255 0.184335
\(288\) 33.8072 0.00691704
\(289\) −4863.68 −0.989962
\(290\) −24.1169 −0.00488343
\(291\) 5992.70 1.20721
\(292\) −2692.47 −0.539605
\(293\) 2561.88 0.510807 0.255403 0.966835i \(-0.417792\pi\)
0.255403 + 0.966835i \(0.417792\pi\)
\(294\) −23.2012 −0.00460245
\(295\) −8720.53 −1.72111
\(296\) −77.3537 −0.0151895
\(297\) −7255.41 −1.41751
\(298\) −55.9356 −0.0108734
\(299\) 7220.00 1.39647
\(300\) 1767.27 0.340112
\(301\) 0 0
\(302\) 33.2461 0.00633476
\(303\) −499.883 −0.0947773
\(304\) −8470.66 −1.59811
\(305\) −2249.50 −0.422315
\(306\) 1.23658 0.000231014 0
\(307\) −8416.19 −1.56462 −0.782309 0.622891i \(-0.785958\pi\)
−0.782309 + 0.622891i \(0.785958\pi\)
\(308\) 2165.80 0.400675
\(309\) 931.032 0.171406
\(310\) 40.6442 0.00744657
\(311\) −100.971 −0.0184102 −0.00920509 0.999958i \(-0.502930\pi\)
−0.00920509 + 0.999958i \(0.502930\pi\)
\(312\) −92.0187 −0.0166972
\(313\) 4616.96 0.833758 0.416879 0.908962i \(-0.363124\pi\)
0.416879 + 0.908962i \(0.363124\pi\)
\(314\) 22.8690 0.00411010
\(315\) −743.687 −0.133022
\(316\) −5317.16 −0.946563
\(317\) 6990.10 1.23850 0.619248 0.785195i \(-0.287438\pi\)
0.619248 + 0.785195i \(0.287438\pi\)
\(318\) 33.4254 0.00589434
\(319\) −4769.83 −0.837176
\(320\) −6833.85 −1.19382
\(321\) −1207.27 −0.209917
\(322\) −9.61602 −0.00166422
\(323\) −929.565 −0.160131
\(324\) 2953.88 0.506496
\(325\) 4098.57 0.699532
\(326\) −32.5867 −0.00553623
\(327\) −3622.68 −0.612644
\(328\) 45.3299 0.00763087
\(329\) 2247.95 0.376698
\(330\) −47.4126 −0.00790903
\(331\) −7239.49 −1.20217 −0.601085 0.799185i \(-0.705265\pi\)
−0.601085 + 0.799185i \(0.705265\pi\)
\(332\) 1941.98 0.321024
\(333\) 2626.61 0.432244
\(334\) 75.6301 0.0123901
\(335\) 8630.08 1.40750
\(336\) −1512.32 −0.245547
\(337\) 6873.75 1.11109 0.555545 0.831487i \(-0.312510\pi\)
0.555545 + 0.831487i \(0.312510\pi\)
\(338\) −67.1470 −0.0108057
\(339\) −7166.17 −1.14812
\(340\) −750.003 −0.119631
\(341\) 8038.58 1.27658
\(342\) −23.3089 −0.00368538
\(343\) −3722.20 −0.585947
\(344\) 0 0
\(345\) −5195.62 −0.810790
\(346\) 32.1595 0.00499684
\(347\) 274.973 0.0425399 0.0212699 0.999774i \(-0.493229\pi\)
0.0212699 + 0.999774i \(0.493229\pi\)
\(348\) 3330.78 0.513071
\(349\) 3858.09 0.591744 0.295872 0.955228i \(-0.404390\pi\)
0.295872 + 0.955228i \(0.404390\pi\)
\(350\) −5.45872 −0.000833660 0
\(351\) 11749.9 1.78679
\(352\) 164.311 0.0248801
\(353\) −8034.04 −1.21136 −0.605678 0.795710i \(-0.707098\pi\)
−0.605678 + 0.795710i \(0.707098\pi\)
\(354\) −48.7978 −0.00732649
\(355\) −816.528 −0.122076
\(356\) −11496.2 −1.71151
\(357\) −165.961 −0.0246039
\(358\) −39.3983 −0.00581639
\(359\) −12330.0 −1.81268 −0.906341 0.422546i \(-0.861136\pi\)
−0.906341 + 0.422546i \(0.861136\pi\)
\(360\) −37.6135 −0.00550668
\(361\) 10662.9 1.55458
\(362\) −23.1774 −0.00336512
\(363\) −3854.13 −0.557270
\(364\) −3507.44 −0.505054
\(365\) 4493.44 0.644377
\(366\) −12.5876 −0.00179772
\(367\) −2953.15 −0.420036 −0.210018 0.977698i \(-0.567352\pi\)
−0.210018 + 0.977698i \(0.567352\pi\)
\(368\) 6001.48 0.850132
\(369\) −1539.21 −0.217150
\(370\) 64.5462 0.00906918
\(371\) 2548.17 0.356589
\(372\) −5613.35 −0.782363
\(373\) 5174.01 0.718230 0.359115 0.933293i \(-0.383079\pi\)
0.359115 + 0.933293i \(0.383079\pi\)
\(374\) 6.01004 0.000830941 0
\(375\) 3975.55 0.547458
\(376\) 113.695 0.0155940
\(377\) 7724.57 1.05527
\(378\) −15.6492 −0.00212939
\(379\) 1962.08 0.265924 0.132962 0.991121i \(-0.457551\pi\)
0.132962 + 0.991121i \(0.457551\pi\)
\(380\) 14137.2 1.90848
\(381\) 2059.66 0.276954
\(382\) −39.0861 −0.00523513
\(383\) −11142.8 −1.48661 −0.743307 0.668951i \(-0.766744\pi\)
−0.743307 + 0.668951i \(0.766744\pi\)
\(384\) −152.984 −0.0203305
\(385\) −3614.49 −0.478471
\(386\) −33.5662 −0.00442610
\(387\) 0 0
\(388\) 11552.9 1.51162
\(389\) −1511.59 −0.197020 −0.0985099 0.995136i \(-0.531408\pi\)
−0.0985099 + 0.995136i \(0.531408\pi\)
\(390\) 76.7831 0.00996940
\(391\) 658.598 0.0851835
\(392\) −89.4574 −0.0115262
\(393\) 777.687 0.0998196
\(394\) 33.5937 0.00429550
\(395\) 8873.78 1.13035
\(396\) −3719.51 −0.472000
\(397\) −4147.44 −0.524317 −0.262159 0.965025i \(-0.584434\pi\)
−0.262159 + 0.965025i \(0.584434\pi\)
\(398\) 41.6522 0.00524581
\(399\) 3128.29 0.392507
\(400\) 3406.85 0.425857
\(401\) 10249.0 1.27633 0.638166 0.769899i \(-0.279693\pi\)
0.638166 + 0.769899i \(0.279693\pi\)
\(402\) 48.2917 0.00599147
\(403\) −13018.2 −1.60914
\(404\) −963.685 −0.118676
\(405\) −4929.71 −0.604838
\(406\) −10.2880 −0.00125760
\(407\) 12765.9 1.55475
\(408\) −8.39382 −0.00101852
\(409\) 11975.0 1.44774 0.723870 0.689937i \(-0.242362\pi\)
0.723870 + 0.689937i \(0.242362\pi\)
\(410\) −37.8246 −0.00455616
\(411\) 8711.93 1.04557
\(412\) 1794.86 0.214628
\(413\) −3720.09 −0.443229
\(414\) 16.5144 0.00196048
\(415\) −3240.96 −0.383355
\(416\) −266.095 −0.0313615
\(417\) 12223.8 1.43549
\(418\) −113.286 −0.0132560
\(419\) −8895.43 −1.03716 −0.518580 0.855029i \(-0.673539\pi\)
−0.518580 + 0.855029i \(0.673539\pi\)
\(420\) 2524.00 0.293235
\(421\) −13596.3 −1.57398 −0.786988 0.616969i \(-0.788360\pi\)
−0.786988 + 0.616969i \(0.788360\pi\)
\(422\) 13.3423 0.00153909
\(423\) −3860.59 −0.443755
\(424\) 128.879 0.0147616
\(425\) 373.866 0.0426710
\(426\) −4.56908 −0.000519654 0
\(427\) −959.614 −0.108756
\(428\) −2327.41 −0.262850
\(429\) 15186.1 1.70907
\(430\) 0 0
\(431\) 2369.68 0.264834 0.132417 0.991194i \(-0.457726\pi\)
0.132417 + 0.991194i \(0.457726\pi\)
\(432\) 9766.86 1.08775
\(433\) 10808.9 1.19964 0.599820 0.800135i \(-0.295239\pi\)
0.599820 + 0.800135i \(0.295239\pi\)
\(434\) 17.3384 0.00191767
\(435\) −5558.71 −0.612690
\(436\) −6983.88 −0.767127
\(437\) −12414.3 −1.35894
\(438\) 25.1441 0.00274300
\(439\) −6203.61 −0.674447 −0.337223 0.941425i \(-0.609488\pi\)
−0.337223 + 0.941425i \(0.609488\pi\)
\(440\) −182.810 −0.0198071
\(441\) 3037.59 0.327998
\(442\) −9.73306 −0.00104741
\(443\) 492.806 0.0528531 0.0264265 0.999651i \(-0.491587\pi\)
0.0264265 + 0.999651i \(0.491587\pi\)
\(444\) −8914.45 −0.952840
\(445\) 19186.0 2.04383
\(446\) 50.7695 0.00539014
\(447\) −12892.6 −1.36420
\(448\) −2915.25 −0.307439
\(449\) 10160.3 1.06791 0.533957 0.845511i \(-0.320704\pi\)
0.533957 + 0.845511i \(0.320704\pi\)
\(450\) 9.37471 0.000982062 0
\(451\) −7480.92 −0.781070
\(452\) −13815.1 −1.43763
\(453\) 7662.89 0.794777
\(454\) −36.2775 −0.00375019
\(455\) 5853.54 0.603117
\(456\) 158.219 0.0162485
\(457\) 5086.43 0.520641 0.260320 0.965522i \(-0.416172\pi\)
0.260320 + 0.965522i \(0.416172\pi\)
\(458\) 103.037 0.0105123
\(459\) 1071.81 0.108993
\(460\) −10016.2 −1.01524
\(461\) −1930.12 −0.194999 −0.0974997 0.995236i \(-0.531085\pi\)
−0.0974997 + 0.995236i \(0.531085\pi\)
\(462\) −20.2258 −0.00203677
\(463\) −3106.92 −0.311859 −0.155929 0.987768i \(-0.549837\pi\)
−0.155929 + 0.987768i \(0.549837\pi\)
\(464\) 6420.89 0.642419
\(465\) 9368.09 0.934268
\(466\) 114.866 0.0114185
\(467\) 16618.6 1.64671 0.823357 0.567523i \(-0.192098\pi\)
0.823357 + 0.567523i \(0.192098\pi\)
\(468\) 6023.61 0.594960
\(469\) 3681.50 0.362465
\(470\) −94.8701 −0.00931071
\(471\) 5271.07 0.515665
\(472\) −188.151 −0.0183482
\(473\) 0 0
\(474\) 49.6554 0.00481170
\(475\) −7047.20 −0.680732
\(476\) −319.944 −0.0308080
\(477\) −4376.18 −0.420066
\(478\) −32.9197 −0.00315003
\(479\) 4267.07 0.407030 0.203515 0.979072i \(-0.434763\pi\)
0.203515 + 0.979072i \(0.434763\pi\)
\(480\) 191.486 0.0182086
\(481\) −20673.9 −1.95977
\(482\) 107.011 0.0101125
\(483\) −2216.40 −0.208798
\(484\) −7430.07 −0.697790
\(485\) −19280.5 −1.80512
\(486\) 46.6045 0.00434984
\(487\) −7588.40 −0.706085 −0.353042 0.935607i \(-0.614853\pi\)
−0.353042 + 0.935607i \(0.614853\pi\)
\(488\) −48.5344 −0.00450215
\(489\) −7510.91 −0.694591
\(490\) 74.6459 0.00688195
\(491\) 15704.9 1.44349 0.721743 0.692161i \(-0.243341\pi\)
0.721743 + 0.692161i \(0.243341\pi\)
\(492\) 5223.94 0.478686
\(493\) 704.625 0.0643706
\(494\) 183.463 0.0167093
\(495\) 6207.46 0.563645
\(496\) −10821.1 −0.979601
\(497\) −348.323 −0.0314374
\(498\) −18.1356 −0.00163188
\(499\) 8093.69 0.726098 0.363049 0.931770i \(-0.381736\pi\)
0.363049 + 0.931770i \(0.381736\pi\)
\(500\) 7664.16 0.685503
\(501\) 17432.0 1.55450
\(502\) 97.4611 0.00866514
\(503\) −9867.83 −0.874722 −0.437361 0.899286i \(-0.644087\pi\)
−0.437361 + 0.899286i \(0.644087\pi\)
\(504\) −16.0455 −0.00141810
\(505\) 1608.29 0.141719
\(506\) 80.2636 0.00705169
\(507\) −15476.7 −1.35571
\(508\) 3970.65 0.346790
\(509\) −5383.79 −0.468825 −0.234413 0.972137i \(-0.575317\pi\)
−0.234413 + 0.972137i \(0.575317\pi\)
\(510\) 7.00405 0.000608127 0
\(511\) 1916.86 0.165943
\(512\) −368.649 −0.0318206
\(513\) −20203.1 −1.73877
\(514\) 15.9617 0.00136972
\(515\) −2995.44 −0.256300
\(516\) 0 0
\(517\) −18763.3 −1.59615
\(518\) 27.5348 0.00233554
\(519\) 7412.45 0.626918
\(520\) 296.054 0.0249670
\(521\) −298.734 −0.0251205 −0.0125602 0.999921i \(-0.503998\pi\)
−0.0125602 + 0.999921i \(0.503998\pi\)
\(522\) 17.6685 0.00148147
\(523\) 4948.95 0.413771 0.206886 0.978365i \(-0.433667\pi\)
0.206886 + 0.978365i \(0.433667\pi\)
\(524\) 1499.24 0.124990
\(525\) −1258.18 −0.104593
\(526\) 103.306 0.00856338
\(527\) −1187.50 −0.0981563
\(528\) 12623.1 1.04044
\(529\) −3371.47 −0.277100
\(530\) −107.540 −0.00881369
\(531\) 6388.81 0.522130
\(532\) 6030.78 0.491481
\(533\) 12115.1 0.984545
\(534\) 107.360 0.00870021
\(535\) 3884.20 0.313885
\(536\) 186.199 0.0150048
\(537\) −9080.92 −0.729741
\(538\) 108.356 0.00868317
\(539\) 14763.4 1.17979
\(540\) −16300.5 −1.29900
\(541\) 23749.8 1.88740 0.943701 0.330799i \(-0.107318\pi\)
0.943701 + 0.330799i \(0.107318\pi\)
\(542\) 106.667 0.00845336
\(543\) −5342.15 −0.422198
\(544\) −24.2728 −0.00191303
\(545\) 11655.3 0.916074
\(546\) 32.7549 0.00256736
\(547\) −487.096 −0.0380744 −0.0190372 0.999819i \(-0.506060\pi\)
−0.0190372 + 0.999819i \(0.506060\pi\)
\(548\) 16795.0 1.30921
\(549\) 1648.02 0.128116
\(550\) 45.5632 0.00353240
\(551\) −13281.8 −1.02691
\(552\) −112.099 −0.00864355
\(553\) 3785.46 0.291093
\(554\) 72.4969 0.00555974
\(555\) 14877.3 1.13785
\(556\) 23565.2 1.79746
\(557\) −18770.9 −1.42791 −0.713956 0.700190i \(-0.753098\pi\)
−0.713956 + 0.700190i \(0.753098\pi\)
\(558\) −29.7767 −0.00225904
\(559\) 0 0
\(560\) 4865.63 0.367162
\(561\) 1385.26 0.104252
\(562\) 53.7942 0.00403767
\(563\) −19245.5 −1.44068 −0.720339 0.693622i \(-0.756014\pi\)
−0.720339 + 0.693622i \(0.756014\pi\)
\(564\) 13102.5 0.978215
\(565\) 23055.9 1.71676
\(566\) 12.8782 0.000956381 0
\(567\) −2102.97 −0.155761
\(568\) −17.6171 −0.00130140
\(569\) 13782.8 1.01548 0.507738 0.861512i \(-0.330482\pi\)
0.507738 + 0.861512i \(0.330482\pi\)
\(570\) −132.023 −0.00970146
\(571\) 1113.80 0.0816307 0.0408153 0.999167i \(-0.487004\pi\)
0.0408153 + 0.999167i \(0.487004\pi\)
\(572\) 29276.1 2.14003
\(573\) −9008.96 −0.656815
\(574\) −16.1356 −0.00117332
\(575\) 4992.95 0.362122
\(576\) 5006.60 0.362167
\(577\) 355.943 0.0256813 0.0128406 0.999918i \(-0.495913\pi\)
0.0128406 + 0.999918i \(0.495913\pi\)
\(578\) 87.5626 0.00630125
\(579\) −7736.68 −0.555311
\(580\) −10716.2 −0.767184
\(581\) −1382.56 −0.0987234
\(582\) −107.889 −0.00768406
\(583\) −21269.2 −1.51095
\(584\) 96.9489 0.00686947
\(585\) −10052.8 −0.710479
\(586\) −46.1223 −0.00325136
\(587\) 2791.25 0.196265 0.0981324 0.995173i \(-0.468713\pi\)
0.0981324 + 0.995173i \(0.468713\pi\)
\(588\) −10309.3 −0.723042
\(589\) 22383.8 1.56589
\(590\) 156.999 0.0109551
\(591\) 7743.02 0.538926
\(592\) −17184.8 −1.19306
\(593\) 20640.7 1.42937 0.714683 0.699449i \(-0.246571\pi\)
0.714683 + 0.699449i \(0.246571\pi\)
\(594\) 130.622 0.00902269
\(595\) 533.952 0.0367897
\(596\) −24854.6 −1.70820
\(597\) 9600.40 0.658155
\(598\) −129.984 −0.00888871
\(599\) 3539.11 0.241409 0.120705 0.992688i \(-0.461485\pi\)
0.120705 + 0.992688i \(0.461485\pi\)
\(600\) −63.6350 −0.00432981
\(601\) −19466.5 −1.32123 −0.660613 0.750727i \(-0.729704\pi\)
−0.660613 + 0.750727i \(0.729704\pi\)
\(602\) 0 0
\(603\) −6322.55 −0.426988
\(604\) 14772.7 0.995185
\(605\) 12400.0 0.833275
\(606\) 8.99957 0.000603271 0
\(607\) 156.745 0.0104812 0.00524060 0.999986i \(-0.498332\pi\)
0.00524060 + 0.999986i \(0.498332\pi\)
\(608\) 457.532 0.0305187
\(609\) −2371.29 −0.157783
\(610\) 40.4985 0.00268810
\(611\) 30386.6 2.01196
\(612\) 549.465 0.0362922
\(613\) −8239.90 −0.542914 −0.271457 0.962451i \(-0.587506\pi\)
−0.271457 + 0.962451i \(0.587506\pi\)
\(614\) 151.520 0.00995902
\(615\) −8718.19 −0.571628
\(616\) −77.9849 −0.00510081
\(617\) −675.335 −0.0440647 −0.0220324 0.999757i \(-0.507014\pi\)
−0.0220324 + 0.999757i \(0.507014\pi\)
\(618\) −16.7617 −0.00109103
\(619\) −3826.89 −0.248491 −0.124245 0.992252i \(-0.539651\pi\)
−0.124245 + 0.992252i \(0.539651\pi\)
\(620\) 18060.0 1.16985
\(621\) 14313.9 0.924956
\(622\) 1.81783 0.000117184 0
\(623\) 8184.54 0.526335
\(624\) −20442.7 −1.31148
\(625\) −19445.5 −1.24451
\(626\) −83.1208 −0.00530699
\(627\) −26111.4 −1.66314
\(628\) 10161.7 0.645693
\(629\) −1885.85 −0.119545
\(630\) 13.3889 0.000846706 0
\(631\) −13119.3 −0.827687 −0.413843 0.910348i \(-0.635814\pi\)
−0.413843 + 0.910348i \(0.635814\pi\)
\(632\) 191.457 0.0120503
\(633\) 3075.27 0.193098
\(634\) −125.845 −0.00788321
\(635\) −6626.59 −0.414123
\(636\) 14852.4 0.925997
\(637\) −23908.8 −1.48713
\(638\) 85.8729 0.00532875
\(639\) 598.203 0.0370337
\(640\) 492.198 0.0303998
\(641\) 19467.8 1.19958 0.599791 0.800156i \(-0.295250\pi\)
0.599791 + 0.800156i \(0.295250\pi\)
\(642\) 21.7350 0.00133616
\(643\) −9713.64 −0.595752 −0.297876 0.954605i \(-0.596278\pi\)
−0.297876 + 0.954605i \(0.596278\pi\)
\(644\) −4272.82 −0.261448
\(645\) 0 0
\(646\) 16.7353 0.00101926
\(647\) −536.886 −0.0326232 −0.0163116 0.999867i \(-0.505192\pi\)
−0.0163116 + 0.999867i \(0.505192\pi\)
\(648\) −106.362 −0.00644797
\(649\) 31051.1 1.87806
\(650\) −73.7880 −0.00445262
\(651\) 3996.33 0.240597
\(652\) −14479.7 −0.869737
\(653\) −1067.84 −0.0639938 −0.0319969 0.999488i \(-0.510187\pi\)
−0.0319969 + 0.999488i \(0.510187\pi\)
\(654\) 65.2203 0.00389957
\(655\) −2502.07 −0.149258
\(656\) 10070.4 0.599365
\(657\) −3291.97 −0.195483
\(658\) −40.4706 −0.00239773
\(659\) 9950.77 0.588205 0.294102 0.955774i \(-0.404979\pi\)
0.294102 + 0.955774i \(0.404979\pi\)
\(660\) −21067.5 −1.24250
\(661\) −10362.8 −0.609785 −0.304892 0.952387i \(-0.598620\pi\)
−0.304892 + 0.952387i \(0.598620\pi\)
\(662\) 130.335 0.00765199
\(663\) −2243.37 −0.131411
\(664\) −69.9258 −0.00408682
\(665\) −10064.7 −0.586908
\(666\) −47.2877 −0.00275129
\(667\) 9410.20 0.546274
\(668\) 33605.8 1.94648
\(669\) 11701.9 0.676263
\(670\) −155.370 −0.00895892
\(671\) 8009.77 0.460825
\(672\) 81.6860 0.00468915
\(673\) −32597.3 −1.86707 −0.933533 0.358493i \(-0.883291\pi\)
−0.933533 + 0.358493i \(0.883291\pi\)
\(674\) −123.751 −0.00707225
\(675\) 8125.57 0.463338
\(676\) −29836.3 −1.69756
\(677\) 5463.36 0.310154 0.155077 0.987902i \(-0.450437\pi\)
0.155077 + 0.987902i \(0.450437\pi\)
\(678\) 129.015 0.00730795
\(679\) −8224.85 −0.464861
\(680\) 27.0057 0.00152297
\(681\) −8361.60 −0.470510
\(682\) −144.721 −0.00812561
\(683\) −2908.18 −0.162926 −0.0814629 0.996676i \(-0.525959\pi\)
−0.0814629 + 0.996676i \(0.525959\pi\)
\(684\) −10357.2 −0.578970
\(685\) −28029.1 −1.56341
\(686\) 67.0121 0.00372964
\(687\) 23749.1 1.31890
\(688\) 0 0
\(689\) 34444.8 1.90456
\(690\) 93.5385 0.00516080
\(691\) −26270.3 −1.44626 −0.723132 0.690709i \(-0.757298\pi\)
−0.723132 + 0.690709i \(0.757298\pi\)
\(692\) 14289.9 0.785000
\(693\) 2648.04 0.145152
\(694\) −4.95044 −0.000270773 0
\(695\) −39327.9 −2.14646
\(696\) −119.933 −0.00653167
\(697\) 1105.12 0.0600566
\(698\) −69.4585 −0.00376654
\(699\) 26475.4 1.43260
\(700\) −2425.55 −0.130967
\(701\) −2836.62 −0.152836 −0.0764178 0.997076i \(-0.524348\pi\)
−0.0764178 + 0.997076i \(0.524348\pi\)
\(702\) −211.537 −0.0113732
\(703\) 35547.3 1.90710
\(704\) 24333.2 1.30269
\(705\) −21866.6 −1.16815
\(706\) 144.640 0.00771046
\(707\) 686.079 0.0364960
\(708\) −21683.0 −1.15099
\(709\) −5284.45 −0.279918 −0.139959 0.990157i \(-0.544697\pi\)
−0.139959 + 0.990157i \(0.544697\pi\)
\(710\) 14.7002 0.000777028 0
\(711\) −6501.08 −0.342911
\(712\) 413.950 0.0217885
\(713\) −15859.0 −0.832993
\(714\) 2.98786 0.000156607 0
\(715\) −48858.7 −2.55554
\(716\) −17506.4 −0.913750
\(717\) −7587.66 −0.395211
\(718\) 221.982 0.0115380
\(719\) 8442.51 0.437904 0.218952 0.975736i \(-0.429736\pi\)
0.218952 + 0.975736i \(0.429736\pi\)
\(720\) −8356.15 −0.432521
\(721\) −1277.82 −0.0660036
\(722\) −191.967 −0.00989512
\(723\) 24665.0 1.26875
\(724\) −10298.7 −0.528658
\(725\) 5341.88 0.273645
\(726\) 69.3872 0.00354711
\(727\) 19342.0 0.986731 0.493366 0.869822i \(-0.335766\pi\)
0.493366 + 0.869822i \(0.335766\pi\)
\(728\) 126.294 0.00642962
\(729\) 20711.6 1.05226
\(730\) −80.8970 −0.00410155
\(731\) 0 0
\(732\) −5593.24 −0.282421
\(733\) −907.180 −0.0457127 −0.0228564 0.999739i \(-0.507276\pi\)
−0.0228564 + 0.999739i \(0.507276\pi\)
\(734\) 53.1666 0.00267359
\(735\) 17205.1 0.863429
\(736\) −324.162 −0.0162347
\(737\) −30729.0 −1.53584
\(738\) 27.7110 0.00138219
\(739\) 26048.6 1.29663 0.648317 0.761370i \(-0.275473\pi\)
0.648317 + 0.761370i \(0.275473\pi\)
\(740\) 28680.7 1.42476
\(741\) 42286.5 2.09640
\(742\) −45.8756 −0.00226974
\(743\) 30883.3 1.52489 0.762447 0.647050i \(-0.223998\pi\)
0.762447 + 0.647050i \(0.223998\pi\)
\(744\) 202.122 0.00995990
\(745\) 41479.7 2.03986
\(746\) −93.1494 −0.00457164
\(747\) 2374.38 0.116297
\(748\) 2670.53 0.130540
\(749\) 1656.96 0.0808331
\(750\) −71.5732 −0.00348465
\(751\) 4168.40 0.202540 0.101270 0.994859i \(-0.467709\pi\)
0.101270 + 0.994859i \(0.467709\pi\)
\(752\) 25258.2 1.22483
\(753\) 22463.8 1.08715
\(754\) −139.068 −0.00671693
\(755\) −24654.0 −1.18841
\(756\) −6953.63 −0.334525
\(757\) 21816.2 1.04746 0.523728 0.851886i \(-0.324541\pi\)
0.523728 + 0.851886i \(0.324541\pi\)
\(758\) −35.3239 −0.00169264
\(759\) 18500.0 0.884725
\(760\) −509.044 −0.0242960
\(761\) 11079.6 0.527774 0.263887 0.964554i \(-0.414995\pi\)
0.263887 + 0.964554i \(0.414995\pi\)
\(762\) −37.0807 −0.00176285
\(763\) 4972.05 0.235911
\(764\) −17367.7 −0.822435
\(765\) −916.999 −0.0433388
\(766\) 200.609 0.00946251
\(767\) −50286.1 −2.36731
\(768\) −16989.8 −0.798266
\(769\) 23438.6 1.09911 0.549555 0.835457i \(-0.314797\pi\)
0.549555 + 0.835457i \(0.314797\pi\)
\(770\) 65.0729 0.00304554
\(771\) 3679.00 0.171850
\(772\) −14914.9 −0.695337
\(773\) −37721.7 −1.75518 −0.877591 0.479411i \(-0.840850\pi\)
−0.877591 + 0.479411i \(0.840850\pi\)
\(774\) 0 0
\(775\) −9002.66 −0.417271
\(776\) −415.988 −0.0192437
\(777\) 6346.49 0.293023
\(778\) 27.2137 0.00125406
\(779\) −20831.0 −0.958085
\(780\) 34118.1 1.56618
\(781\) 2907.40 0.133207
\(782\) −11.8570 −0.000542205 0
\(783\) 15314.3 0.698961
\(784\) −19873.7 −0.905325
\(785\) −16958.8 −0.771062
\(786\) −14.0010 −0.000635367 0
\(787\) −11707.4 −0.530270 −0.265135 0.964211i \(-0.585417\pi\)
−0.265135 + 0.964211i \(0.585417\pi\)
\(788\) 14927.2 0.674820
\(789\) 23810.9 1.07439
\(790\) −159.758 −0.00719484
\(791\) 9835.42 0.442108
\(792\) 133.930 0.00600882
\(793\) −12971.5 −0.580874
\(794\) 74.6678 0.00333735
\(795\) −24787.0 −1.10579
\(796\) 18507.9 0.824113
\(797\) 1717.85 0.0763482 0.0381741 0.999271i \(-0.487846\pi\)
0.0381741 + 0.999271i \(0.487846\pi\)
\(798\) −56.3197 −0.00249836
\(799\) 2771.82 0.122728
\(800\) −184.017 −0.00813247
\(801\) −14056.0 −0.620030
\(802\) −184.516 −0.00812404
\(803\) −15999.7 −0.703136
\(804\) 21458.1 0.941256
\(805\) 7130.88 0.312212
\(806\) 234.371 0.0102424
\(807\) 24974.9 1.08942
\(808\) 34.6998 0.00151081
\(809\) −20559.3 −0.893482 −0.446741 0.894663i \(-0.647415\pi\)
−0.446741 + 0.894663i \(0.647415\pi\)
\(810\) 88.7514 0.00384988
\(811\) 12479.9 0.540354 0.270177 0.962811i \(-0.412918\pi\)
0.270177 + 0.962811i \(0.412918\pi\)
\(812\) −4571.43 −0.197569
\(813\) 24585.6 1.06058
\(814\) −229.829 −0.00989619
\(815\) 24165.1 1.03861
\(816\) −1864.76 −0.0799995
\(817\) 0 0
\(818\) −215.590 −0.00921507
\(819\) −4288.40 −0.182966
\(820\) −16807.1 −0.715769
\(821\) −29309.3 −1.24592 −0.622962 0.782252i \(-0.714071\pi\)
−0.622962 + 0.782252i \(0.714071\pi\)
\(822\) −156.844 −0.00665518
\(823\) −21999.6 −0.931782 −0.465891 0.884842i \(-0.654266\pi\)
−0.465891 + 0.884842i \(0.654266\pi\)
\(824\) −64.6284 −0.00273233
\(825\) 10501.9 0.443185
\(826\) 66.9740 0.00282122
\(827\) 30534.9 1.28392 0.641960 0.766738i \(-0.278121\pi\)
0.641960 + 0.766738i \(0.278121\pi\)
\(828\) 7338.06 0.307990
\(829\) 26025.4 1.09035 0.545174 0.838323i \(-0.316464\pi\)
0.545174 + 0.838323i \(0.316464\pi\)
\(830\) 58.3481 0.00244011
\(831\) 16709.8 0.697541
\(832\) −39406.8 −1.64205
\(833\) −2180.93 −0.0907139
\(834\) −220.069 −0.00913712
\(835\) −56084.4 −2.32441
\(836\) −50338.1 −2.08251
\(837\) −25809.1 −1.06582
\(838\) 160.148 0.00660168
\(839\) 18134.8 0.746224 0.373112 0.927786i \(-0.378291\pi\)
0.373112 + 0.927786i \(0.378291\pi\)
\(840\) −90.8829 −0.00373304
\(841\) −14321.2 −0.587198
\(842\) 244.779 0.0100186
\(843\) 12399.0 0.506578
\(844\) 5928.58 0.241789
\(845\) 49793.7 2.02716
\(846\) 69.5035 0.00282456
\(847\) 5289.71 0.214589
\(848\) 28631.5 1.15945
\(849\) 2968.30 0.119990
\(850\) −6.73084 −0.000271607 0
\(851\) −25185.3 −1.01450
\(852\) −2030.24 −0.0816373
\(853\) −14999.0 −0.602059 −0.301029 0.953615i \(-0.597330\pi\)
−0.301029 + 0.953615i \(0.597330\pi\)
\(854\) 17.2763 0.000692250 0
\(855\) 17285.0 0.691385
\(856\) 83.8041 0.00334622
\(857\) −19754.8 −0.787409 −0.393705 0.919237i \(-0.628807\pi\)
−0.393705 + 0.919237i \(0.628807\pi\)
\(858\) −273.401 −0.0108785
\(859\) −31691.4 −1.25879 −0.629393 0.777087i \(-0.716696\pi\)
−0.629393 + 0.777087i \(0.716696\pi\)
\(860\) 0 0
\(861\) −3719.09 −0.147208
\(862\) −42.6622 −0.00168571
\(863\) −11419.1 −0.450420 −0.225210 0.974310i \(-0.572307\pi\)
−0.225210 + 0.974310i \(0.572307\pi\)
\(864\) −527.544 −0.0207725
\(865\) −23848.3 −0.937417
\(866\) −194.597 −0.00763588
\(867\) 20182.3 0.790573
\(868\) 7704.22 0.301265
\(869\) −31596.7 −1.23342
\(870\) 100.075 0.00389986
\(871\) 49764.6 1.93594
\(872\) 251.472 0.00976594
\(873\) 14125.2 0.547613
\(874\) 223.498 0.00864982
\(875\) −5456.36 −0.210810
\(876\) 11172.6 0.430923
\(877\) −21841.3 −0.840966 −0.420483 0.907301i \(-0.638139\pi\)
−0.420483 + 0.907301i \(0.638139\pi\)
\(878\) 111.686 0.00429295
\(879\) −10630.7 −0.407925
\(880\) −40612.8 −1.55575
\(881\) −18076.0 −0.691257 −0.345628 0.938372i \(-0.612334\pi\)
−0.345628 + 0.938372i \(0.612334\pi\)
\(882\) −54.6869 −0.00208776
\(883\) −26624.2 −1.01469 −0.507347 0.861742i \(-0.669374\pi\)
−0.507347 + 0.861742i \(0.669374\pi\)
\(884\) −4324.82 −0.164547
\(885\) 36186.6 1.37446
\(886\) −8.87215 −0.000336417 0
\(887\) −31435.2 −1.18996 −0.594978 0.803742i \(-0.702839\pi\)
−0.594978 + 0.803742i \(0.702839\pi\)
\(888\) 320.986 0.0121302
\(889\) −2826.84 −0.106647
\(890\) −345.412 −0.0130092
\(891\) 17553.2 0.659993
\(892\) 22559.1 0.846787
\(893\) −52247.5 −1.95789
\(894\) 232.110 0.00868335
\(895\) 29216.3 1.09117
\(896\) 209.967 0.00782868
\(897\) −29960.1 −1.11520
\(898\) −182.919 −0.00679743
\(899\) −16967.3 −0.629467
\(900\) 4165.59 0.154281
\(901\) 3142.01 0.116177
\(902\) 134.682 0.00497163
\(903\) 0 0
\(904\) 497.446 0.0183018
\(905\) 17187.5 0.631304
\(906\) −137.958 −0.00505887
\(907\) 17535.3 0.641950 0.320975 0.947088i \(-0.395989\pi\)
0.320975 + 0.947088i \(0.395989\pi\)
\(908\) −16119.7 −0.589152
\(909\) −1178.26 −0.0429927
\(910\) −105.383 −0.00383893
\(911\) 10181.4 0.370278 0.185139 0.982712i \(-0.440726\pi\)
0.185139 + 0.982712i \(0.440726\pi\)
\(912\) 35149.8 1.27623
\(913\) 11540.0 0.418313
\(914\) −91.5727 −0.00331396
\(915\) 9334.51 0.337256
\(916\) 45784.0 1.65147
\(917\) −1067.36 −0.0384376
\(918\) −19.2961 −0.000693756 0
\(919\) 24370.5 0.874764 0.437382 0.899276i \(-0.355906\pi\)
0.437382 + 0.899276i \(0.355906\pi\)
\(920\) 360.659 0.0129245
\(921\) 34923.8 1.24949
\(922\) 34.7487 0.00124120
\(923\) −4708.44 −0.167909
\(924\) −8987.19 −0.319975
\(925\) −14296.9 −0.508195
\(926\) 55.9349 0.00198503
\(927\) 2194.51 0.0777531
\(928\) −346.816 −0.0122681
\(929\) 10550.6 0.372608 0.186304 0.982492i \(-0.440349\pi\)
0.186304 + 0.982492i \(0.440349\pi\)
\(930\) −168.657 −0.00594675
\(931\) 41109.4 1.44716
\(932\) 51039.8 1.79385
\(933\) 418.991 0.0147022
\(934\) −299.190 −0.0104816
\(935\) −4456.82 −0.155886
\(936\) −216.895 −0.00757417
\(937\) −26213.4 −0.913931 −0.456966 0.889484i \(-0.651064\pi\)
−0.456966 + 0.889484i \(0.651064\pi\)
\(938\) −66.2794 −0.00230714
\(939\) −19158.5 −0.665830
\(940\) −42154.9 −1.46270
\(941\) −12985.5 −0.449856 −0.224928 0.974375i \(-0.572215\pi\)
−0.224928 + 0.974375i \(0.572215\pi\)
\(942\) −94.8969 −0.00328228
\(943\) 14758.8 0.509664
\(944\) −41799.3 −1.44116
\(945\) 11604.9 0.399477
\(946\) 0 0
\(947\) 19335.2 0.663474 0.331737 0.943372i \(-0.392365\pi\)
0.331737 + 0.943372i \(0.392365\pi\)
\(948\) 22064.1 0.755915
\(949\) 25911.0 0.886309
\(950\) 126.873 0.00433296
\(951\) −29006.1 −0.989050
\(952\) 11.5203 0.000392202 0
\(953\) −29785.2 −1.01242 −0.506210 0.862410i \(-0.668954\pi\)
−0.506210 + 0.862410i \(0.668954\pi\)
\(954\) 78.7860 0.00267378
\(955\) 28984.8 0.982121
\(956\) −14627.7 −0.494867
\(957\) 19792.8 0.668560
\(958\) −76.8216 −0.00259081
\(959\) −11956.9 −0.402617
\(960\) 28357.7 0.953375
\(961\) −1196.05 −0.0401482
\(962\) 372.200 0.0124742
\(963\) −2845.63 −0.0952225
\(964\) 47549.8 1.58867
\(965\) 24891.4 0.830346
\(966\) 39.9026 0.00132903
\(967\) 31419.2 1.04485 0.522426 0.852684i \(-0.325027\pi\)
0.522426 + 0.852684i \(0.325027\pi\)
\(968\) 267.538 0.00888325
\(969\) 3857.31 0.127879
\(970\) 347.113 0.0114898
\(971\) −4021.58 −0.132913 −0.0664565 0.997789i \(-0.521169\pi\)
−0.0664565 + 0.997789i \(0.521169\pi\)
\(972\) 20708.4 0.683356
\(973\) −16776.9 −0.552766
\(974\) 136.617 0.00449433
\(975\) −17007.4 −0.558639
\(976\) −10782.3 −0.353621
\(977\) 3043.64 0.0996671 0.0498335 0.998758i \(-0.484131\pi\)
0.0498335 + 0.998758i \(0.484131\pi\)
\(978\) 135.222 0.00442117
\(979\) −68315.3 −2.23020
\(980\) 33168.4 1.08115
\(981\) −8538.91 −0.277907
\(982\) −282.741 −0.00918800
\(983\) 20451.1 0.663569 0.331785 0.943355i \(-0.392349\pi\)
0.331785 + 0.943355i \(0.392349\pi\)
\(984\) −188.101 −0.00609393
\(985\) −24911.9 −0.805845
\(986\) −12.6856 −0.000409728 0
\(987\) −9328.08 −0.300827
\(988\) 81520.8 2.62502
\(989\) 0 0
\(990\) −111.755 −0.00358768
\(991\) −945.176 −0.0302972 −0.0151486 0.999885i \(-0.504822\pi\)
−0.0151486 + 0.999885i \(0.504822\pi\)
\(992\) 584.488 0.0187072
\(993\) 30040.9 0.960040
\(994\) 6.27097 0.000200104 0
\(995\) −30887.7 −0.984125
\(996\) −8058.43 −0.256367
\(997\) 2417.17 0.0767828 0.0383914 0.999263i \(-0.487777\pi\)
0.0383914 + 0.999263i \(0.487777\pi\)
\(998\) −145.713 −0.00462172
\(999\) −40986.8 −1.29806
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 1849.4.a.j.1.24 yes 50
43.42 odd 2 1849.4.a.i.1.27 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.27 50 43.42 odd 2
1849.4.a.j.1.24 yes 50 1.1 even 1 trivial