Properties

Label 1805.2.a.j.1.1
Level $1805$
Weight $2$
Character 1805.1
Self dual yes
Analytic conductor $14.413$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.4129975648\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.2225.1
Defining polynomial: \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.43828\) of defining polynomial
Character \(\chi\) \(=\) 1805.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.43828 q^{2} +2.94523 q^{3} +3.94523 q^{4} +1.00000 q^{5} -7.18129 q^{6} -3.82025 q^{7} -4.74301 q^{8} +5.67435 q^{9} +O(q^{10})\) \(q-2.43828 q^{2} +2.94523 q^{3} +3.94523 q^{4} +1.00000 q^{5} -7.18129 q^{6} -3.82025 q^{7} -4.74301 q^{8} +5.67435 q^{9} -2.43828 q^{10} -2.12498 q^{11} +11.6196 q^{12} -3.65438 q^{13} +9.31485 q^{14} +2.94523 q^{15} +3.67435 q^{16} -3.04243 q^{17} -13.8357 q^{18} +3.94523 q^{20} -11.2515 q^{21} +5.18129 q^{22} -4.81167 q^{23} -13.9692 q^{24} +1.00000 q^{25} +8.91042 q^{26} +7.87657 q^{27} -15.0717 q^{28} +6.03385 q^{29} -7.18129 q^{30} +3.57184 q^{31} +0.526911 q^{32} -6.25853 q^{33} +7.41831 q^{34} -3.82025 q^{35} +22.3866 q^{36} +3.93134 q^{37} -10.7630 q^{39} -4.74301 q^{40} -7.60945 q^{41} +27.4343 q^{42} -5.60415 q^{43} -8.38351 q^{44} +5.67435 q^{45} +11.7322 q^{46} -8.41831 q^{47} +10.8218 q^{48} +7.59430 q^{49} -2.43828 q^{50} -8.96065 q^{51} -14.4174 q^{52} +4.80028 q^{53} -19.2053 q^{54} -2.12498 q^{55} +18.1195 q^{56} -14.7122 q^{58} -5.13510 q^{59} +11.6196 q^{60} -13.5100 q^{61} -8.70916 q^{62} -21.6774 q^{63} -8.63346 q^{64} -3.65438 q^{65} +15.2601 q^{66} -5.38101 q^{67} -12.0031 q^{68} -14.1714 q^{69} +9.31485 q^{70} -0.123434 q^{71} -26.9135 q^{72} -12.4860 q^{73} -9.58572 q^{74} +2.94523 q^{75} +8.11794 q^{77} +26.2432 q^{78} -4.25699 q^{79} +3.67435 q^{80} +6.17521 q^{81} +18.5540 q^{82} +4.39739 q^{83} -44.3897 q^{84} -3.04243 q^{85} +13.6645 q^{86} +17.7711 q^{87} +10.0788 q^{88} -0.0772394 q^{89} -13.8357 q^{90} +13.9607 q^{91} -18.9831 q^{92} +10.5199 q^{93} +20.5262 q^{94} +1.55187 q^{96} -18.0231 q^{97} -18.5171 q^{98} -12.0579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - q^{3} + 3 q^{4} + 4 q^{5} - 7 q^{6} - 11 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - q^{3} + 3 q^{4} + 4 q^{5} - 7 q^{6} - 11 q^{7} - 6 q^{8} + 5 q^{9} - q^{10} + 16 q^{12} + 2 q^{13} + 11 q^{14} - q^{15} - 3 q^{16} - 7 q^{17} - 17 q^{18} + 3 q^{20} - 2 q^{21} - q^{22} - 11 q^{23} - 13 q^{24} + 4 q^{25} + 9 q^{26} + 14 q^{27} - 13 q^{28} + 15 q^{29} - 7 q^{30} + q^{31} - 3 q^{32} - 12 q^{33} + 22 q^{34} - 11 q^{35} + 16 q^{36} + 11 q^{37} - 29 q^{39} - 6 q^{40} - 22 q^{41} + 19 q^{42} - 26 q^{43} - 12 q^{44} + 5 q^{45} - 10 q^{46} - 26 q^{47} + 13 q^{48} + 13 q^{49} - q^{50} + 11 q^{51} - 27 q^{52} + 16 q^{53} - 25 q^{54} + 8 q^{56} - 3 q^{58} + 10 q^{59} + 16 q^{60} + 2 q^{61} - 31 q^{62} - 17 q^{63} + 4 q^{64} + 2 q^{65} + 22 q^{66} - 3 q^{67} + 4 q^{68} - 14 q^{69} + 11 q^{70} - 18 q^{71} - 29 q^{72} - 24 q^{73} - 17 q^{74} - q^{75} - 6 q^{77} + 15 q^{78} - 30 q^{79} - 3 q^{80} - 4 q^{81} - 13 q^{82} - 12 q^{83} - 52 q^{84} - 7 q^{85} + 16 q^{86} - q^{87} + 23 q^{88} - 9 q^{89} - 17 q^{90} + 9 q^{91} - 25 q^{92} + 7 q^{93} + 11 q^{94} - 6 q^{96} - 19 q^{97} - 48 q^{98} - 9 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43828 −1.72413 −0.862063 0.506801i \(-0.830828\pi\)
−0.862063 + 0.506801i \(0.830828\pi\)
\(3\) 2.94523 1.70043 0.850213 0.526438i \(-0.176473\pi\)
0.850213 + 0.526438i \(0.176473\pi\)
\(4\) 3.94523 1.97261
\(5\) 1.00000 0.447214
\(6\) −7.18129 −2.93175
\(7\) −3.82025 −1.44392 −0.721959 0.691936i \(-0.756758\pi\)
−0.721959 + 0.691936i \(0.756758\pi\)
\(8\) −4.74301 −1.67691
\(9\) 5.67435 1.89145
\(10\) −2.43828 −0.771053
\(11\) −2.12498 −0.640704 −0.320352 0.947299i \(-0.603801\pi\)
−0.320352 + 0.947299i \(0.603801\pi\)
\(12\) 11.6196 3.35428
\(13\) −3.65438 −1.01354 −0.506772 0.862080i \(-0.669161\pi\)
−0.506772 + 0.862080i \(0.669161\pi\)
\(14\) 9.31485 2.48950
\(15\) 2.94523 0.760454
\(16\) 3.67435 0.918588
\(17\) −3.04243 −0.737898 −0.368949 0.929450i \(-0.620282\pi\)
−0.368949 + 0.929450i \(0.620282\pi\)
\(18\) −13.8357 −3.26110
\(19\) 0 0
\(20\) 3.94523 0.882179
\(21\) −11.2515 −2.45528
\(22\) 5.18129 1.10466
\(23\) −4.81167 −1.00330 −0.501651 0.865070i \(-0.667274\pi\)
−0.501651 + 0.865070i \(0.667274\pi\)
\(24\) −13.9692 −2.85146
\(25\) 1.00000 0.200000
\(26\) 8.91042 1.74748
\(27\) 7.87657 1.51585
\(28\) −15.0717 −2.84829
\(29\) 6.03385 1.12046 0.560229 0.828338i \(-0.310713\pi\)
0.560229 + 0.828338i \(0.310713\pi\)
\(30\) −7.18129 −1.31112
\(31\) 3.57184 0.641521 0.320761 0.947160i \(-0.396061\pi\)
0.320761 + 0.947160i \(0.396061\pi\)
\(32\) 0.526911 0.0931455
\(33\) −6.25853 −1.08947
\(34\) 7.41831 1.27223
\(35\) −3.82025 −0.645740
\(36\) 22.3866 3.73110
\(37\) 3.93134 0.646309 0.323154 0.946346i \(-0.395257\pi\)
0.323154 + 0.946346i \(0.395257\pi\)
\(38\) 0 0
\(39\) −10.7630 −1.72346
\(40\) −4.74301 −0.749936
\(41\) −7.60945 −1.18840 −0.594198 0.804318i \(-0.702531\pi\)
−0.594198 + 0.804318i \(0.702531\pi\)
\(42\) 27.4343 4.23321
\(43\) −5.60415 −0.854625 −0.427312 0.904104i \(-0.640540\pi\)
−0.427312 + 0.904104i \(0.640540\pi\)
\(44\) −8.38351 −1.26386
\(45\) 5.67435 0.845882
\(46\) 11.7322 1.72982
\(47\) −8.41831 −1.22794 −0.613969 0.789330i \(-0.710428\pi\)
−0.613969 + 0.789330i \(0.710428\pi\)
\(48\) 10.8218 1.56199
\(49\) 7.59430 1.08490
\(50\) −2.43828 −0.344825
\(51\) −8.96065 −1.25474
\(52\) −14.4174 −1.99933
\(53\) 4.80028 0.659369 0.329685 0.944091i \(-0.393058\pi\)
0.329685 + 0.944091i \(0.393058\pi\)
\(54\) −19.2053 −2.61351
\(55\) −2.12498 −0.286532
\(56\) 18.1195 2.42132
\(57\) 0 0
\(58\) −14.7122 −1.93181
\(59\) −5.13510 −0.668533 −0.334266 0.942479i \(-0.608489\pi\)
−0.334266 + 0.942479i \(0.608489\pi\)
\(60\) 11.6196 1.50008
\(61\) −13.5100 −1.72978 −0.864891 0.501960i \(-0.832612\pi\)
−0.864891 + 0.501960i \(0.832612\pi\)
\(62\) −8.70916 −1.10606
\(63\) −21.6774 −2.73110
\(64\) −8.63346 −1.07918
\(65\) −3.65438 −0.453270
\(66\) 15.2601 1.87839
\(67\) −5.38101 −0.657395 −0.328698 0.944435i \(-0.606610\pi\)
−0.328698 + 0.944435i \(0.606610\pi\)
\(68\) −12.0031 −1.45559
\(69\) −14.1714 −1.70604
\(70\) 9.31485 1.11334
\(71\) −0.123434 −0.0146489 −0.00732443 0.999973i \(-0.502331\pi\)
−0.00732443 + 0.999973i \(0.502331\pi\)
\(72\) −26.9135 −3.17179
\(73\) −12.4860 −1.46138 −0.730689 0.682710i \(-0.760801\pi\)
−0.730689 + 0.682710i \(0.760801\pi\)
\(74\) −9.58572 −1.11432
\(75\) 2.94523 0.340085
\(76\) 0 0
\(77\) 8.11794 0.925125
\(78\) 26.2432 2.97146
\(79\) −4.25699 −0.478949 −0.239474 0.970903i \(-0.576975\pi\)
−0.239474 + 0.970903i \(0.576975\pi\)
\(80\) 3.67435 0.410805
\(81\) 6.17521 0.686134
\(82\) 18.5540 2.04895
\(83\) 4.39739 0.482677 0.241338 0.970441i \(-0.422414\pi\)
0.241338 + 0.970441i \(0.422414\pi\)
\(84\) −44.3897 −4.84331
\(85\) −3.04243 −0.329998
\(86\) 13.6645 1.47348
\(87\) 17.7711 1.90526
\(88\) 10.0788 1.07440
\(89\) −0.0772394 −0.00818736 −0.00409368 0.999992i \(-0.501303\pi\)
−0.00409368 + 0.999992i \(0.501303\pi\)
\(90\) −13.8357 −1.45841
\(91\) 13.9607 1.46347
\(92\) −18.9831 −1.97913
\(93\) 10.5199 1.09086
\(94\) 20.5262 2.11712
\(95\) 0 0
\(96\) 1.55187 0.158387
\(97\) −18.0231 −1.82996 −0.914982 0.403495i \(-0.867795\pi\)
−0.914982 + 0.403495i \(0.867795\pi\)
\(98\) −18.5171 −1.87051
\(99\) −12.0579 −1.21186
\(100\) 3.94523 0.394523
\(101\) 18.6498 1.85573 0.927864 0.372918i \(-0.121643\pi\)
0.927864 + 0.372918i \(0.121643\pi\)
\(102\) 21.8486 2.16333
\(103\) 0.377423 0.0371886 0.0185943 0.999827i \(-0.494081\pi\)
0.0185943 + 0.999827i \(0.494081\pi\)
\(104\) 17.3328 1.69962
\(105\) −11.2515 −1.09803
\(106\) −11.7044 −1.13684
\(107\) 2.76144 0.266958 0.133479 0.991052i \(-0.457385\pi\)
0.133479 + 0.991052i \(0.457385\pi\)
\(108\) 31.0748 2.99018
\(109\) −3.00308 −0.287643 −0.143822 0.989604i \(-0.545939\pi\)
−0.143822 + 0.989604i \(0.545939\pi\)
\(110\) 5.18129 0.494017
\(111\) 11.5787 1.09900
\(112\) −14.0369 −1.32637
\(113\) 3.61708 0.340266 0.170133 0.985421i \(-0.445580\pi\)
0.170133 + 0.985421i \(0.445580\pi\)
\(114\) 0 0
\(115\) −4.81167 −0.448690
\(116\) 23.8049 2.21023
\(117\) −20.7362 −1.91707
\(118\) 12.5208 1.15264
\(119\) 11.6229 1.06547
\(120\) −13.9692 −1.27521
\(121\) −6.48448 −0.589498
\(122\) 32.9413 2.98236
\(123\) −22.4116 −2.02078
\(124\) 14.0917 1.26547
\(125\) 1.00000 0.0894427
\(126\) 52.8557 4.70876
\(127\) 13.6188 1.20847 0.604236 0.796805i \(-0.293478\pi\)
0.604236 + 0.796805i \(0.293478\pi\)
\(128\) 19.9970 1.76750
\(129\) −16.5055 −1.45323
\(130\) 8.91042 0.781495
\(131\) 5.67059 0.495442 0.247721 0.968831i \(-0.420318\pi\)
0.247721 + 0.968831i \(0.420318\pi\)
\(132\) −24.6913 −2.14910
\(133\) 0 0
\(134\) 13.1204 1.13343
\(135\) 7.87657 0.677907
\(136\) 14.4303 1.23739
\(137\) −8.10501 −0.692457 −0.346229 0.938150i \(-0.612538\pi\)
−0.346229 + 0.938150i \(0.612538\pi\)
\(138\) 34.5540 2.94143
\(139\) −17.5325 −1.48709 −0.743543 0.668688i \(-0.766856\pi\)
−0.743543 + 0.668688i \(0.766856\pi\)
\(140\) −15.0717 −1.27379
\(141\) −24.7938 −2.08802
\(142\) 0.300966 0.0252565
\(143\) 7.76547 0.649382
\(144\) 20.8496 1.73746
\(145\) 6.03385 0.501084
\(146\) 30.4445 2.51960
\(147\) 22.3669 1.84479
\(148\) 15.5100 1.27492
\(149\) 19.1952 1.57253 0.786265 0.617889i \(-0.212012\pi\)
0.786265 + 0.617889i \(0.212012\pi\)
\(150\) −7.18129 −0.586350
\(151\) −11.1473 −0.907152 −0.453576 0.891218i \(-0.649852\pi\)
−0.453576 + 0.891218i \(0.649852\pi\)
\(152\) 0 0
\(153\) −17.2638 −1.39570
\(154\) −19.7938 −1.59503
\(155\) 3.57184 0.286897
\(156\) −42.4624 −3.39971
\(157\) 11.1452 0.889486 0.444743 0.895658i \(-0.353295\pi\)
0.444743 + 0.895658i \(0.353295\pi\)
\(158\) 10.3797 0.825768
\(159\) 14.1379 1.12121
\(160\) 0.526911 0.0416560
\(161\) 18.3818 1.44869
\(162\) −15.0569 −1.18298
\(163\) −6.68669 −0.523742 −0.261871 0.965103i \(-0.584340\pi\)
−0.261871 + 0.965103i \(0.584340\pi\)
\(164\) −30.0210 −2.34425
\(165\) −6.25853 −0.487226
\(166\) −10.7221 −0.832195
\(167\) −18.6569 −1.44371 −0.721856 0.692043i \(-0.756711\pi\)
−0.721856 + 0.692043i \(0.756711\pi\)
\(168\) 53.3659 4.11727
\(169\) 0.354510 0.0272700
\(170\) 7.41831 0.568959
\(171\) 0 0
\(172\) −22.1096 −1.68584
\(173\) 14.7385 1.12054 0.560272 0.828308i \(-0.310696\pi\)
0.560272 + 0.828308i \(0.310696\pi\)
\(174\) −43.3309 −3.28490
\(175\) −3.82025 −0.288784
\(176\) −7.80791 −0.588543
\(177\) −15.1240 −1.13679
\(178\) 0.188331 0.0141160
\(179\) 12.1961 0.911582 0.455791 0.890087i \(-0.349357\pi\)
0.455791 + 0.890087i \(0.349357\pi\)
\(180\) 22.3866 1.66860
\(181\) 13.1841 0.979966 0.489983 0.871732i \(-0.337003\pi\)
0.489983 + 0.871732i \(0.337003\pi\)
\(182\) −34.0400 −2.52321
\(183\) −39.7901 −2.94137
\(184\) 22.8218 1.68244
\(185\) 3.93134 0.289038
\(186\) −25.6504 −1.88078
\(187\) 6.46510 0.472775
\(188\) −33.2121 −2.42224
\(189\) −30.0904 −2.18876
\(190\) 0 0
\(191\) 4.61708 0.334080 0.167040 0.985950i \(-0.446579\pi\)
0.167040 + 0.985950i \(0.446579\pi\)
\(192\) −25.4275 −1.83507
\(193\) 5.22468 0.376081 0.188040 0.982161i \(-0.439786\pi\)
0.188040 + 0.982161i \(0.439786\pi\)
\(194\) 43.9453 3.15509
\(195\) −10.7630 −0.770753
\(196\) 29.9612 2.14009
\(197\) 21.1783 1.50889 0.754445 0.656363i \(-0.227906\pi\)
0.754445 + 0.656363i \(0.227906\pi\)
\(198\) 29.4005 2.08940
\(199\) 15.3752 1.08992 0.544960 0.838462i \(-0.316545\pi\)
0.544960 + 0.838462i \(0.316545\pi\)
\(200\) −4.74301 −0.335381
\(201\) −15.8483 −1.11785
\(202\) −45.4736 −3.19951
\(203\) −23.0508 −1.61785
\(204\) −35.3518 −2.47512
\(205\) −7.60945 −0.531467
\(206\) −0.920265 −0.0641179
\(207\) −27.3031 −1.89770
\(208\) −13.4275 −0.931029
\(209\) 0 0
\(210\) 27.4343 1.89315
\(211\) −20.8659 −1.43647 −0.718235 0.695800i \(-0.755050\pi\)
−0.718235 + 0.695800i \(0.755050\pi\)
\(212\) 18.9382 1.30068
\(213\) −0.363540 −0.0249093
\(214\) −6.73316 −0.460270
\(215\) −5.60415 −0.382200
\(216\) −37.3586 −2.54193
\(217\) −13.6453 −0.926305
\(218\) 7.32237 0.495934
\(219\) −36.7741 −2.48497
\(220\) −8.38351 −0.565216
\(221\) 11.1182 0.747892
\(222\) −28.2321 −1.89482
\(223\) −13.6759 −0.915806 −0.457903 0.889002i \(-0.651399\pi\)
−0.457903 + 0.889002i \(0.651399\pi\)
\(224\) −2.01293 −0.134495
\(225\) 5.67435 0.378290
\(226\) −8.81947 −0.586662
\(227\) −3.71196 −0.246372 −0.123186 0.992384i \(-0.539311\pi\)
−0.123186 + 0.992384i \(0.539311\pi\)
\(228\) 0 0
\(229\) 11.3086 0.747293 0.373646 0.927571i \(-0.378107\pi\)
0.373646 + 0.927571i \(0.378107\pi\)
\(230\) 11.7322 0.773599
\(231\) 23.9092 1.57311
\(232\) −28.6186 −1.87890
\(233\) −10.6753 −0.699362 −0.349681 0.936869i \(-0.613710\pi\)
−0.349681 + 0.936869i \(0.613710\pi\)
\(234\) 50.5608 3.30527
\(235\) −8.41831 −0.549150
\(236\) −20.2591 −1.31876
\(237\) −12.5378 −0.814417
\(238\) −28.3398 −1.83700
\(239\) −17.2813 −1.11783 −0.558916 0.829224i \(-0.688783\pi\)
−0.558916 + 0.829224i \(0.688783\pi\)
\(240\) 10.8218 0.698544
\(241\) −17.4986 −1.12719 −0.563593 0.826052i \(-0.690581\pi\)
−0.563593 + 0.826052i \(0.690581\pi\)
\(242\) 15.8110 1.01637
\(243\) −5.44232 −0.349125
\(244\) −53.3001 −3.41219
\(245\) 7.59430 0.485182
\(246\) 54.6457 3.48408
\(247\) 0 0
\(248\) −16.9413 −1.07577
\(249\) 12.9513 0.820756
\(250\) −2.43828 −0.154211
\(251\) 17.9012 1.12991 0.564956 0.825121i \(-0.308893\pi\)
0.564956 + 0.825121i \(0.308893\pi\)
\(252\) −85.5224 −5.38740
\(253\) 10.2247 0.642820
\(254\) −33.2065 −2.08356
\(255\) −8.96065 −0.561138
\(256\) −31.4914 −1.96821
\(257\) 26.7208 1.66680 0.833400 0.552671i \(-0.186391\pi\)
0.833400 + 0.552671i \(0.186391\pi\)
\(258\) 40.2450 2.50555
\(259\) −15.0187 −0.933217
\(260\) −14.4174 −0.894127
\(261\) 34.2382 2.11929
\(262\) −13.8265 −0.854204
\(263\) −19.7817 −1.21979 −0.609895 0.792482i \(-0.708789\pi\)
−0.609895 + 0.792482i \(0.708789\pi\)
\(264\) 29.6843 1.82694
\(265\) 4.80028 0.294879
\(266\) 0 0
\(267\) −0.227487 −0.0139220
\(268\) −21.2293 −1.29679
\(269\) −7.04833 −0.429744 −0.214872 0.976642i \(-0.568933\pi\)
−0.214872 + 0.976642i \(0.568933\pi\)
\(270\) −19.2053 −1.16880
\(271\) 26.1672 1.58955 0.794773 0.606907i \(-0.207590\pi\)
0.794773 + 0.606907i \(0.207590\pi\)
\(272\) −11.1790 −0.677825
\(273\) 41.1173 2.48853
\(274\) 19.7623 1.19388
\(275\) −2.12498 −0.128141
\(276\) −55.9096 −3.36536
\(277\) 2.86953 0.172413 0.0862066 0.996277i \(-0.472525\pi\)
0.0862066 + 0.996277i \(0.472525\pi\)
\(278\) 42.7492 2.56393
\(279\) 20.2679 1.21341
\(280\) 18.1195 1.08285
\(281\) 22.4401 1.33866 0.669332 0.742963i \(-0.266580\pi\)
0.669332 + 0.742963i \(0.266580\pi\)
\(282\) 60.4544 3.60001
\(283\) −4.68139 −0.278280 −0.139140 0.990273i \(-0.544434\pi\)
−0.139140 + 0.990273i \(0.544434\pi\)
\(284\) −0.486973 −0.0288965
\(285\) 0 0
\(286\) −18.9344 −1.11962
\(287\) 29.0700 1.71595
\(288\) 2.98988 0.176180
\(289\) −7.74360 −0.455506
\(290\) −14.7122 −0.863933
\(291\) −53.0820 −3.11172
\(292\) −49.2602 −2.88273
\(293\) −3.26229 −0.190585 −0.0952926 0.995449i \(-0.530379\pi\)
−0.0952926 + 0.995449i \(0.530379\pi\)
\(294\) −54.5369 −3.18066
\(295\) −5.13510 −0.298977
\(296\) −18.6464 −1.08380
\(297\) −16.7375 −0.971209
\(298\) −46.8033 −2.71124
\(299\) 17.5837 1.01689
\(300\) 11.6196 0.670857
\(301\) 21.4093 1.23401
\(302\) 27.1802 1.56404
\(303\) 54.9280 3.15553
\(304\) 0 0
\(305\) −13.5100 −0.773582
\(306\) 42.0941 2.40636
\(307\) 1.71746 0.0980207 0.0490103 0.998798i \(-0.484393\pi\)
0.0490103 + 0.998798i \(0.484393\pi\)
\(308\) 32.0271 1.82491
\(309\) 1.11160 0.0632365
\(310\) −8.70916 −0.494647
\(311\) −0.892946 −0.0506343 −0.0253172 0.999679i \(-0.508060\pi\)
−0.0253172 + 0.999679i \(0.508060\pi\)
\(312\) 51.0489 2.89008
\(313\) 11.5358 0.652040 0.326020 0.945363i \(-0.394292\pi\)
0.326020 + 0.945363i \(0.394292\pi\)
\(314\) −27.1752 −1.53359
\(315\) −21.6774 −1.22139
\(316\) −16.7948 −0.944780
\(317\) −18.8246 −1.05729 −0.528647 0.848842i \(-0.677301\pi\)
−0.528647 + 0.848842i \(0.677301\pi\)
\(318\) −34.4722 −1.93311
\(319\) −12.8218 −0.717883
\(320\) −8.63346 −0.482625
\(321\) 8.13305 0.453943
\(322\) −44.8200 −2.49772
\(323\) 0 0
\(324\) 24.3626 1.35348
\(325\) −3.65438 −0.202709
\(326\) 16.3041 0.902998
\(327\) −8.84476 −0.489116
\(328\) 36.0917 1.99283
\(329\) 32.1601 1.77304
\(330\) 15.2601 0.840039
\(331\) 15.5779 0.856240 0.428120 0.903722i \(-0.359176\pi\)
0.428120 + 0.903722i \(0.359176\pi\)
\(332\) 17.3487 0.952134
\(333\) 22.3078 1.22246
\(334\) 45.4908 2.48914
\(335\) −5.38101 −0.293996
\(336\) −41.3419 −2.25539
\(337\) 6.43425 0.350496 0.175248 0.984524i \(-0.443927\pi\)
0.175248 + 0.984524i \(0.443927\pi\)
\(338\) −0.864396 −0.0470170
\(339\) 10.6531 0.578598
\(340\) −12.0031 −0.650959
\(341\) −7.59007 −0.411026
\(342\) 0 0
\(343\) −2.27039 −0.122590
\(344\) 26.5805 1.43313
\(345\) −14.1714 −0.762965
\(346\) −35.9366 −1.93196
\(347\) −19.3367 −1.03805 −0.519023 0.854760i \(-0.673704\pi\)
−0.519023 + 0.854760i \(0.673704\pi\)
\(348\) 70.1108 3.75833
\(349\) 7.78870 0.416920 0.208460 0.978031i \(-0.433155\pi\)
0.208460 + 0.978031i \(0.433155\pi\)
\(350\) 9.31485 0.497900
\(351\) −28.7840 −1.53638
\(352\) −1.11967 −0.0596788
\(353\) −24.7007 −1.31468 −0.657342 0.753593i \(-0.728319\pi\)
−0.657342 + 0.753593i \(0.728319\pi\)
\(354\) 36.8767 1.95997
\(355\) −0.123434 −0.00655117
\(356\) −0.304727 −0.0161505
\(357\) 34.2319 1.81175
\(358\) −29.7376 −1.57168
\(359\) 24.8224 1.31008 0.655038 0.755596i \(-0.272653\pi\)
0.655038 + 0.755596i \(0.272653\pi\)
\(360\) −26.9135 −1.41847
\(361\) 0 0
\(362\) −32.1466 −1.68959
\(363\) −19.0982 −1.00240
\(364\) 55.0779 2.88687
\(365\) −12.4860 −0.653548
\(366\) 97.0195 5.07129
\(367\) −7.01716 −0.366293 −0.183146 0.983086i \(-0.558628\pi\)
−0.183146 + 0.983086i \(0.558628\pi\)
\(368\) −17.6798 −0.921621
\(369\) −43.1787 −2.24779
\(370\) −9.58572 −0.498338
\(371\) −18.3383 −0.952075
\(372\) 41.5033 2.15184
\(373\) 36.2105 1.87491 0.937455 0.348107i \(-0.113175\pi\)
0.937455 + 0.348107i \(0.113175\pi\)
\(374\) −15.7637 −0.815124
\(375\) 2.94523 0.152091
\(376\) 39.9281 2.05914
\(377\) −22.0500 −1.13563
\(378\) 73.3690 3.77370
\(379\) 28.2455 1.45087 0.725437 0.688288i \(-0.241638\pi\)
0.725437 + 0.688288i \(0.241638\pi\)
\(380\) 0 0
\(381\) 40.1104 2.05492
\(382\) −11.2578 −0.575997
\(383\) −26.4312 −1.35057 −0.675287 0.737555i \(-0.735980\pi\)
−0.675287 + 0.737555i \(0.735980\pi\)
\(384\) 58.8957 3.00551
\(385\) 8.11794 0.413728
\(386\) −12.7392 −0.648411
\(387\) −31.7999 −1.61648
\(388\) −71.1050 −3.60981
\(389\) −5.61736 −0.284811 −0.142406 0.989808i \(-0.545484\pi\)
−0.142406 + 0.989808i \(0.545484\pi\)
\(390\) 26.2432 1.32888
\(391\) 14.6392 0.740335
\(392\) −36.0199 −1.81928
\(393\) 16.7012 0.842462
\(394\) −51.6387 −2.60152
\(395\) −4.25699 −0.214192
\(396\) −47.5710 −2.39053
\(397\) −29.0391 −1.45743 −0.728715 0.684818i \(-0.759882\pi\)
−0.728715 + 0.684818i \(0.759882\pi\)
\(398\) −37.4891 −1.87916
\(399\) 0 0
\(400\) 3.67435 0.183718
\(401\) −25.4613 −1.27148 −0.635739 0.771904i \(-0.719305\pi\)
−0.635739 + 0.771904i \(0.719305\pi\)
\(402\) 38.6426 1.92732
\(403\) −13.0529 −0.650210
\(404\) 73.5778 3.66063
\(405\) 6.17521 0.306849
\(406\) 56.2044 2.78938
\(407\) −8.35401 −0.414093
\(408\) 42.5005 2.10409
\(409\) 19.8024 0.979166 0.489583 0.871957i \(-0.337149\pi\)
0.489583 + 0.871957i \(0.337149\pi\)
\(410\) 18.5540 0.916317
\(411\) −23.8711 −1.17747
\(412\) 1.48902 0.0733588
\(413\) 19.6174 0.965307
\(414\) 66.5727 3.27187
\(415\) 4.39739 0.215859
\(416\) −1.92553 −0.0944070
\(417\) −51.6371 −2.52868
\(418\) 0 0
\(419\) 0.172123 0.00840877 0.00420439 0.999991i \(-0.498662\pi\)
0.00420439 + 0.999991i \(0.498662\pi\)
\(420\) −44.3897 −2.16599
\(421\) −17.4056 −0.848297 −0.424149 0.905593i \(-0.639427\pi\)
−0.424149 + 0.905593i \(0.639427\pi\)
\(422\) 50.8771 2.47666
\(423\) −47.7685 −2.32258
\(424\) −22.7678 −1.10570
\(425\) −3.04243 −0.147580
\(426\) 0.886412 0.0429468
\(427\) 51.6117 2.49766
\(428\) 10.8945 0.526605
\(429\) 22.8711 1.10423
\(430\) 13.6645 0.658961
\(431\) 5.06518 0.243981 0.121990 0.992531i \(-0.461072\pi\)
0.121990 + 0.992531i \(0.461072\pi\)
\(432\) 28.9413 1.39244
\(433\) −12.5169 −0.601524 −0.300762 0.953699i \(-0.597241\pi\)
−0.300762 + 0.953699i \(0.597241\pi\)
\(434\) 33.2712 1.59707
\(435\) 17.7711 0.852057
\(436\) −11.8478 −0.567409
\(437\) 0 0
\(438\) 89.6658 4.28440
\(439\) 14.7581 0.704367 0.352183 0.935931i \(-0.385439\pi\)
0.352183 + 0.935931i \(0.385439\pi\)
\(440\) 10.0788 0.480487
\(441\) 43.0928 2.05204
\(442\) −27.1094 −1.28946
\(443\) 5.35950 0.254638 0.127319 0.991862i \(-0.459363\pi\)
0.127319 + 0.991862i \(0.459363\pi\)
\(444\) 45.6805 2.16790
\(445\) −0.0772394 −0.00366150
\(446\) 33.3457 1.57896
\(447\) 56.5341 2.67397
\(448\) 32.9820 1.55825
\(449\) 7.16065 0.337932 0.168966 0.985622i \(-0.445957\pi\)
0.168966 + 0.985622i \(0.445957\pi\)
\(450\) −13.8357 −0.652220
\(451\) 16.1699 0.761411
\(452\) 14.2702 0.671214
\(453\) −32.8312 −1.54255
\(454\) 9.05082 0.424776
\(455\) 13.9607 0.654485
\(456\) 0 0
\(457\) 32.3884 1.51507 0.757534 0.652796i \(-0.226404\pi\)
0.757534 + 0.652796i \(0.226404\pi\)
\(458\) −27.5736 −1.28843
\(459\) −23.9639 −1.11854
\(460\) −18.9831 −0.885092
\(461\) −25.2124 −1.17426 −0.587130 0.809493i \(-0.699742\pi\)
−0.587130 + 0.809493i \(0.699742\pi\)
\(462\) −58.2973 −2.71224
\(463\) −40.8494 −1.89843 −0.949216 0.314627i \(-0.898121\pi\)
−0.949216 + 0.314627i \(0.898121\pi\)
\(464\) 22.1705 1.02924
\(465\) 10.5199 0.487847
\(466\) 26.0294 1.20579
\(467\) 14.6209 0.676577 0.338288 0.941042i \(-0.390152\pi\)
0.338288 + 0.941042i \(0.390152\pi\)
\(468\) −81.8092 −3.78163
\(469\) 20.5568 0.949225
\(470\) 20.5262 0.946805
\(471\) 32.8252 1.51250
\(472\) 24.3558 1.12107
\(473\) 11.9087 0.547562
\(474\) 30.5707 1.40416
\(475\) 0 0
\(476\) 45.8548 2.10175
\(477\) 27.2385 1.24716
\(478\) 42.1366 1.92729
\(479\) 1.06944 0.0488640 0.0244320 0.999701i \(-0.492222\pi\)
0.0244320 + 0.999701i \(0.492222\pi\)
\(480\) 1.55187 0.0708329
\(481\) −14.3666 −0.655062
\(482\) 42.6666 1.94341
\(483\) 54.1385 2.46339
\(484\) −25.5827 −1.16285
\(485\) −18.0231 −0.818385
\(486\) 13.2699 0.601936
\(487\) 6.25304 0.283352 0.141676 0.989913i \(-0.454751\pi\)
0.141676 + 0.989913i \(0.454751\pi\)
\(488\) 64.0782 2.90068
\(489\) −19.6938 −0.890585
\(490\) −18.5171 −0.836516
\(491\) −0.813681 −0.0367209 −0.0183605 0.999831i \(-0.505845\pi\)
−0.0183605 + 0.999831i \(0.505845\pi\)
\(492\) −88.4186 −3.98622
\(493\) −18.3576 −0.826784
\(494\) 0 0
\(495\) −12.0579 −0.541960
\(496\) 13.1242 0.589294
\(497\) 0.471547 0.0211518
\(498\) −31.5790 −1.41509
\(499\) 1.57636 0.0705676 0.0352838 0.999377i \(-0.488766\pi\)
0.0352838 + 0.999377i \(0.488766\pi\)
\(500\) 3.94523 0.176436
\(501\) −54.9487 −2.45493
\(502\) −43.6481 −1.94811
\(503\) 3.00182 0.133845 0.0669223 0.997758i \(-0.478682\pi\)
0.0669223 + 0.997758i \(0.478682\pi\)
\(504\) 102.816 4.57980
\(505\) 18.6498 0.829907
\(506\) −24.9307 −1.10830
\(507\) 1.04411 0.0463707
\(508\) 53.7292 2.38385
\(509\) 32.7217 1.45036 0.725182 0.688557i \(-0.241755\pi\)
0.725182 + 0.688557i \(0.241755\pi\)
\(510\) 21.8486 0.967473
\(511\) 47.6997 2.11011
\(512\) 36.7910 1.62595
\(513\) 0 0
\(514\) −65.1529 −2.87377
\(515\) 0.377423 0.0166313
\(516\) −65.1179 −2.86665
\(517\) 17.8887 0.786745
\(518\) 36.6199 1.60898
\(519\) 43.4081 1.90540
\(520\) 17.3328 0.760092
\(521\) 16.4073 0.718819 0.359409 0.933180i \(-0.382978\pi\)
0.359409 + 0.933180i \(0.382978\pi\)
\(522\) −83.4824 −3.65393
\(523\) 20.4437 0.893940 0.446970 0.894549i \(-0.352503\pi\)
0.446970 + 0.894549i \(0.352503\pi\)
\(524\) 22.3718 0.977315
\(525\) −11.2515 −0.491055
\(526\) 48.2333 2.10307
\(527\) −10.8671 −0.473378
\(528\) −22.9960 −1.00077
\(529\) 0.152154 0.00661541
\(530\) −11.7044 −0.508409
\(531\) −29.1384 −1.26450
\(532\) 0 0
\(533\) 27.8079 1.20449
\(534\) 0.554678 0.0240033
\(535\) 2.76144 0.119387
\(536\) 25.5222 1.10239
\(537\) 35.9203 1.55008
\(538\) 17.1858 0.740933
\(539\) −16.1377 −0.695101
\(540\) 31.0748 1.33725
\(541\) −28.8016 −1.23828 −0.619139 0.785281i \(-0.712518\pi\)
−0.619139 + 0.785281i \(0.712518\pi\)
\(542\) −63.8031 −2.74058
\(543\) 38.8301 1.66636
\(544\) −1.60309 −0.0687320
\(545\) −3.00308 −0.128638
\(546\) −100.256 −4.29054
\(547\) −26.9553 −1.15253 −0.576264 0.817264i \(-0.695490\pi\)
−0.576264 + 0.817264i \(0.695490\pi\)
\(548\) −31.9761 −1.36595
\(549\) −76.6606 −3.27180
\(550\) 5.18129 0.220931
\(551\) 0 0
\(552\) 67.2153 2.86087
\(553\) 16.2628 0.691563
\(554\) −6.99672 −0.297262
\(555\) 11.5787 0.491488
\(556\) −69.1696 −2.93345
\(557\) 7.95439 0.337039 0.168519 0.985698i \(-0.446101\pi\)
0.168519 + 0.985698i \(0.446101\pi\)
\(558\) −49.4188 −2.09207
\(559\) 20.4797 0.866199
\(560\) −14.0369 −0.593169
\(561\) 19.0412 0.803919
\(562\) −54.7153 −2.30803
\(563\) 34.0931 1.43685 0.718426 0.695603i \(-0.244863\pi\)
0.718426 + 0.695603i \(0.244863\pi\)
\(564\) −97.8172 −4.11885
\(565\) 3.61708 0.152172
\(566\) 11.4146 0.479789
\(567\) −23.5908 −0.990722
\(568\) 0.585446 0.0245648
\(569\) −25.7236 −1.07839 −0.539195 0.842181i \(-0.681271\pi\)
−0.539195 + 0.842181i \(0.681271\pi\)
\(570\) 0 0
\(571\) −31.6325 −1.32378 −0.661890 0.749601i \(-0.730245\pi\)
−0.661890 + 0.749601i \(0.730245\pi\)
\(572\) 30.6365 1.28098
\(573\) 13.5983 0.568079
\(574\) −70.8809 −2.95851
\(575\) −4.81167 −0.200660
\(576\) −48.9893 −2.04122
\(577\) 26.8689 1.11856 0.559282 0.828977i \(-0.311077\pi\)
0.559282 + 0.828977i \(0.311077\pi\)
\(578\) 18.8811 0.785350
\(579\) 15.3879 0.639498
\(580\) 23.8049 0.988445
\(581\) −16.7991 −0.696946
\(582\) 129.429 5.36500
\(583\) −10.2005 −0.422461
\(584\) 59.2213 2.45060
\(585\) −20.7362 −0.857338
\(586\) 7.95439 0.328593
\(587\) 42.5145 1.75476 0.877380 0.479796i \(-0.159289\pi\)
0.877380 + 0.479796i \(0.159289\pi\)
\(588\) 88.2426 3.63906
\(589\) 0 0
\(590\) 12.5208 0.515474
\(591\) 62.3748 2.56576
\(592\) 14.4451 0.593691
\(593\) −23.2139 −0.953280 −0.476640 0.879099i \(-0.658145\pi\)
−0.476640 + 0.879099i \(0.658145\pi\)
\(594\) 40.8108 1.67449
\(595\) 11.6229 0.476491
\(596\) 75.7293 3.10199
\(597\) 45.2834 1.85333
\(598\) −42.8740 −1.75325
\(599\) 0.313115 0.0127935 0.00639676 0.999980i \(-0.497964\pi\)
0.00639676 + 0.999980i \(0.497964\pi\)
\(600\) −13.9692 −0.570292
\(601\) 20.9580 0.854893 0.427447 0.904041i \(-0.359413\pi\)
0.427447 + 0.904041i \(0.359413\pi\)
\(602\) −52.2018 −2.12759
\(603\) −30.5338 −1.24343
\(604\) −43.9785 −1.78946
\(605\) −6.48448 −0.263631
\(606\) −133.930 −5.44053
\(607\) 10.1085 0.410290 0.205145 0.978732i \(-0.434233\pi\)
0.205145 + 0.978732i \(0.434233\pi\)
\(608\) 0 0
\(609\) −67.8899 −2.75104
\(610\) 32.9413 1.33375
\(611\) 30.7637 1.24457
\(612\) −68.1097 −2.75317
\(613\) −36.3560 −1.46840 −0.734202 0.678931i \(-0.762444\pi\)
−0.734202 + 0.678931i \(0.762444\pi\)
\(614\) −4.18766 −0.169000
\(615\) −22.4116 −0.903721
\(616\) −38.5035 −1.55135
\(617\) 35.3399 1.42273 0.711365 0.702822i \(-0.248077\pi\)
0.711365 + 0.702822i \(0.248077\pi\)
\(618\) −2.71039 −0.109028
\(619\) −32.5878 −1.30982 −0.654908 0.755709i \(-0.727292\pi\)
−0.654908 + 0.755709i \(0.727292\pi\)
\(620\) 14.0917 0.565937
\(621\) −37.8994 −1.52085
\(622\) 2.17726 0.0873000
\(623\) 0.295074 0.0118219
\(624\) −39.5470 −1.58315
\(625\) 1.00000 0.0400000
\(626\) −28.1275 −1.12420
\(627\) 0 0
\(628\) 43.9704 1.75461
\(629\) −11.9608 −0.476910
\(630\) 52.8557 2.10582
\(631\) 1.66950 0.0664616 0.0332308 0.999448i \(-0.489420\pi\)
0.0332308 + 0.999448i \(0.489420\pi\)
\(632\) 20.1909 0.803153
\(633\) −61.4549 −2.44261
\(634\) 45.8997 1.82291
\(635\) 13.6188 0.540445
\(636\) 55.7772 2.21171
\(637\) −27.7525 −1.09959
\(638\) 31.2632 1.23772
\(639\) −0.700405 −0.0277076
\(640\) 19.9970 0.790451
\(641\) −21.3997 −0.845238 −0.422619 0.906307i \(-0.638889\pi\)
−0.422619 + 0.906307i \(0.638889\pi\)
\(642\) −19.8307 −0.782655
\(643\) −8.43473 −0.332633 −0.166317 0.986072i \(-0.553187\pi\)
−0.166317 + 0.986072i \(0.553187\pi\)
\(644\) 72.5202 2.85770
\(645\) −16.5055 −0.649903
\(646\) 0 0
\(647\) −29.2025 −1.14807 −0.574034 0.818831i \(-0.694622\pi\)
−0.574034 + 0.818831i \(0.694622\pi\)
\(648\) −29.2891 −1.15058
\(649\) 10.9120 0.428332
\(650\) 8.91042 0.349495
\(651\) −40.1885 −1.57511
\(652\) −26.3805 −1.03314
\(653\) −7.61427 −0.297970 −0.148985 0.988839i \(-0.547601\pi\)
−0.148985 + 0.988839i \(0.547601\pi\)
\(654\) 21.5660 0.843299
\(655\) 5.67059 0.221568
\(656\) −27.9598 −1.09165
\(657\) −70.8501 −2.76412
\(658\) −78.4153 −3.05695
\(659\) 18.2941 0.712637 0.356318 0.934365i \(-0.384032\pi\)
0.356318 + 0.934365i \(0.384032\pi\)
\(660\) −24.6913 −0.961108
\(661\) 20.3586 0.791859 0.395930 0.918281i \(-0.370422\pi\)
0.395930 + 0.918281i \(0.370422\pi\)
\(662\) −37.9834 −1.47627
\(663\) 32.7456 1.27174
\(664\) −20.8569 −0.809404
\(665\) 0 0
\(666\) −54.3928 −2.10768
\(667\) −29.0329 −1.12416
\(668\) −73.6056 −2.84789
\(669\) −40.2786 −1.55726
\(670\) 13.1204 0.506887
\(671\) 28.7085 1.10828
\(672\) −5.92853 −0.228698
\(673\) −29.6829 −1.14419 −0.572096 0.820186i \(-0.693870\pi\)
−0.572096 + 0.820186i \(0.693870\pi\)
\(674\) −15.6885 −0.604299
\(675\) 7.87657 0.303169
\(676\) 1.39862 0.0537932
\(677\) −9.17128 −0.352481 −0.176240 0.984347i \(-0.556394\pi\)
−0.176240 + 0.984347i \(0.556394\pi\)
\(678\) −25.9753 −0.997576
\(679\) 68.8526 2.64232
\(680\) 14.4303 0.553376
\(681\) −10.9326 −0.418937
\(682\) 18.5067 0.708660
\(683\) 15.6556 0.599043 0.299522 0.954089i \(-0.403173\pi\)
0.299522 + 0.954089i \(0.403173\pi\)
\(684\) 0 0
\(685\) −8.10501 −0.309676
\(686\) 5.53586 0.211360
\(687\) 33.3064 1.27072
\(688\) −20.5916 −0.785048
\(689\) −17.5421 −0.668299
\(690\) 34.5540 1.31545
\(691\) −13.7912 −0.524643 −0.262321 0.964981i \(-0.584488\pi\)
−0.262321 + 0.964981i \(0.584488\pi\)
\(692\) 58.1466 2.21040
\(693\) 46.0640 1.74983
\(694\) 47.1483 1.78972
\(695\) −17.5325 −0.665045
\(696\) −84.2883 −3.19494
\(697\) 23.1513 0.876916
\(698\) −18.9911 −0.718822
\(699\) −31.4412 −1.18921
\(700\) −15.0717 −0.569658
\(701\) −13.7313 −0.518622 −0.259311 0.965794i \(-0.583496\pi\)
−0.259311 + 0.965794i \(0.583496\pi\)
\(702\) 70.1835 2.64891
\(703\) 0 0
\(704\) 18.3459 0.691437
\(705\) −24.7938 −0.933790
\(706\) 60.2272 2.26668
\(707\) −71.2470 −2.67952
\(708\) −59.6677 −2.24245
\(709\) −12.3146 −0.462483 −0.231242 0.972896i \(-0.574279\pi\)
−0.231242 + 0.972896i \(0.574279\pi\)
\(710\) 0.300966 0.0112950
\(711\) −24.1557 −0.905908
\(712\) 0.366347 0.0137294
\(713\) −17.1865 −0.643640
\(714\) −83.4671 −3.12368
\(715\) 7.76547 0.290412
\(716\) 48.1165 1.79820
\(717\) −50.8972 −1.90079
\(718\) −60.5240 −2.25874
\(719\) −6.92307 −0.258187 −0.129094 0.991632i \(-0.541207\pi\)
−0.129094 + 0.991632i \(0.541207\pi\)
\(720\) 20.8496 0.777017
\(721\) −1.44185 −0.0536973
\(722\) 0 0
\(723\) −51.5374 −1.91670
\(724\) 52.0142 1.93309
\(725\) 6.03385 0.224092
\(726\) 46.5669 1.72826
\(727\) 34.2263 1.26938 0.634692 0.772765i \(-0.281127\pi\)
0.634692 + 0.772765i \(0.281127\pi\)
\(728\) −66.2155 −2.45411
\(729\) −34.5545 −1.27980
\(730\) 30.4445 1.12680
\(731\) 17.0503 0.630626
\(732\) −156.981 −5.80218
\(733\) 37.5214 1.38589 0.692943 0.720993i \(-0.256314\pi\)
0.692943 + 0.720993i \(0.256314\pi\)
\(734\) 17.1098 0.631535
\(735\) 22.3669 0.825017
\(736\) −2.53532 −0.0934531
\(737\) 11.4345 0.421196
\(738\) 105.282 3.87548
\(739\) −38.6683 −1.42244 −0.711218 0.702972i \(-0.751856\pi\)
−0.711218 + 0.702972i \(0.751856\pi\)
\(740\) 15.5100 0.570160
\(741\) 0 0
\(742\) 44.7139 1.64150
\(743\) −34.5415 −1.26720 −0.633602 0.773659i \(-0.718424\pi\)
−0.633602 + 0.773659i \(0.718424\pi\)
\(744\) −49.8959 −1.82927
\(745\) 19.1952 0.703257
\(746\) −88.2915 −3.23258
\(747\) 24.9523 0.912959
\(748\) 25.5063 0.932601
\(749\) −10.5494 −0.385466
\(750\) −7.18129 −0.262224
\(751\) −33.3178 −1.21578 −0.607892 0.794020i \(-0.707985\pi\)
−0.607892 + 0.794020i \(0.707985\pi\)
\(752\) −30.9318 −1.12797
\(753\) 52.7230 1.92133
\(754\) 53.7642 1.95798
\(755\) −11.1473 −0.405691
\(756\) −118.714 −4.31757
\(757\) 27.2310 0.989728 0.494864 0.868970i \(-0.335218\pi\)
0.494864 + 0.868970i \(0.335218\pi\)
\(758\) −68.8706 −2.50149
\(759\) 30.1140 1.09307
\(760\) 0 0
\(761\) 20.1113 0.729033 0.364516 0.931197i \(-0.381234\pi\)
0.364516 + 0.931197i \(0.381234\pi\)
\(762\) −97.8006 −3.54294
\(763\) 11.4725 0.415334
\(764\) 18.2154 0.659011
\(765\) −17.2638 −0.624175
\(766\) 64.4469 2.32856
\(767\) 18.7656 0.677587
\(768\) −92.7493 −3.34680
\(769\) −3.25931 −0.117534 −0.0587669 0.998272i \(-0.518717\pi\)
−0.0587669 + 0.998272i \(0.518717\pi\)
\(770\) −19.7938 −0.713320
\(771\) 78.6988 2.83427
\(772\) 20.6125 0.741861
\(773\) 49.6874 1.78713 0.893565 0.448933i \(-0.148196\pi\)
0.893565 + 0.448933i \(0.148196\pi\)
\(774\) 77.5372 2.78702
\(775\) 3.57184 0.128304
\(776\) 85.4835 3.06868
\(777\) −44.2335 −1.58687
\(778\) 13.6967 0.491051
\(779\) 0 0
\(780\) −42.4624 −1.52040
\(781\) 0.262293 0.00938559
\(782\) −35.6945 −1.27643
\(783\) 47.5260 1.69844
\(784\) 27.9041 0.996576
\(785\) 11.1452 0.397790
\(786\) −40.7222 −1.45251
\(787\) 27.1159 0.966578 0.483289 0.875461i \(-0.339442\pi\)
0.483289 + 0.875461i \(0.339442\pi\)
\(788\) 83.5531 2.97646
\(789\) −58.2615 −2.07416
\(790\) 10.3797 0.369295
\(791\) −13.8181 −0.491317
\(792\) 57.1905 2.03218
\(793\) 49.3708 1.75321
\(794\) 70.8055 2.51279
\(795\) 14.1379 0.501420
\(796\) 60.6586 2.14999
\(797\) 27.3573 0.969044 0.484522 0.874779i \(-0.338994\pi\)
0.484522 + 0.874779i \(0.338994\pi\)
\(798\) 0 0
\(799\) 25.6122 0.906093
\(800\) 0.526911 0.0186291
\(801\) −0.438283 −0.0154860
\(802\) 62.0820 2.19219
\(803\) 26.5325 0.936311
\(804\) −62.5251 −2.20509
\(805\) 18.3818 0.647872
\(806\) 31.8266 1.12104
\(807\) −20.7589 −0.730748
\(808\) −88.4564 −3.11188
\(809\) −12.3922 −0.435686 −0.217843 0.975984i \(-0.569902\pi\)
−0.217843 + 0.975984i \(0.569902\pi\)
\(810\) −15.0569 −0.529046
\(811\) −14.5389 −0.510528 −0.255264 0.966871i \(-0.582162\pi\)
−0.255264 + 0.966871i \(0.582162\pi\)
\(812\) −90.9407 −3.19139
\(813\) 77.0683 2.70290
\(814\) 20.3694 0.713948
\(815\) −6.68669 −0.234225
\(816\) −32.9246 −1.15259
\(817\) 0 0
\(818\) −48.2839 −1.68821
\(819\) 79.2176 2.76809
\(820\) −30.0210 −1.04838
\(821\) 6.47357 0.225929 0.112965 0.993599i \(-0.463965\pi\)
0.112965 + 0.993599i \(0.463965\pi\)
\(822\) 58.2044 2.03011
\(823\) 0.210155 0.00732553 0.00366276 0.999993i \(-0.498834\pi\)
0.00366276 + 0.999993i \(0.498834\pi\)
\(824\) −1.79012 −0.0623619
\(825\) −6.25853 −0.217894
\(826\) −47.8327 −1.66431
\(827\) −23.1396 −0.804643 −0.402322 0.915498i \(-0.631797\pi\)
−0.402322 + 0.915498i \(0.631797\pi\)
\(828\) −107.717 −3.74342
\(829\) −24.6843 −0.857321 −0.428660 0.903466i \(-0.641014\pi\)
−0.428660 + 0.903466i \(0.641014\pi\)
\(830\) −10.7221 −0.372169
\(831\) 8.45141 0.293176
\(832\) 31.5500 1.09380
\(833\) −23.1052 −0.800547
\(834\) 125.906 4.35977
\(835\) −18.6569 −0.645648
\(836\) 0 0
\(837\) 28.1338 0.972448
\(838\) −0.419685 −0.0144978
\(839\) −31.2238 −1.07797 −0.538983 0.842317i \(-0.681191\pi\)
−0.538983 + 0.842317i \(0.681191\pi\)
\(840\) 53.3659 1.84130
\(841\) 7.40738 0.255427
\(842\) 42.4398 1.46257
\(843\) 66.0912 2.27630
\(844\) −82.3208 −2.83360
\(845\) 0.354510 0.0121955
\(846\) 116.473 4.00443
\(847\) 24.7723 0.851187
\(848\) 17.6379 0.605689
\(849\) −13.7877 −0.473194
\(850\) 7.41831 0.254446
\(851\) −18.9163 −0.648443
\(852\) −1.43425 −0.0491364
\(853\) 27.1366 0.929140 0.464570 0.885536i \(-0.346209\pi\)
0.464570 + 0.885536i \(0.346209\pi\)
\(854\) −125.844 −4.30629
\(855\) 0 0
\(856\) −13.0975 −0.447664
\(857\) 47.6457 1.62755 0.813773 0.581183i \(-0.197410\pi\)
0.813773 + 0.581183i \(0.197410\pi\)
\(858\) −55.7661 −1.90382
\(859\) −19.6361 −0.669974 −0.334987 0.942223i \(-0.608732\pi\)
−0.334987 + 0.942223i \(0.608732\pi\)
\(860\) −22.1096 −0.753932
\(861\) 85.6177 2.91784
\(862\) −12.3503 −0.420654
\(863\) −49.3684 −1.68052 −0.840260 0.542183i \(-0.817598\pi\)
−0.840260 + 0.542183i \(0.817598\pi\)
\(864\) 4.15025 0.141194
\(865\) 14.7385 0.501123
\(866\) 30.5197 1.03710
\(867\) −22.8066 −0.774554
\(868\) −53.8339 −1.82724
\(869\) 9.04600 0.306865
\(870\) −43.3309 −1.46905
\(871\) 19.6643 0.666299
\(872\) 14.2437 0.482351
\(873\) −102.269 −3.46129
\(874\) 0 0
\(875\) −3.82025 −0.129148
\(876\) −145.082 −4.90188
\(877\) 41.1968 1.39112 0.695559 0.718469i \(-0.255157\pi\)
0.695559 + 0.718469i \(0.255157\pi\)
\(878\) −35.9845 −1.21442
\(879\) −9.60819 −0.324076
\(880\) −7.80791 −0.263205
\(881\) −10.4510 −0.352103 −0.176052 0.984381i \(-0.556333\pi\)
−0.176052 + 0.984381i \(0.556333\pi\)
\(882\) −105.072 −3.53797
\(883\) −50.2957 −1.69259 −0.846293 0.532717i \(-0.821171\pi\)
−0.846293 + 0.532717i \(0.821171\pi\)
\(884\) 43.8639 1.47530
\(885\) −15.1240 −0.508388
\(886\) −13.0680 −0.439027
\(887\) −0.201711 −0.00677278 −0.00338639 0.999994i \(-0.501078\pi\)
−0.00338639 + 0.999994i \(0.501078\pi\)
\(888\) −54.9178 −1.84292
\(889\) −52.0272 −1.74494
\(890\) 0.188331 0.00631288
\(891\) −13.1222 −0.439609
\(892\) −53.9545 −1.80653
\(893\) 0 0
\(894\) −137.846 −4.61027
\(895\) 12.1961 0.407672
\(896\) −76.3935 −2.55213
\(897\) 51.7879 1.72915
\(898\) −17.4597 −0.582637
\(899\) 21.5520 0.718798
\(900\) 22.3866 0.746220
\(901\) −14.6045 −0.486548
\(902\) −39.4268 −1.31277
\(903\) 63.0551 2.09834
\(904\) −17.1558 −0.570595
\(905\) 13.1841 0.438254
\(906\) 80.0518 2.65954
\(907\) 6.11841 0.203158 0.101579 0.994827i \(-0.467610\pi\)
0.101579 + 0.994827i \(0.467610\pi\)
\(908\) −14.6445 −0.485996
\(909\) 105.826 3.51002
\(910\) −34.0400 −1.12842
\(911\) −0.960234 −0.0318140 −0.0159070 0.999873i \(-0.505064\pi\)
−0.0159070 + 0.999873i \(0.505064\pi\)
\(912\) 0 0
\(913\) −9.34435 −0.309253
\(914\) −78.9722 −2.61217
\(915\) −39.7901 −1.31542
\(916\) 44.6149 1.47412
\(917\) −21.6631 −0.715378
\(918\) 58.4308 1.92851
\(919\) −51.3264 −1.69310 −0.846551 0.532307i \(-0.821325\pi\)
−0.846551 + 0.532307i \(0.821325\pi\)
\(920\) 22.8218 0.752412
\(921\) 5.05831 0.166677
\(922\) 61.4750 2.02457
\(923\) 0.451073 0.0148473
\(924\) 94.3270 3.10313
\(925\) 3.93134 0.129262
\(926\) 99.6023 3.27314
\(927\) 2.14163 0.0703404
\(928\) 3.17930 0.104366
\(929\) −46.0177 −1.50979 −0.754896 0.655844i \(-0.772313\pi\)
−0.754896 + 0.655844i \(0.772313\pi\)
\(930\) −25.6504 −0.841111
\(931\) 0 0
\(932\) −42.1165 −1.37957
\(933\) −2.62993 −0.0860999
\(934\) −35.6500 −1.16650
\(935\) 6.46510 0.211431
\(936\) 98.3522 3.21474
\(937\) −3.79467 −0.123966 −0.0619832 0.998077i \(-0.519743\pi\)
−0.0619832 + 0.998077i \(0.519743\pi\)
\(938\) −50.1233 −1.63658
\(939\) 33.9754 1.10875
\(940\) −33.2121 −1.08326
\(941\) 23.1763 0.755526 0.377763 0.925902i \(-0.376693\pi\)
0.377763 + 0.925902i \(0.376693\pi\)
\(942\) −80.0371 −2.60775
\(943\) 36.6142 1.19232
\(944\) −18.8682 −0.614106
\(945\) −30.0904 −0.978842
\(946\) −29.0367 −0.944066
\(947\) 18.3891 0.597565 0.298783 0.954321i \(-0.403419\pi\)
0.298783 + 0.954321i \(0.403419\pi\)
\(948\) −49.4644 −1.60653
\(949\) 45.6287 1.48117
\(950\) 0 0
\(951\) −55.4427 −1.79785
\(952\) −55.1273 −1.78669
\(953\) 14.6072 0.473174 0.236587 0.971610i \(-0.423971\pi\)
0.236587 + 0.971610i \(0.423971\pi\)
\(954\) −66.4151 −2.15027
\(955\) 4.61708 0.149405
\(956\) −68.1785 −2.20505
\(957\) −37.7631 −1.22071
\(958\) −2.60760 −0.0842477
\(959\) 30.9631 0.999852
\(960\) −25.4275 −0.820669
\(961\) −18.2420 −0.588450
\(962\) 35.0299 1.12941
\(963\) 15.6694 0.504938
\(964\) −69.0361 −2.22350
\(965\) 5.22468 0.168188
\(966\) −132.005 −4.24719
\(967\) 59.4737 1.91254 0.956272 0.292478i \(-0.0944798\pi\)
0.956272 + 0.292478i \(0.0944798\pi\)
\(968\) 30.7559 0.988533
\(969\) 0 0
\(970\) 43.9453 1.41100
\(971\) 22.3008 0.715667 0.357833 0.933785i \(-0.383516\pi\)
0.357833 + 0.933785i \(0.383516\pi\)
\(972\) −21.4712 −0.688689
\(973\) 66.9785 2.14723
\(974\) −15.2467 −0.488535
\(975\) −10.7630 −0.344691
\(976\) −49.6406 −1.58896
\(977\) −15.2734 −0.488638 −0.244319 0.969695i \(-0.578564\pi\)
−0.244319 + 0.969695i \(0.578564\pi\)
\(978\) 48.0191 1.53548
\(979\) 0.164132 0.00524567
\(980\) 29.9612 0.957077
\(981\) −17.0406 −0.544063
\(982\) 1.98398 0.0633115
\(983\) −41.4127 −1.32086 −0.660431 0.750887i \(-0.729626\pi\)
−0.660431 + 0.750887i \(0.729626\pi\)
\(984\) 106.298 3.38866
\(985\) 21.1783 0.674797
\(986\) 44.7610 1.42548
\(987\) 94.7186 3.01493
\(988\) 0 0
\(989\) 26.9653 0.857447
\(990\) 29.4005 0.934408
\(991\) −18.9609 −0.602314 −0.301157 0.953575i \(-0.597373\pi\)
−0.301157 + 0.953575i \(0.597373\pi\)
\(992\) 1.88204 0.0597549
\(993\) 45.8805 1.45597
\(994\) −1.14976 −0.0364683
\(995\) 15.3752 0.487427
\(996\) 51.0958 1.61903
\(997\) −22.5133 −0.713002 −0.356501 0.934295i \(-0.616030\pi\)
−0.356501 + 0.934295i \(0.616030\pi\)
\(998\) −3.84361 −0.121668
\(999\) 30.9655 0.979704
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 1805.2.a.j.1.1 4
5.4 even 2 9025.2.a.bo.1.4 4
19.18 odd 2 1805.2.a.n.1.4 yes 4
95.94 odd 2 9025.2.a.bh.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.a.j.1.1 4 1.1 even 1 trivial
1805.2.a.n.1.4 yes 4 19.18 odd 2
9025.2.a.bh.1.1 4 95.94 odd 2
9025.2.a.bo.1.4 4 5.4 even 2