Properties

Label 1805.2.a.j.1.3
Level $1805$
Weight $2$
Character 1805.1
Self dual yes
Analytic conductor $14.413$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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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 1.3
Root \(-0.820249\) of defining polynomial
Character \(\chi\) \(=\) 1805.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.820249 q^{2} -2.32719 q^{3} -1.32719 q^{4} +1.00000 q^{5} -1.90888 q^{6} -0.561717 q^{7} -2.72913 q^{8} +2.41582 q^{9} +O(q^{10})\) \(q+0.820249 q^{2} -2.32719 q^{3} -1.32719 q^{4} +1.00000 q^{5} -1.90888 q^{6} -0.561717 q^{7} -2.72913 q^{8} +2.41582 q^{9} +0.820249 q^{10} -0.111092 q^{11} +3.08863 q^{12} +6.89045 q^{13} -0.460748 q^{14} -2.32719 q^{15} +0.415819 q^{16} -3.81167 q^{17} +1.98157 q^{18} -1.32719 q^{20} +1.30722 q^{21} -0.0911232 q^{22} -4.04243 q^{23} +6.35120 q^{24} +1.00000 q^{25} +5.65189 q^{26} +1.35950 q^{27} +0.745506 q^{28} +9.29239 q^{29} -1.90888 q^{30} -4.18987 q^{31} +5.79933 q^{32} +0.258532 q^{33} -3.12652 q^{34} -0.561717 q^{35} -3.20625 q^{36} +2.68669 q^{37} -16.0354 q^{39} -2.72913 q^{40} -10.0988 q^{41} +1.07225 q^{42} -9.63192 q^{43} +0.147440 q^{44} +2.41582 q^{45} -3.31580 q^{46} +2.12652 q^{47} -0.967690 q^{48} -6.68447 q^{49} +0.820249 q^{50} +8.87048 q^{51} -9.14494 q^{52} -5.74455 q^{53} +1.11513 q^{54} -0.111092 q^{55} +1.53300 q^{56} +7.62207 q^{58} +7.89903 q^{59} +3.08863 q^{60} +5.56575 q^{61} -3.43674 q^{62} -1.35701 q^{63} +3.92526 q^{64} +6.89045 q^{65} +0.212061 q^{66} -10.6534 q^{67} +5.05881 q^{68} +9.40752 q^{69} -0.460748 q^{70} -6.64050 q^{71} -6.59307 q^{72} -8.45825 q^{73} +2.20376 q^{74} -2.32719 q^{75} +0.0624023 q^{77} -13.1530 q^{78} -6.27087 q^{79} +0.415819 q^{80} -10.4113 q^{81} -8.28349 q^{82} -8.16132 q^{83} -1.73493 q^{84} -3.81167 q^{85} -7.90057 q^{86} -21.6252 q^{87} +0.303184 q^{88} +1.16741 q^{89} +1.98157 q^{90} -3.87048 q^{91} +5.36508 q^{92} +9.75064 q^{93} +1.74428 q^{94} -13.4961 q^{96} -8.24746 q^{97} -5.48294 q^{98} -0.268378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - q^{3} + 3 q^{4} + 4 q^{5} - 7 q^{6} - 11 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.820249 0.580004 0.290002 0.957026i \(-0.406344\pi\)
0.290002 + 0.957026i \(0.406344\pi\)
\(3\) −2.32719 −1.34360 −0.671802 0.740731i \(-0.734480\pi\)
−0.671802 + 0.740731i \(0.734480\pi\)
\(4\) −1.32719 −0.663596
\(5\) 1.00000 0.447214
\(6\) −1.90888 −0.779296
\(7\) −0.561717 −0.212309 −0.106154 0.994350i \(-0.533854\pi\)
−0.106154 + 0.994350i \(0.533854\pi\)
\(8\) −2.72913 −0.964892
\(9\) 2.41582 0.805273
\(10\) 0.820249 0.259386
\(11\) −0.111092 −0.0334955 −0.0167478 0.999860i \(-0.505331\pi\)
−0.0167478 + 0.999860i \(0.505331\pi\)
\(12\) 3.08863 0.891610
\(13\) 6.89045 1.91107 0.955534 0.294882i \(-0.0952805\pi\)
0.955534 + 0.294882i \(0.0952805\pi\)
\(14\) −0.460748 −0.123140
\(15\) −2.32719 −0.600878
\(16\) 0.415819 0.103955
\(17\) −3.81167 −0.924465 −0.462233 0.886759i \(-0.652952\pi\)
−0.462233 + 0.886759i \(0.652952\pi\)
\(18\) 1.98157 0.467061
\(19\) 0 0
\(20\) −1.32719 −0.296769
\(21\) 1.30722 0.285259
\(22\) −0.0911232 −0.0194275
\(23\) −4.04243 −0.842906 −0.421453 0.906850i \(-0.638480\pi\)
−0.421453 + 0.906850i \(0.638480\pi\)
\(24\) 6.35120 1.29643
\(25\) 1.00000 0.200000
\(26\) 5.65189 1.10843
\(27\) 1.35950 0.261636
\(28\) 0.745506 0.140887
\(29\) 9.29239 1.72555 0.862776 0.505586i \(-0.168724\pi\)
0.862776 + 0.505586i \(0.168724\pi\)
\(30\) −1.90888 −0.348512
\(31\) −4.18987 −0.752524 −0.376262 0.926513i \(-0.622791\pi\)
−0.376262 + 0.926513i \(0.622791\pi\)
\(32\) 5.79933 1.02519
\(33\) 0.258532 0.0450047
\(34\) −3.12652 −0.536193
\(35\) −0.561717 −0.0949475
\(36\) −3.20625 −0.534376
\(37\) 2.68669 0.441690 0.220845 0.975309i \(-0.429119\pi\)
0.220845 + 0.975309i \(0.429119\pi\)
\(38\) 0 0
\(39\) −16.0354 −2.56772
\(40\) −2.72913 −0.431513
\(41\) −10.0988 −1.57716 −0.788580 0.614932i \(-0.789183\pi\)
−0.788580 + 0.614932i \(0.789183\pi\)
\(42\) 1.07225 0.165451
\(43\) −9.63192 −1.46885 −0.734427 0.678688i \(-0.762549\pi\)
−0.734427 + 0.678688i \(0.762549\pi\)
\(44\) 0.147440 0.0222275
\(45\) 2.41582 0.360129
\(46\) −3.31580 −0.488888
\(47\) 2.12652 0.310185 0.155092 0.987900i \(-0.450433\pi\)
0.155092 + 0.987900i \(0.450433\pi\)
\(48\) −0.967690 −0.139674
\(49\) −6.68447 −0.954925
\(50\) 0.820249 0.116001
\(51\) 8.87048 1.24212
\(52\) −9.14494 −1.26818
\(53\) −5.74455 −0.789075 −0.394537 0.918880i \(-0.629095\pi\)
−0.394537 + 0.918880i \(0.629095\pi\)
\(54\) 1.11513 0.151750
\(55\) −0.111092 −0.0149797
\(56\) 1.53300 0.204855
\(57\) 0 0
\(58\) 7.62207 1.00083
\(59\) 7.89903 1.02837 0.514183 0.857680i \(-0.328095\pi\)
0.514183 + 0.857680i \(0.328095\pi\)
\(60\) 3.08863 0.398740
\(61\) 5.56575 0.712622 0.356311 0.934367i \(-0.384034\pi\)
0.356311 + 0.934367i \(0.384034\pi\)
\(62\) −3.43674 −0.436467
\(63\) −1.35701 −0.170967
\(64\) 3.92526 0.490657
\(65\) 6.89045 0.854655
\(66\) 0.212061 0.0261029
\(67\) −10.6534 −1.30152 −0.650762 0.759282i \(-0.725550\pi\)
−0.650762 + 0.759282i \(0.725550\pi\)
\(68\) 5.05881 0.613471
\(69\) 9.40752 1.13253
\(70\) −0.460748 −0.0550699
\(71\) −6.64050 −0.788082 −0.394041 0.919093i \(-0.628923\pi\)
−0.394041 + 0.919093i \(0.628923\pi\)
\(72\) −6.59307 −0.777001
\(73\) −8.45825 −0.989964 −0.494982 0.868903i \(-0.664825\pi\)
−0.494982 + 0.868903i \(0.664825\pi\)
\(74\) 2.20376 0.256182
\(75\) −2.32719 −0.268721
\(76\) 0 0
\(77\) 0.0624023 0.00711140
\(78\) −13.1530 −1.48929
\(79\) −6.27087 −0.705528 −0.352764 0.935712i \(-0.614758\pi\)
−0.352764 + 0.935712i \(0.614758\pi\)
\(80\) 0.415819 0.0464899
\(81\) −10.4113 −1.15681
\(82\) −8.28349 −0.914759
\(83\) −8.16132 −0.895822 −0.447911 0.894078i \(-0.647832\pi\)
−0.447911 + 0.894078i \(0.647832\pi\)
\(84\) −1.73493 −0.189297
\(85\) −3.81167 −0.413434
\(86\) −7.90057 −0.851941
\(87\) −21.6252 −2.31846
\(88\) 0.303184 0.0323196
\(89\) 1.16741 0.123745 0.0618726 0.998084i \(-0.480293\pi\)
0.0618726 + 0.998084i \(0.480293\pi\)
\(90\) 1.98157 0.208876
\(91\) −3.87048 −0.405737
\(92\) 5.36508 0.559348
\(93\) 9.75064 1.01109
\(94\) 1.74428 0.179908
\(95\) 0 0
\(96\) −13.4961 −1.37744
\(97\) −8.24746 −0.837402 −0.418701 0.908124i \(-0.637515\pi\)
−0.418701 + 0.908124i \(0.637515\pi\)
\(98\) −5.48294 −0.553860
\(99\) −0.268378 −0.0269730
\(100\) −1.32719 −0.132719
\(101\) −11.7400 −1.16817 −0.584087 0.811691i \(-0.698547\pi\)
−0.584087 + 0.811691i \(0.698547\pi\)
\(102\) 7.27601 0.720432
\(103\) −19.4676 −1.91820 −0.959099 0.283069i \(-0.908647\pi\)
−0.959099 + 0.283069i \(0.908647\pi\)
\(104\) −18.8049 −1.84397
\(105\) 1.30722 0.127572
\(106\) −4.71196 −0.457666
\(107\) 16.5648 1.60138 0.800690 0.599079i \(-0.204466\pi\)
0.800690 + 0.599079i \(0.204466\pi\)
\(108\) −1.80432 −0.173621
\(109\) 14.0588 1.34659 0.673295 0.739374i \(-0.264878\pi\)
0.673295 + 0.739374i \(0.264878\pi\)
\(110\) −0.0911232 −0.00868826
\(111\) −6.25245 −0.593456
\(112\) −0.233572 −0.0220705
\(113\) 8.88950 0.836254 0.418127 0.908389i \(-0.362687\pi\)
0.418127 + 0.908389i \(0.362687\pi\)
\(114\) 0 0
\(115\) −4.04243 −0.376959
\(116\) −12.3328 −1.14507
\(117\) 16.6461 1.53893
\(118\) 6.47917 0.596456
\(119\) 2.14108 0.196272
\(120\) 6.35120 0.579782
\(121\) −10.9877 −0.998878
\(122\) 4.56531 0.413323
\(123\) 23.5017 2.11908
\(124\) 5.56076 0.499371
\(125\) 1.00000 0.0894427
\(126\) −1.11308 −0.0991613
\(127\) −7.76469 −0.689005 −0.344503 0.938785i \(-0.611952\pi\)
−0.344503 + 0.938785i \(0.611952\pi\)
\(128\) −8.37897 −0.740603
\(129\) 22.4153 1.97356
\(130\) 5.65189 0.495703
\(131\) −4.58042 −0.400193 −0.200097 0.979776i \(-0.564126\pi\)
−0.200097 + 0.979776i \(0.564126\pi\)
\(132\) −0.343122 −0.0298649
\(133\) 0 0
\(134\) −8.73847 −0.754889
\(135\) 1.35950 0.117007
\(136\) 10.4025 0.892009
\(137\) 1.19518 0.102111 0.0510554 0.998696i \(-0.483741\pi\)
0.0510554 + 0.998696i \(0.483741\pi\)
\(138\) 7.71651 0.656873
\(139\) 8.06036 0.683670 0.341835 0.939760i \(-0.388952\pi\)
0.341835 + 0.939760i \(0.388952\pi\)
\(140\) 0.745506 0.0630067
\(141\) −4.94881 −0.416765
\(142\) −5.44686 −0.457091
\(143\) −0.765474 −0.0640122
\(144\) 1.00454 0.0837119
\(145\) 9.29239 0.771691
\(146\) −6.93787 −0.574183
\(147\) 15.5560 1.28304
\(148\) −3.56575 −0.293103
\(149\) 9.89499 0.810629 0.405315 0.914177i \(-0.367162\pi\)
0.405315 + 0.914177i \(0.367162\pi\)
\(150\) −1.90888 −0.155859
\(151\) −20.7413 −1.68790 −0.843951 0.536421i \(-0.819776\pi\)
−0.843951 + 0.536421i \(0.819776\pi\)
\(152\) 0 0
\(153\) −9.20830 −0.744447
\(154\) 0.0511854 0.00412464
\(155\) −4.18987 −0.336539
\(156\) 21.2820 1.70393
\(157\) −12.9092 −1.03026 −0.515131 0.857111i \(-0.672257\pi\)
−0.515131 + 0.857111i \(0.672257\pi\)
\(158\) −5.14368 −0.409209
\(159\) 13.3687 1.06020
\(160\) 5.79933 0.458477
\(161\) 2.27070 0.178956
\(162\) −8.53984 −0.670953
\(163\) −7.93134 −0.621231 −0.310615 0.950536i \(-0.600535\pi\)
−0.310615 + 0.950536i \(0.600535\pi\)
\(164\) 13.4030 1.04660
\(165\) 0.258532 0.0201267
\(166\) −6.69432 −0.519580
\(167\) 5.69132 0.440408 0.220204 0.975454i \(-0.429328\pi\)
0.220204 + 0.975454i \(0.429328\pi\)
\(168\) −3.56757 −0.275244
\(169\) 34.4783 2.65218
\(170\) −3.12652 −0.239793
\(171\) 0 0
\(172\) 12.7834 0.974725
\(173\) −7.12043 −0.541357 −0.270678 0.962670i \(-0.587248\pi\)
−0.270678 + 0.962670i \(0.587248\pi\)
\(174\) −17.7380 −1.34472
\(175\) −0.561717 −0.0424618
\(176\) −0.0461942 −0.00348202
\(177\) −18.3826 −1.38172
\(178\) 0.957567 0.0717727
\(179\) −2.37647 −0.177626 −0.0888129 0.996048i \(-0.528307\pi\)
−0.0888129 + 0.996048i \(0.528307\pi\)
\(180\) −3.20625 −0.238980
\(181\) 20.1766 1.49971 0.749857 0.661600i \(-0.230122\pi\)
0.749857 + 0.661600i \(0.230122\pi\)
\(182\) −3.17476 −0.235329
\(183\) −12.9526 −0.957482
\(184\) 11.0323 0.813313
\(185\) 2.68669 0.197530
\(186\) 7.99795 0.586438
\(187\) 0.423446 0.0309655
\(188\) −2.82230 −0.205837
\(189\) −0.763655 −0.0555477
\(190\) 0 0
\(191\) 9.88950 0.715579 0.357789 0.933802i \(-0.383531\pi\)
0.357789 + 0.933802i \(0.383531\pi\)
\(192\) −9.13482 −0.659249
\(193\) −4.55092 −0.327582 −0.163791 0.986495i \(-0.552372\pi\)
−0.163791 + 0.986495i \(0.552372\pi\)
\(194\) −6.76497 −0.485697
\(195\) −16.0354 −1.14832
\(196\) 8.87158 0.633684
\(197\) −12.4701 −0.888457 −0.444229 0.895914i \(-0.646522\pi\)
−0.444229 + 0.895914i \(0.646522\pi\)
\(198\) −0.220137 −0.0156445
\(199\) −19.9932 −1.41728 −0.708642 0.705569i \(-0.750692\pi\)
−0.708642 + 0.705569i \(0.750692\pi\)
\(200\) −2.72913 −0.192978
\(201\) 24.7926 1.74873
\(202\) −9.62973 −0.677546
\(203\) −5.21969 −0.366350
\(204\) −11.7728 −0.824263
\(205\) −10.0988 −0.705327
\(206\) −15.9683 −1.11256
\(207\) −9.76579 −0.678769
\(208\) 2.86518 0.198664
\(209\) 0 0
\(210\) 1.07225 0.0739921
\(211\) 16.8102 1.15726 0.578631 0.815589i \(-0.303587\pi\)
0.578631 + 0.815589i \(0.303587\pi\)
\(212\) 7.62412 0.523627
\(213\) 15.4537 1.05887
\(214\) 13.5873 0.928806
\(215\) −9.63192 −0.656891
\(216\) −3.71025 −0.252451
\(217\) 2.35352 0.159768
\(218\) 11.5317 0.781027
\(219\) 19.6840 1.33012
\(220\) 0.147440 0.00994043
\(221\) −26.2641 −1.76672
\(222\) −5.12857 −0.344207
\(223\) −1.88641 −0.126324 −0.0631618 0.998003i \(-0.520118\pi\)
−0.0631618 + 0.998003i \(0.520118\pi\)
\(224\) −3.25758 −0.217656
\(225\) 2.41582 0.161055
\(226\) 7.29160 0.485030
\(227\) −10.7044 −0.710479 −0.355239 0.934775i \(-0.615601\pi\)
−0.355239 + 0.934775i \(0.615601\pi\)
\(228\) 0 0
\(229\) 8.34388 0.551379 0.275690 0.961247i \(-0.411094\pi\)
0.275690 + 0.961247i \(0.411094\pi\)
\(230\) −3.31580 −0.218638
\(231\) −0.145222 −0.00955491
\(232\) −25.3601 −1.66497
\(233\) −2.14436 −0.140481 −0.0702407 0.997530i \(-0.522377\pi\)
−0.0702407 + 0.997530i \(0.522377\pi\)
\(234\) 13.6539 0.892586
\(235\) 2.12652 0.138719
\(236\) −10.4835 −0.682419
\(237\) 14.5935 0.947951
\(238\) 1.75622 0.113839
\(239\) 25.0796 1.62227 0.811134 0.584861i \(-0.198851\pi\)
0.811134 + 0.584861i \(0.198851\pi\)
\(240\) −0.967690 −0.0624641
\(241\) 11.3527 0.731294 0.365647 0.930754i \(-0.380848\pi\)
0.365647 + 0.930754i \(0.380848\pi\)
\(242\) −9.01262 −0.579353
\(243\) 20.1505 1.29266
\(244\) −7.38682 −0.472893
\(245\) −6.68447 −0.427055
\(246\) 19.2773 1.22907
\(247\) 0 0
\(248\) 11.4347 0.726104
\(249\) 18.9930 1.20363
\(250\) 0.820249 0.0518771
\(251\) −6.92245 −0.436941 −0.218471 0.975844i \(-0.570107\pi\)
−0.218471 + 0.975844i \(0.570107\pi\)
\(252\) 1.80101 0.113453
\(253\) 0.449082 0.0282336
\(254\) −6.36898 −0.399626
\(255\) 8.87048 0.555491
\(256\) −14.7234 −0.920210
\(257\) 1.89721 0.118345 0.0591724 0.998248i \(-0.481154\pi\)
0.0591724 + 0.998248i \(0.481154\pi\)
\(258\) 18.3861 1.14467
\(259\) −1.50916 −0.0937747
\(260\) −9.14494 −0.567145
\(261\) 22.4487 1.38954
\(262\) −3.75709 −0.232114
\(263\) −11.5446 −0.711868 −0.355934 0.934511i \(-0.615837\pi\)
−0.355934 + 0.934511i \(0.615837\pi\)
\(264\) −0.705568 −0.0434247
\(265\) −5.74455 −0.352885
\(266\) 0 0
\(267\) −2.71678 −0.166265
\(268\) 14.1391 0.863685
\(269\) −3.02056 −0.184167 −0.0920833 0.995751i \(-0.529353\pi\)
−0.0920833 + 0.995751i \(0.529353\pi\)
\(270\) 1.11513 0.0678647
\(271\) 8.81150 0.535260 0.267630 0.963522i \(-0.413759\pi\)
0.267630 + 0.963522i \(0.413759\pi\)
\(272\) −1.58496 −0.0961025
\(273\) 9.00735 0.545150
\(274\) 0.980343 0.0592247
\(275\) −0.111092 −0.00669910
\(276\) −12.4856 −0.751543
\(277\) −9.68919 −0.582167 −0.291083 0.956698i \(-0.594016\pi\)
−0.291083 + 0.956698i \(0.594016\pi\)
\(278\) 6.61150 0.396531
\(279\) −10.1220 −0.605987
\(280\) 1.53300 0.0916140
\(281\) −18.6762 −1.11413 −0.557063 0.830470i \(-0.688072\pi\)
−0.557063 + 0.830470i \(0.688072\pi\)
\(282\) −4.05926 −0.241726
\(283\) −7.46451 −0.443719 −0.221859 0.975079i \(-0.571213\pi\)
−0.221859 + 0.975079i \(0.571213\pi\)
\(284\) 8.81321 0.522968
\(285\) 0 0
\(286\) −0.627880 −0.0371273
\(287\) 5.67264 0.334845
\(288\) 14.0101 0.825554
\(289\) −2.47118 −0.145364
\(290\) 7.62207 0.447583
\(291\) 19.1934 1.12514
\(292\) 11.2257 0.656935
\(293\) −3.73771 −0.218359 −0.109180 0.994022i \(-0.534822\pi\)
−0.109180 + 0.994022i \(0.534822\pi\)
\(294\) 12.7598 0.744169
\(295\) 7.89903 0.459899
\(296\) −7.33232 −0.426183
\(297\) −0.151030 −0.00876364
\(298\) 8.11636 0.470168
\(299\) −27.8542 −1.61085
\(300\) 3.08863 0.178322
\(301\) 5.41041 0.311851
\(302\) −17.0130 −0.978989
\(303\) 27.3212 1.56956
\(304\) 0 0
\(305\) 5.56575 0.318694
\(306\) −7.55310 −0.431782
\(307\) 23.2825 1.32880 0.664402 0.747375i \(-0.268686\pi\)
0.664402 + 0.747375i \(0.268686\pi\)
\(308\) −0.0828198 −0.00471909
\(309\) 45.3048 2.57730
\(310\) −3.43674 −0.195194
\(311\) 23.4553 1.33003 0.665013 0.746832i \(-0.268426\pi\)
0.665013 + 0.746832i \(0.268426\pi\)
\(312\) 43.7626 2.47757
\(313\) −15.0079 −0.848297 −0.424148 0.905593i \(-0.639427\pi\)
−0.424148 + 0.905593i \(0.639427\pi\)
\(314\) −10.5887 −0.597556
\(315\) −1.35701 −0.0764586
\(316\) 8.32265 0.468186
\(317\) −19.3000 −1.08400 −0.541998 0.840380i \(-0.682332\pi\)
−0.541998 + 0.840380i \(0.682332\pi\)
\(318\) 10.9656 0.614923
\(319\) −1.03231 −0.0577983
\(320\) 3.92526 0.219428
\(321\) −38.5495 −2.15162
\(322\) 1.86254 0.103795
\(323\) 0 0
\(324\) 13.8178 0.767653
\(325\) 6.89045 0.382213
\(326\) −6.50568 −0.360316
\(327\) −32.7175 −1.80928
\(328\) 27.5608 1.52179
\(329\) −1.19450 −0.0658550
\(330\) 0.212061 0.0116736
\(331\) 19.1303 1.05150 0.525748 0.850641i \(-0.323786\pi\)
0.525748 + 0.850641i \(0.323786\pi\)
\(332\) 10.8316 0.594463
\(333\) 6.49056 0.355681
\(334\) 4.66830 0.255438
\(335\) −10.6534 −0.582059
\(336\) 0.543568 0.0296540
\(337\) 25.5100 1.38962 0.694810 0.719193i \(-0.255489\pi\)
0.694810 + 0.719193i \(0.255489\pi\)
\(338\) 28.2808 1.53827
\(339\) −20.6876 −1.12359
\(340\) 5.05881 0.274353
\(341\) 0.465462 0.0252062
\(342\) 0 0
\(343\) 7.68680 0.415048
\(344\) 26.2867 1.41728
\(345\) 9.40752 0.506484
\(346\) −5.84053 −0.313989
\(347\) −34.3847 −1.84587 −0.922933 0.384960i \(-0.874215\pi\)
−0.922933 + 0.384960i \(0.874215\pi\)
\(348\) 28.7007 1.53852
\(349\) −28.6428 −1.53321 −0.766607 0.642117i \(-0.778057\pi\)
−0.766607 + 0.642117i \(0.778057\pi\)
\(350\) −0.460748 −0.0246280
\(351\) 9.36758 0.500004
\(352\) −0.644259 −0.0343391
\(353\) 23.5203 1.25186 0.625930 0.779879i \(-0.284719\pi\)
0.625930 + 0.779879i \(0.284719\pi\)
\(354\) −15.0783 −0.801401
\(355\) −6.64050 −0.352441
\(356\) −1.54938 −0.0821167
\(357\) −4.98270 −0.263712
\(358\) −1.94930 −0.103024
\(359\) 9.77437 0.515871 0.257936 0.966162i \(-0.416958\pi\)
0.257936 + 0.966162i \(0.416958\pi\)
\(360\) −6.59307 −0.347486
\(361\) 0 0
\(362\) 16.5498 0.869839
\(363\) 25.5704 1.34210
\(364\) 5.13687 0.269245
\(365\) −8.45825 −0.442725
\(366\) −10.6243 −0.555343
\(367\) −2.03857 −0.106412 −0.0532062 0.998584i \(-0.516944\pi\)
−0.0532062 + 0.998584i \(0.516944\pi\)
\(368\) −1.68092 −0.0876240
\(369\) −24.3968 −1.27004
\(370\) 2.20376 0.114568
\(371\) 3.22681 0.167528
\(372\) −12.9410 −0.670958
\(373\) −12.9613 −0.671110 −0.335555 0.942021i \(-0.608924\pi\)
−0.335555 + 0.942021i \(0.608924\pi\)
\(374\) 0.347331 0.0179601
\(375\) −2.32719 −0.120176
\(376\) −5.80354 −0.299295
\(377\) 64.0287 3.29765
\(378\) −0.626387 −0.0322179
\(379\) −6.82911 −0.350788 −0.175394 0.984498i \(-0.556120\pi\)
−0.175394 + 0.984498i \(0.556120\pi\)
\(380\) 0 0
\(381\) 18.0699 0.925750
\(382\) 8.11185 0.415038
\(383\) −17.1311 −0.875356 −0.437678 0.899132i \(-0.644199\pi\)
−0.437678 + 0.899132i \(0.644199\pi\)
\(384\) 19.4995 0.995077
\(385\) 0.0624023 0.00318031
\(386\) −3.73289 −0.189999
\(387\) −23.2690 −1.18283
\(388\) 10.9460 0.555696
\(389\) 18.4370 0.934794 0.467397 0.884048i \(-0.345192\pi\)
0.467397 + 0.884048i \(0.345192\pi\)
\(390\) −13.1530 −0.666029
\(391\) 15.4084 0.779237
\(392\) 18.2428 0.921399
\(393\) 10.6595 0.537701
\(394\) −10.2286 −0.515308
\(395\) −6.27087 −0.315522
\(396\) 0.356189 0.0178992
\(397\) −3.44622 −0.172961 −0.0864805 0.996254i \(-0.527562\pi\)
−0.0864805 + 0.996254i \(0.527562\pi\)
\(398\) −16.3994 −0.822030
\(399\) 0 0
\(400\) 0.415819 0.0207909
\(401\) −12.4272 −0.620585 −0.310293 0.950641i \(-0.600427\pi\)
−0.310293 + 0.950641i \(0.600427\pi\)
\(402\) 20.3361 1.01427
\(403\) −28.8701 −1.43812
\(404\) 15.5812 0.775196
\(405\) −10.4113 −0.517340
\(406\) −4.28145 −0.212485
\(407\) −0.298470 −0.0147946
\(408\) −24.2087 −1.19851
\(409\) −2.53190 −0.125194 −0.0625972 0.998039i \(-0.519938\pi\)
−0.0625972 + 0.998039i \(0.519938\pi\)
\(410\) −8.28349 −0.409093
\(411\) −2.78141 −0.137197
\(412\) 25.8372 1.27291
\(413\) −4.43702 −0.218331
\(414\) −8.01038 −0.393689
\(415\) −8.16132 −0.400624
\(416\) 39.9600 1.95920
\(417\) −18.7580 −0.918583
\(418\) 0 0
\(419\) 0.647537 0.0316342 0.0158171 0.999875i \(-0.494965\pi\)
0.0158171 + 0.999875i \(0.494965\pi\)
\(420\) −1.73493 −0.0846561
\(421\) −4.37148 −0.213053 −0.106526 0.994310i \(-0.533973\pi\)
−0.106526 + 0.994310i \(0.533973\pi\)
\(422\) 13.7886 0.671217
\(423\) 5.13728 0.249783
\(424\) 15.6776 0.761372
\(425\) −3.81167 −0.184893
\(426\) 12.6759 0.614149
\(427\) −3.12638 −0.151296
\(428\) −21.9847 −1.06267
\(429\) 1.78141 0.0860071
\(430\) −7.90057 −0.380999
\(431\) −30.0094 −1.44550 −0.722752 0.691107i \(-0.757123\pi\)
−0.722752 + 0.691107i \(0.757123\pi\)
\(432\) 0.565306 0.0271983
\(433\) −17.6077 −0.846173 −0.423086 0.906089i \(-0.639053\pi\)
−0.423086 + 0.906089i \(0.639053\pi\)
\(434\) 1.93047 0.0926658
\(435\) −21.6252 −1.03685
\(436\) −18.6587 −0.893591
\(437\) 0 0
\(438\) 16.1458 0.771474
\(439\) −25.8827 −1.23532 −0.617658 0.786447i \(-0.711918\pi\)
−0.617658 + 0.786447i \(0.711918\pi\)
\(440\) 0.303184 0.0144537
\(441\) −16.1485 −0.768975
\(442\) −21.5431 −1.02470
\(443\) 11.8766 0.564273 0.282136 0.959374i \(-0.408957\pi\)
0.282136 + 0.959374i \(0.408957\pi\)
\(444\) 8.29819 0.393815
\(445\) 1.16741 0.0553405
\(446\) −1.54733 −0.0732681
\(447\) −23.0275 −1.08917
\(448\) −2.20488 −0.104171
\(449\) −29.4524 −1.38995 −0.694973 0.719035i \(-0.744584\pi\)
−0.694973 + 0.719035i \(0.744584\pi\)
\(450\) 1.98157 0.0934123
\(451\) 1.12189 0.0528278
\(452\) −11.7981 −0.554934
\(453\) 48.2689 2.26787
\(454\) −8.78031 −0.412080
\(455\) −3.87048 −0.181451
\(456\) 0 0
\(457\) 24.3329 1.13825 0.569123 0.822253i \(-0.307283\pi\)
0.569123 + 0.822253i \(0.307283\pi\)
\(458\) 6.84406 0.319802
\(459\) −5.18197 −0.241874
\(460\) 5.36508 0.250148
\(461\) 34.5042 1.60702 0.803511 0.595290i \(-0.202963\pi\)
0.803511 + 0.595290i \(0.202963\pi\)
\(462\) −0.119118 −0.00554188
\(463\) −4.89328 −0.227410 −0.113705 0.993515i \(-0.536272\pi\)
−0.113705 + 0.993515i \(0.536272\pi\)
\(464\) 3.86395 0.179379
\(465\) 9.75064 0.452175
\(466\) −1.75891 −0.0814798
\(467\) 15.6840 0.725769 0.362885 0.931834i \(-0.381792\pi\)
0.362885 + 0.931834i \(0.381792\pi\)
\(468\) −22.0925 −1.02123
\(469\) 5.98421 0.276325
\(470\) 1.74428 0.0804574
\(471\) 30.0421 1.38427
\(472\) −21.5575 −0.992262
\(473\) 1.07003 0.0492000
\(474\) 11.9703 0.549815
\(475\) 0 0
\(476\) −2.84162 −0.130245
\(477\) −13.8778 −0.635421
\(478\) 20.5716 0.940921
\(479\) 15.1666 0.692981 0.346490 0.938054i \(-0.387373\pi\)
0.346490 + 0.938054i \(0.387373\pi\)
\(480\) −13.4961 −0.616012
\(481\) 18.5125 0.844098
\(482\) 9.31208 0.424153
\(483\) −5.28436 −0.240447
\(484\) 14.5827 0.662851
\(485\) −8.24746 −0.374498
\(486\) 16.5285 0.749746
\(487\) −14.8366 −0.672312 −0.336156 0.941806i \(-0.609127\pi\)
−0.336156 + 0.941806i \(0.609127\pi\)
\(488\) −15.1896 −0.687603
\(489\) 18.4577 0.834688
\(490\) −5.48294 −0.247694
\(491\) 21.7022 0.979408 0.489704 0.871889i \(-0.337105\pi\)
0.489704 + 0.871889i \(0.337105\pi\)
\(492\) −31.1913 −1.40621
\(493\) −35.4195 −1.59521
\(494\) 0 0
\(495\) −0.268378 −0.0120627
\(496\) −1.74223 −0.0782283
\(497\) 3.73008 0.167317
\(498\) 15.5790 0.698110
\(499\) −20.5764 −0.921124 −0.460562 0.887627i \(-0.652352\pi\)
−0.460562 + 0.887627i \(0.652352\pi\)
\(500\) −1.32719 −0.0593538
\(501\) −13.2448 −0.591734
\(502\) −5.67813 −0.253427
\(503\) −34.8559 −1.55415 −0.777074 0.629409i \(-0.783297\pi\)
−0.777074 + 0.629409i \(0.783297\pi\)
\(504\) 3.70344 0.164964
\(505\) −11.7400 −0.522424
\(506\) 0.368359 0.0163756
\(507\) −80.2376 −3.56348
\(508\) 10.3052 0.457221
\(509\) 30.7078 1.36110 0.680551 0.732701i \(-0.261741\pi\)
0.680551 + 0.732701i \(0.261741\pi\)
\(510\) 7.27601 0.322187
\(511\) 4.75114 0.210178
\(512\) 4.68111 0.206878
\(513\) 0 0
\(514\) 1.55619 0.0686404
\(515\) −19.4676 −0.857845
\(516\) −29.7494 −1.30964
\(517\) −0.236239 −0.0103898
\(518\) −1.23789 −0.0543897
\(519\) 16.5706 0.727369
\(520\) −18.8049 −0.824650
\(521\) 10.9533 0.479874 0.239937 0.970788i \(-0.422873\pi\)
0.239937 + 0.970788i \(0.422873\pi\)
\(522\) 18.4135 0.805939
\(523\) 4.44485 0.194360 0.0971799 0.995267i \(-0.469018\pi\)
0.0971799 + 0.995267i \(0.469018\pi\)
\(524\) 6.07909 0.265566
\(525\) 1.30722 0.0570519
\(526\) −9.46941 −0.412886
\(527\) 15.9704 0.695682
\(528\) 0.107503 0.00467845
\(529\) −6.65873 −0.289510
\(530\) −4.71196 −0.204675
\(531\) 19.0826 0.828115
\(532\) 0 0
\(533\) −69.5849 −3.01406
\(534\) −2.22844 −0.0964341
\(535\) 16.5648 0.716159
\(536\) 29.0746 1.25583
\(537\) 5.53050 0.238659
\(538\) −2.47761 −0.106817
\(539\) 0.742592 0.0319857
\(540\) −1.80432 −0.0776455
\(541\) 6.38522 0.274522 0.137261 0.990535i \(-0.456170\pi\)
0.137261 + 0.990535i \(0.456170\pi\)
\(542\) 7.22762 0.310453
\(543\) −46.9548 −2.01502
\(544\) −22.1051 −0.947749
\(545\) 14.0588 0.602213
\(546\) 7.38827 0.316189
\(547\) −10.6627 −0.455904 −0.227952 0.973672i \(-0.573203\pi\)
−0.227952 + 0.973672i \(0.573203\pi\)
\(548\) −1.58623 −0.0677603
\(549\) 13.4459 0.573855
\(550\) −0.0911232 −0.00388551
\(551\) 0 0
\(552\) −25.6743 −1.09277
\(553\) 3.52245 0.149790
\(554\) −7.94755 −0.337659
\(555\) −6.25245 −0.265402
\(556\) −10.6976 −0.453681
\(557\) −3.06585 −0.129904 −0.0649521 0.997888i \(-0.520689\pi\)
−0.0649521 + 0.997888i \(0.520689\pi\)
\(558\) −8.30254 −0.351475
\(559\) −66.3683 −2.80708
\(560\) −0.233572 −0.00987023
\(561\) −0.985440 −0.0416053
\(562\) −15.3191 −0.646198
\(563\) 35.1561 1.48165 0.740827 0.671696i \(-0.234434\pi\)
0.740827 + 0.671696i \(0.234434\pi\)
\(564\) 6.56802 0.276564
\(565\) 8.88950 0.373984
\(566\) −6.12276 −0.257359
\(567\) 5.84819 0.245601
\(568\) 18.1228 0.760414
\(569\) 42.2302 1.77038 0.885190 0.465229i \(-0.154028\pi\)
0.885190 + 0.465229i \(0.154028\pi\)
\(570\) 0 0
\(571\) −24.3462 −1.01886 −0.509429 0.860513i \(-0.670143\pi\)
−0.509429 + 0.860513i \(0.670143\pi\)
\(572\) 1.01593 0.0424782
\(573\) −23.0148 −0.961455
\(574\) 4.65298 0.194211
\(575\) −4.04243 −0.168581
\(576\) 9.48271 0.395113
\(577\) −9.74424 −0.405658 −0.202829 0.979214i \(-0.565014\pi\)
−0.202829 + 0.979214i \(0.565014\pi\)
\(578\) −2.02699 −0.0843115
\(579\) 10.5909 0.440141
\(580\) −12.3328 −0.512090
\(581\) 4.58435 0.190191
\(582\) 15.7434 0.652584
\(583\) 0.638174 0.0264305
\(584\) 23.0836 0.955208
\(585\) 16.6461 0.688231
\(586\) −3.06585 −0.126649
\(587\) 15.9708 0.659186 0.329593 0.944123i \(-0.393089\pi\)
0.329593 + 0.944123i \(0.393089\pi\)
\(588\) −20.6459 −0.851421
\(589\) 0 0
\(590\) 6.47917 0.266743
\(591\) 29.0203 1.19373
\(592\) 1.11718 0.0459157
\(593\) −0.404153 −0.0165966 −0.00829829 0.999966i \(-0.502641\pi\)
−0.00829829 + 0.999966i \(0.502641\pi\)
\(594\) −0.123882 −0.00508294
\(595\) 2.14108 0.0877756
\(596\) −13.1325 −0.537930
\(597\) 46.5281 1.90427
\(598\) −22.8474 −0.934299
\(599\) −17.0426 −0.696342 −0.348171 0.937431i \(-0.613197\pi\)
−0.348171 + 0.937431i \(0.613197\pi\)
\(600\) 6.35120 0.259287
\(601\) 0.819125 0.0334128 0.0167064 0.999860i \(-0.494682\pi\)
0.0167064 + 0.999860i \(0.494682\pi\)
\(602\) 4.43788 0.180875
\(603\) −25.7368 −1.04808
\(604\) 27.5276 1.12008
\(605\) −10.9877 −0.446712
\(606\) 22.4102 0.910353
\(607\) −18.2675 −0.741455 −0.370728 0.928742i \(-0.620892\pi\)
−0.370728 + 0.928742i \(0.620892\pi\)
\(608\) 0 0
\(609\) 12.1472 0.492230
\(610\) 4.56531 0.184844
\(611\) 14.6527 0.592784
\(612\) 12.2212 0.494012
\(613\) 27.6822 1.11807 0.559037 0.829142i \(-0.311171\pi\)
0.559037 + 0.829142i \(0.311171\pi\)
\(614\) 19.0975 0.770712
\(615\) 23.5017 0.947681
\(616\) −0.170304 −0.00686173
\(617\) −40.1940 −1.61815 −0.809075 0.587706i \(-0.800031\pi\)
−0.809075 + 0.587706i \(0.800031\pi\)
\(618\) 37.1612 1.49484
\(619\) 46.3862 1.86442 0.932209 0.361920i \(-0.117879\pi\)
0.932209 + 0.361920i \(0.117879\pi\)
\(620\) 5.56076 0.223326
\(621\) −5.49569 −0.220535
\(622\) 19.2392 0.771420
\(623\) −0.655753 −0.0262722
\(624\) −6.66782 −0.266926
\(625\) 1.00000 0.0400000
\(626\) −12.3102 −0.492015
\(627\) 0 0
\(628\) 17.1329 0.683678
\(629\) −10.2408 −0.408327
\(630\) −1.11308 −0.0443463
\(631\) −47.5023 −1.89104 −0.945519 0.325568i \(-0.894444\pi\)
−0.945519 + 0.325568i \(0.894444\pi\)
\(632\) 17.1140 0.680759
\(633\) −39.1206 −1.55490
\(634\) −15.8308 −0.628722
\(635\) −7.76469 −0.308132
\(636\) −17.7428 −0.703547
\(637\) −46.0590 −1.82493
\(638\) −0.846752 −0.0335232
\(639\) −16.0422 −0.634621
\(640\) −8.37897 −0.331208
\(641\) −13.1626 −0.519891 −0.259946 0.965623i \(-0.583705\pi\)
−0.259946 + 0.965623i \(0.583705\pi\)
\(642\) −31.6202 −1.24795
\(643\) −35.4538 −1.39816 −0.699081 0.715042i \(-0.746407\pi\)
−0.699081 + 0.715042i \(0.746407\pi\)
\(644\) −3.01366 −0.118755
\(645\) 22.4153 0.882602
\(646\) 0 0
\(647\) 3.38283 0.132993 0.0664964 0.997787i \(-0.478818\pi\)
0.0664964 + 0.997787i \(0.478818\pi\)
\(648\) 28.4137 1.11619
\(649\) −0.877520 −0.0344457
\(650\) 5.65189 0.221685
\(651\) −5.47710 −0.214664
\(652\) 10.5264 0.412246
\(653\) −0.621795 −0.0243327 −0.0121664 0.999926i \(-0.503873\pi\)
−0.0121664 + 0.999926i \(0.503873\pi\)
\(654\) −26.8365 −1.04939
\(655\) −4.58042 −0.178972
\(656\) −4.19925 −0.163953
\(657\) −20.4336 −0.797191
\(658\) −0.979789 −0.0381961
\(659\) −11.6203 −0.452664 −0.226332 0.974050i \(-0.572673\pi\)
−0.226332 + 0.974050i \(0.572673\pi\)
\(660\) −0.343122 −0.0133560
\(661\) −13.2897 −0.516911 −0.258456 0.966023i \(-0.583214\pi\)
−0.258456 + 0.966023i \(0.583214\pi\)
\(662\) 15.6916 0.609871
\(663\) 61.1216 2.37377
\(664\) 22.2733 0.864371
\(665\) 0 0
\(666\) 5.32388 0.206296
\(667\) −37.5638 −1.45448
\(668\) −7.55347 −0.292253
\(669\) 4.39004 0.169729
\(670\) −8.73847 −0.337596
\(671\) −0.618311 −0.0238696
\(672\) 7.58101 0.292444
\(673\) −23.9351 −0.922630 −0.461315 0.887236i \(-0.652622\pi\)
−0.461315 + 0.887236i \(0.652622\pi\)
\(674\) 20.9246 0.805985
\(675\) 1.35950 0.0523272
\(676\) −45.7593 −1.75997
\(677\) −3.71727 −0.142866 −0.0714331 0.997445i \(-0.522757\pi\)
−0.0714331 + 0.997445i \(0.522757\pi\)
\(678\) −16.9690 −0.651689
\(679\) 4.63273 0.177788
\(680\) 10.4025 0.398919
\(681\) 24.9113 0.954603
\(682\) 0.381795 0.0146197
\(683\) −1.40634 −0.0538120 −0.0269060 0.999638i \(-0.508565\pi\)
−0.0269060 + 0.999638i \(0.508565\pi\)
\(684\) 0 0
\(685\) 1.19518 0.0456654
\(686\) 6.30509 0.240729
\(687\) −19.4178 −0.740836
\(688\) −4.00513 −0.152694
\(689\) −39.5826 −1.50798
\(690\) 7.71651 0.293762
\(691\) 2.20762 0.0839820 0.0419910 0.999118i \(-0.486630\pi\)
0.0419910 + 0.999118i \(0.486630\pi\)
\(692\) 9.45018 0.359242
\(693\) 0.150753 0.00572662
\(694\) −28.2040 −1.07061
\(695\) 8.06036 0.305747
\(696\) 59.0178 2.23706
\(697\) 38.4931 1.45803
\(698\) −23.4942 −0.889270
\(699\) 4.99033 0.188751
\(700\) 0.745506 0.0281775
\(701\) −3.95566 −0.149403 −0.0747016 0.997206i \(-0.523800\pi\)
−0.0747016 + 0.997206i \(0.523800\pi\)
\(702\) 7.68375 0.290004
\(703\) 0 0
\(704\) −0.436065 −0.0164348
\(705\) −4.94881 −0.186383
\(706\) 19.2925 0.726084
\(707\) 6.59456 0.248014
\(708\) 24.3972 0.916902
\(709\) −31.8658 −1.19674 −0.598372 0.801218i \(-0.704186\pi\)
−0.598372 + 0.801218i \(0.704186\pi\)
\(710\) −5.44686 −0.204417
\(711\) −15.1493 −0.568143
\(712\) −3.18601 −0.119401
\(713\) 16.9373 0.634306
\(714\) −4.08705 −0.152954
\(715\) −0.765474 −0.0286271
\(716\) 3.15403 0.117872
\(717\) −58.3651 −2.17969
\(718\) 8.01742 0.299207
\(719\) −34.2360 −1.27679 −0.638393 0.769710i \(-0.720401\pi\)
−0.638393 + 0.769710i \(0.720401\pi\)
\(720\) 1.00454 0.0374371
\(721\) 10.9353 0.407251
\(722\) 0 0
\(723\) −26.4200 −0.982570
\(724\) −26.7782 −0.995203
\(725\) 9.29239 0.345111
\(726\) 20.9741 0.778421
\(727\) −29.5181 −1.09477 −0.547383 0.836882i \(-0.684376\pi\)
−0.547383 + 0.836882i \(0.684376\pi\)
\(728\) 10.5630 0.391492
\(729\) −15.6603 −0.580011
\(730\) −6.93787 −0.256782
\(731\) 36.7137 1.35790
\(732\) 17.1905 0.635381
\(733\) 28.2212 1.04237 0.521187 0.853442i \(-0.325489\pi\)
0.521187 + 0.853442i \(0.325489\pi\)
\(734\) −1.67213 −0.0617195
\(735\) 15.5560 0.573794
\(736\) −23.4434 −0.864135
\(737\) 1.18351 0.0435952
\(738\) −20.0114 −0.736630
\(739\) −24.0957 −0.886373 −0.443187 0.896429i \(-0.646152\pi\)
−0.443187 + 0.896429i \(0.646152\pi\)
\(740\) −3.56575 −0.131080
\(741\) 0 0
\(742\) 2.64679 0.0971667
\(743\) 12.9103 0.473632 0.236816 0.971554i \(-0.423896\pi\)
0.236816 + 0.971554i \(0.423896\pi\)
\(744\) −26.6107 −0.975596
\(745\) 9.89499 0.362524
\(746\) −10.6315 −0.389247
\(747\) −19.7163 −0.721381
\(748\) −0.561994 −0.0205485
\(749\) −9.30473 −0.339987
\(750\) −1.90888 −0.0697023
\(751\) 37.7129 1.37616 0.688082 0.725633i \(-0.258453\pi\)
0.688082 + 0.725633i \(0.258453\pi\)
\(752\) 0.884246 0.0322451
\(753\) 16.1099 0.587076
\(754\) 52.5195 1.91265
\(755\) −20.7413 −0.754852
\(756\) 1.01352 0.0368612
\(757\) −34.7933 −1.26458 −0.632292 0.774730i \(-0.717886\pi\)
−0.632292 + 0.774730i \(0.717886\pi\)
\(758\) −5.60157 −0.203458
\(759\) −1.04510 −0.0379347
\(760\) 0 0
\(761\) 4.00019 0.145007 0.0725034 0.997368i \(-0.476901\pi\)
0.0725034 + 0.997368i \(0.476901\pi\)
\(762\) 14.8218 0.536939
\(763\) −7.89707 −0.285893
\(764\) −13.1253 −0.474855
\(765\) −9.20830 −0.332927
\(766\) −14.0517 −0.507710
\(767\) 54.4279 1.96528
\(768\) 34.2641 1.23640
\(769\) −9.59479 −0.345997 −0.172998 0.984922i \(-0.555346\pi\)
−0.172998 + 0.984922i \(0.555346\pi\)
\(770\) 0.0511854 0.00184459
\(771\) −4.41517 −0.159009
\(772\) 6.03994 0.217382
\(773\) 2.23562 0.0804096 0.0402048 0.999191i \(-0.487199\pi\)
0.0402048 + 0.999191i \(0.487199\pi\)
\(774\) −19.0864 −0.686045
\(775\) −4.18987 −0.150505
\(776\) 22.5083 0.808003
\(777\) 3.51210 0.125996
\(778\) 15.1230 0.542184
\(779\) 0 0
\(780\) 21.2820 0.762019
\(781\) 0.737707 0.0263972
\(782\) 12.6387 0.451960
\(783\) 12.6330 0.451467
\(784\) −2.77953 −0.0992689
\(785\) −12.9092 −0.460747
\(786\) 8.74346 0.311869
\(787\) 19.6480 0.700376 0.350188 0.936679i \(-0.386118\pi\)
0.350188 + 0.936679i \(0.386118\pi\)
\(788\) 16.5502 0.589576
\(789\) 26.8664 0.956469
\(790\) −5.14368 −0.183004
\(791\) −4.99338 −0.177544
\(792\) 0.732438 0.0260261
\(793\) 38.3506 1.36187
\(794\) −2.82676 −0.100318
\(795\) 13.3687 0.474138
\(796\) 26.5349 0.940503
\(797\) −15.8851 −0.562680 −0.281340 0.959608i \(-0.590779\pi\)
−0.281340 + 0.959608i \(0.590779\pi\)
\(798\) 0 0
\(799\) −8.10558 −0.286755
\(800\) 5.79933 0.205037
\(801\) 2.82025 0.0996486
\(802\) −10.1934 −0.359942
\(803\) 0.939645 0.0331593
\(804\) −32.9045 −1.16045
\(805\) 2.27070 0.0800318
\(806\) −23.6807 −0.834117
\(807\) 7.02942 0.247447
\(808\) 32.0400 1.12716
\(809\) 9.82989 0.345600 0.172800 0.984957i \(-0.444718\pi\)
0.172800 + 0.984957i \(0.444718\pi\)
\(810\) −8.53984 −0.300059
\(811\) 29.0667 1.02067 0.510335 0.859976i \(-0.329521\pi\)
0.510335 + 0.859976i \(0.329521\pi\)
\(812\) 6.92752 0.243108
\(813\) −20.5060 −0.719178
\(814\) −0.244820 −0.00858094
\(815\) −7.93134 −0.277823
\(816\) 3.68851 0.129124
\(817\) 0 0
\(818\) −2.07679 −0.0726133
\(819\) −9.35038 −0.326729
\(820\) 13.4030 0.468052
\(821\) 9.14446 0.319144 0.159572 0.987186i \(-0.448989\pi\)
0.159572 + 0.987186i \(0.448989\pi\)
\(822\) −2.28145 −0.0795746
\(823\) 25.8030 0.899436 0.449718 0.893171i \(-0.351524\pi\)
0.449718 + 0.893171i \(0.351524\pi\)
\(824\) 53.1295 1.85085
\(825\) 0.258532 0.00900095
\(826\) −3.63946 −0.126633
\(827\) 4.28552 0.149022 0.0745110 0.997220i \(-0.476260\pi\)
0.0745110 + 0.997220i \(0.476260\pi\)
\(828\) 12.9611 0.450428
\(829\) 5.70557 0.198163 0.0990813 0.995079i \(-0.468410\pi\)
0.0990813 + 0.995079i \(0.468410\pi\)
\(830\) −6.69432 −0.232363
\(831\) 22.5486 0.782202
\(832\) 27.0468 0.937679
\(833\) 25.4790 0.882795
\(834\) −15.3862 −0.532781
\(835\) 5.69132 0.196956
\(836\) 0 0
\(837\) −5.69614 −0.196887
\(838\) 0.531142 0.0183480
\(839\) −15.5188 −0.535769 −0.267884 0.963451i \(-0.586325\pi\)
−0.267884 + 0.963451i \(0.586325\pi\)
\(840\) −3.56757 −0.123093
\(841\) 57.3484 1.97753
\(842\) −3.58570 −0.123571
\(843\) 43.4630 1.49695
\(844\) −22.3104 −0.767954
\(845\) 34.4783 1.18609
\(846\) 4.21385 0.144875
\(847\) 6.17195 0.212071
\(848\) −2.38869 −0.0820280
\(849\) 17.3713 0.596183
\(850\) −3.12652 −0.107239
\(851\) −10.8608 −0.372303
\(852\) −20.5100 −0.702662
\(853\) −49.8235 −1.70592 −0.852962 0.521972i \(-0.825196\pi\)
−0.852962 + 0.521972i \(0.825196\pi\)
\(854\) −2.56441 −0.0877523
\(855\) 0 0
\(856\) −45.2074 −1.54516
\(857\) −43.1178 −1.47288 −0.736438 0.676505i \(-0.763494\pi\)
−0.736438 + 0.676505i \(0.763494\pi\)
\(858\) 1.46120 0.0498844
\(859\) 17.9279 0.611691 0.305845 0.952081i \(-0.401061\pi\)
0.305845 + 0.952081i \(0.401061\pi\)
\(860\) 12.7834 0.435910
\(861\) −13.2013 −0.449900
\(862\) −24.6152 −0.838398
\(863\) 55.6045 1.89280 0.946399 0.322999i \(-0.104691\pi\)
0.946399 + 0.322999i \(0.104691\pi\)
\(864\) 7.88419 0.268226
\(865\) −7.12043 −0.242102
\(866\) −14.4427 −0.490784
\(867\) 5.75091 0.195311
\(868\) −3.12357 −0.106021
\(869\) 0.696644 0.0236320
\(870\) −17.7380 −0.601375
\(871\) −73.4069 −2.48730
\(872\) −38.3683 −1.29931
\(873\) −19.9244 −0.674337
\(874\) 0 0
\(875\) −0.561717 −0.0189895
\(876\) −26.1244 −0.882661
\(877\) 12.1639 0.410744 0.205372 0.978684i \(-0.434160\pi\)
0.205372 + 0.978684i \(0.434160\pi\)
\(878\) −21.2303 −0.716488
\(879\) 8.69836 0.293388
\(880\) −0.0461942 −0.00155720
\(881\) 28.8330 0.971408 0.485704 0.874123i \(-0.338563\pi\)
0.485704 + 0.874123i \(0.338563\pi\)
\(882\) −13.2458 −0.446009
\(883\) −0.648525 −0.0218246 −0.0109123 0.999940i \(-0.503474\pi\)
−0.0109123 + 0.999940i \(0.503474\pi\)
\(884\) 34.8575 1.17238
\(885\) −18.3826 −0.617923
\(886\) 9.74174 0.327280
\(887\) 45.2362 1.51888 0.759441 0.650577i \(-0.225473\pi\)
0.759441 + 0.650577i \(0.225473\pi\)
\(888\) 17.0637 0.572621
\(889\) 4.36156 0.146282
\(890\) 0.957567 0.0320977
\(891\) 1.15661 0.0387479
\(892\) 2.50363 0.0838277
\(893\) 0 0
\(894\) −18.8883 −0.631720
\(895\) −2.37647 −0.0794366
\(896\) 4.70661 0.157237
\(897\) 64.8220 2.16434
\(898\) −24.1583 −0.806174
\(899\) −38.9339 −1.29852
\(900\) −3.20625 −0.106875
\(901\) 21.8963 0.729472
\(902\) 0.920230 0.0306403
\(903\) −12.5911 −0.419004
\(904\) −24.2606 −0.806894
\(905\) 20.1766 0.670692
\(906\) 39.5925 1.31537
\(907\) −15.1528 −0.503142 −0.251571 0.967839i \(-0.580947\pi\)
−0.251571 + 0.967839i \(0.580947\pi\)
\(908\) 14.2068 0.471471
\(909\) −28.3617 −0.940699
\(910\) −3.17476 −0.105242
\(911\) 31.7373 1.05150 0.525752 0.850638i \(-0.323784\pi\)
0.525752 + 0.850638i \(0.323784\pi\)
\(912\) 0 0
\(913\) 0.906658 0.0300060
\(914\) 19.9591 0.660187
\(915\) −12.9526 −0.428199
\(916\) −11.0739 −0.365893
\(917\) 2.57290 0.0849646
\(918\) −4.25051 −0.140288
\(919\) 5.31327 0.175269 0.0876343 0.996153i \(-0.472069\pi\)
0.0876343 + 0.996153i \(0.472069\pi\)
\(920\) 11.0323 0.363725
\(921\) −54.1829 −1.78539
\(922\) 28.3021 0.932079
\(923\) −45.7560 −1.50608
\(924\) 0.192737 0.00634059
\(925\) 2.68669 0.0883379
\(926\) −4.01371 −0.131899
\(927\) −47.0302 −1.54467
\(928\) 53.8896 1.76901
\(929\) −3.54458 −0.116294 −0.0581469 0.998308i \(-0.518519\pi\)
−0.0581469 + 0.998308i \(0.518519\pi\)
\(930\) 7.99795 0.262263
\(931\) 0 0
\(932\) 2.84597 0.0932228
\(933\) −54.5849 −1.78703
\(934\) 12.8648 0.420949
\(935\) 0.423446 0.0138482
\(936\) −45.4292 −1.48490
\(937\) 31.2800 1.02187 0.510936 0.859619i \(-0.329299\pi\)
0.510936 + 0.859619i \(0.329299\pi\)
\(938\) 4.90854 0.160270
\(939\) 34.9263 1.13978
\(940\) −2.82230 −0.0920532
\(941\) 45.5106 1.48360 0.741802 0.670619i \(-0.233971\pi\)
0.741802 + 0.670619i \(0.233971\pi\)
\(942\) 24.6420 0.802879
\(943\) 40.8235 1.32940
\(944\) 3.28457 0.106903
\(945\) −0.763655 −0.0248417
\(946\) 0.877691 0.0285362
\(947\) −21.0071 −0.682640 −0.341320 0.939947i \(-0.610874\pi\)
−0.341320 + 0.939947i \(0.610874\pi\)
\(948\) −19.3684 −0.629056
\(949\) −58.2812 −1.89189
\(950\) 0 0
\(951\) 44.9148 1.45646
\(952\) −5.84327 −0.189382
\(953\) −32.6629 −1.05806 −0.529028 0.848604i \(-0.677443\pi\)
−0.529028 + 0.848604i \(0.677443\pi\)
\(954\) −11.3833 −0.368546
\(955\) 9.88950 0.320017
\(956\) −33.2855 −1.07653
\(957\) 2.40238 0.0776580
\(958\) 12.4404 0.401932
\(959\) −0.671351 −0.0216791
\(960\) −9.13482 −0.294825
\(961\) −13.4450 −0.433708
\(962\) 15.1849 0.489580
\(963\) 40.0176 1.28955
\(964\) −15.0673 −0.485284
\(965\) −4.55092 −0.146499
\(966\) −4.33449 −0.139460
\(967\) −21.8080 −0.701299 −0.350650 0.936507i \(-0.614039\pi\)
−0.350650 + 0.936507i \(0.614039\pi\)
\(968\) 29.9867 0.963809
\(969\) 0 0
\(970\) −6.76497 −0.217210
\(971\) 55.8370 1.79189 0.895947 0.444162i \(-0.146498\pi\)
0.895947 + 0.444162i \(0.146498\pi\)
\(972\) −26.7436 −0.857801
\(973\) −4.52764 −0.145149
\(974\) −12.1697 −0.389943
\(975\) −16.0354 −0.513544
\(976\) 2.31435 0.0740804
\(977\) 0.543879 0.0174002 0.00870012 0.999962i \(-0.497231\pi\)
0.00870012 + 0.999962i \(0.497231\pi\)
\(978\) 15.1400 0.484122
\(979\) −0.129690 −0.00414491
\(980\) 8.87158 0.283392
\(981\) 33.9635 1.08437
\(982\) 17.8012 0.568060
\(983\) 11.0176 0.351407 0.175704 0.984443i \(-0.443780\pi\)
0.175704 + 0.984443i \(0.443780\pi\)
\(984\) −64.1392 −2.04468
\(985\) −12.4701 −0.397330
\(986\) −29.0528 −0.925230
\(987\) 2.77983 0.0884830
\(988\) 0 0
\(989\) 38.9364 1.23811
\(990\) −0.220137 −0.00699642
\(991\) 28.1970 0.895707 0.447854 0.894107i \(-0.352189\pi\)
0.447854 + 0.894107i \(0.352189\pi\)
\(992\) −24.2984 −0.771477
\(993\) −44.5198 −1.41279
\(994\) 3.05959 0.0970445
\(995\) −19.9932 −0.633828
\(996\) −25.2073 −0.798724
\(997\) −30.5688 −0.968123 −0.484062 0.875034i \(-0.660839\pi\)
−0.484062 + 0.875034i \(0.660839\pi\)
\(998\) −16.8777 −0.534256
\(999\) 3.65256 0.115562
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.1.3 4
5.4 even 2 9025.2.a.bo.1.2 4
19.18 odd 2 1805.2.a.n.1.2 yes 4
95.94 odd 2 9025.2.a.bh.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.a.j.1.3 4 1.1 even 1 trivial
1805.2.a.n.1.2 yes 4 19.18 odd 2
9025.2.a.bh.1.3 4 95.94 odd 2
9025.2.a.bo.1.2 4 5.4 even 2