Properties

Label 3549.2.a.bf.1.1
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - x^{8} - 11 x^{7} + 8 x^{6} + 37 x^{5} - 18 x^{4} - 41 x^{3} + 12 x^{2} + 6 x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.31147\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.31147 q^{2} -1.00000 q^{3} +3.34288 q^{4} -1.46052 q^{5} +2.31147 q^{6} -1.00000 q^{7} -3.10401 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.31147 q^{2} -1.00000 q^{3} +3.34288 q^{4} -1.46052 q^{5} +2.31147 q^{6} -1.00000 q^{7} -3.10401 q^{8} +1.00000 q^{9} +3.37595 q^{10} -0.0565977 q^{11} -3.34288 q^{12} +2.31147 q^{14} +1.46052 q^{15} +0.489065 q^{16} +5.75421 q^{17} -2.31147 q^{18} +0.807619 q^{19} -4.88235 q^{20} +1.00000 q^{21} +0.130824 q^{22} +6.01403 q^{23} +3.10401 q^{24} -2.86687 q^{25} -1.00000 q^{27} -3.34288 q^{28} +3.22124 q^{29} -3.37595 q^{30} -5.59058 q^{31} +5.07756 q^{32} +0.0565977 q^{33} -13.3007 q^{34} +1.46052 q^{35} +3.34288 q^{36} -0.780896 q^{37} -1.86679 q^{38} +4.53348 q^{40} +5.30154 q^{41} -2.31147 q^{42} +2.38217 q^{43} -0.189199 q^{44} -1.46052 q^{45} -13.9012 q^{46} +3.32663 q^{47} -0.489065 q^{48} +1.00000 q^{49} +6.62667 q^{50} -5.75421 q^{51} -9.52747 q^{53} +2.31147 q^{54} +0.0826623 q^{55} +3.10401 q^{56} -0.807619 q^{57} -7.44578 q^{58} -10.3267 q^{59} +4.88235 q^{60} +8.88239 q^{61} +12.9224 q^{62} -1.00000 q^{63} -12.7147 q^{64} -0.130824 q^{66} -7.80744 q^{67} +19.2356 q^{68} -6.01403 q^{69} -3.37595 q^{70} +11.4706 q^{71} -3.10401 q^{72} -13.1445 q^{73} +1.80501 q^{74} +2.86687 q^{75} +2.69977 q^{76} +0.0565977 q^{77} +10.8565 q^{79} -0.714292 q^{80} +1.00000 q^{81} -12.2543 q^{82} +7.70243 q^{83} +3.34288 q^{84} -8.40417 q^{85} -5.50631 q^{86} -3.22124 q^{87} +0.175680 q^{88} -8.12369 q^{89} +3.37595 q^{90} +20.1042 q^{92} +5.59058 q^{93} -7.68939 q^{94} -1.17955 q^{95} -5.07756 q^{96} -3.93035 q^{97} -2.31147 q^{98} -0.0565977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + O(q^{10}) \) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + q^{10} + q^{11} - 5q^{12} - q^{14} + 9q^{15} + 5q^{16} + 11q^{17} + q^{18} - 7q^{19} - 23q^{20} + 9q^{21} - 3q^{22} + 22q^{23} - 6q^{24} - 8q^{25} - 9q^{27} - 5q^{28} + 11q^{29} - q^{30} - 7q^{31} + 18q^{32} - q^{33} + 6q^{34} + 9q^{35} + 5q^{36} + q^{37} - 6q^{38} - 14q^{40} - 16q^{41} + q^{42} + 32q^{43} - 18q^{44} - 9q^{45} + 9q^{46} + 12q^{47} - 5q^{48} + 9q^{49} - 10q^{50} - 11q^{51} + 13q^{53} - q^{54} + 9q^{55} - 6q^{56} + 7q^{57} - 4q^{58} - 29q^{59} + 23q^{60} - 12q^{61} + 30q^{62} - 9q^{63} + 6q^{64} + 3q^{66} + 20q^{67} + 34q^{68} - 22q^{69} - q^{70} + 2q^{71} + 6q^{72} - q^{73} + 43q^{74} + 8q^{75} - 13q^{76} - q^{77} + 3q^{79} + 39q^{80} + 9q^{81} - 19q^{82} - 24q^{83} + 5q^{84} - 15q^{85} + 28q^{86} - 11q^{87} - 19q^{88} - 11q^{89} + q^{90} + 73q^{92} + 7q^{93} + 15q^{94} + 39q^{95} - 18q^{96} - 20q^{97} + q^{98} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31147 −1.63445 −0.817227 0.576316i \(-0.804490\pi\)
−0.817227 + 0.576316i \(0.804490\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.34288 1.67144
\(5\) −1.46052 −0.653166 −0.326583 0.945168i \(-0.605897\pi\)
−0.326583 + 0.945168i \(0.605897\pi\)
\(6\) 2.31147 0.943652
\(7\) −1.00000 −0.377964
\(8\) −3.10401 −1.09743
\(9\) 1.00000 0.333333
\(10\) 3.37595 1.06757
\(11\) −0.0565977 −0.0170648 −0.00853242 0.999964i \(-0.502716\pi\)
−0.00853242 + 0.999964i \(0.502716\pi\)
\(12\) −3.34288 −0.965005
\(13\) 0 0
\(14\) 2.31147 0.617765
\(15\) 1.46052 0.377106
\(16\) 0.489065 0.122266
\(17\) 5.75421 1.39560 0.697801 0.716292i \(-0.254162\pi\)
0.697801 + 0.716292i \(0.254162\pi\)
\(18\) −2.31147 −0.544818
\(19\) 0.807619 0.185281 0.0926403 0.995700i \(-0.470469\pi\)
0.0926403 + 0.995700i \(0.470469\pi\)
\(20\) −4.88235 −1.09173
\(21\) 1.00000 0.218218
\(22\) 0.130824 0.0278917
\(23\) 6.01403 1.25401 0.627006 0.779014i \(-0.284280\pi\)
0.627006 + 0.779014i \(0.284280\pi\)
\(24\) 3.10401 0.633604
\(25\) −2.86687 −0.573374
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −3.34288 −0.631744
\(29\) 3.22124 0.598168 0.299084 0.954227i \(-0.403319\pi\)
0.299084 + 0.954227i \(0.403319\pi\)
\(30\) −3.37595 −0.616362
\(31\) −5.59058 −1.00410 −0.502049 0.864839i \(-0.667420\pi\)
−0.502049 + 0.864839i \(0.667420\pi\)
\(32\) 5.07756 0.897595
\(33\) 0.0565977 0.00985239
\(34\) −13.3007 −2.28105
\(35\) 1.46052 0.246874
\(36\) 3.34288 0.557146
\(37\) −0.780896 −0.128378 −0.0641892 0.997938i \(-0.520446\pi\)
−0.0641892 + 0.997938i \(0.520446\pi\)
\(38\) −1.86679 −0.302833
\(39\) 0 0
\(40\) 4.53348 0.716807
\(41\) 5.30154 0.827961 0.413980 0.910286i \(-0.364138\pi\)
0.413980 + 0.910286i \(0.364138\pi\)
\(42\) −2.31147 −0.356667
\(43\) 2.38217 0.363278 0.181639 0.983365i \(-0.441860\pi\)
0.181639 + 0.983365i \(0.441860\pi\)
\(44\) −0.189199 −0.0285228
\(45\) −1.46052 −0.217722
\(46\) −13.9012 −2.04963
\(47\) 3.32663 0.485239 0.242620 0.970122i \(-0.421993\pi\)
0.242620 + 0.970122i \(0.421993\pi\)
\(48\) −0.489065 −0.0705905
\(49\) 1.00000 0.142857
\(50\) 6.62667 0.937153
\(51\) −5.75421 −0.805751
\(52\) 0 0
\(53\) −9.52747 −1.30870 −0.654350 0.756192i \(-0.727058\pi\)
−0.654350 + 0.756192i \(0.727058\pi\)
\(54\) 2.31147 0.314551
\(55\) 0.0826623 0.0111462
\(56\) 3.10401 0.414791
\(57\) −0.807619 −0.106972
\(58\) −7.44578 −0.977678
\(59\) −10.3267 −1.34443 −0.672214 0.740357i \(-0.734656\pi\)
−0.672214 + 0.740357i \(0.734656\pi\)
\(60\) 4.88235 0.630309
\(61\) 8.88239 1.13727 0.568637 0.822589i \(-0.307471\pi\)
0.568637 + 0.822589i \(0.307471\pi\)
\(62\) 12.9224 1.64115
\(63\) −1.00000 −0.125988
\(64\) −12.7147 −1.58934
\(65\) 0 0
\(66\) −0.130824 −0.0161033
\(67\) −7.80744 −0.953830 −0.476915 0.878949i \(-0.658245\pi\)
−0.476915 + 0.878949i \(0.658245\pi\)
\(68\) 19.2356 2.33266
\(69\) −6.01403 −0.724005
\(70\) −3.37595 −0.403504
\(71\) 11.4706 1.36131 0.680657 0.732602i \(-0.261694\pi\)
0.680657 + 0.732602i \(0.261694\pi\)
\(72\) −3.10401 −0.365811
\(73\) −13.1445 −1.53845 −0.769223 0.638980i \(-0.779357\pi\)
−0.769223 + 0.638980i \(0.779357\pi\)
\(74\) 1.80501 0.209829
\(75\) 2.86687 0.331037
\(76\) 2.69977 0.309685
\(77\) 0.0565977 0.00644991
\(78\) 0 0
\(79\) 10.8565 1.22145 0.610726 0.791842i \(-0.290878\pi\)
0.610726 + 0.791842i \(0.290878\pi\)
\(80\) −0.714292 −0.0798602
\(81\) 1.00000 0.111111
\(82\) −12.2543 −1.35326
\(83\) 7.70243 0.845452 0.422726 0.906258i \(-0.361073\pi\)
0.422726 + 0.906258i \(0.361073\pi\)
\(84\) 3.34288 0.364738
\(85\) −8.40417 −0.911560
\(86\) −5.50631 −0.593760
\(87\) −3.22124 −0.345353
\(88\) 0.175680 0.0187275
\(89\) −8.12369 −0.861109 −0.430555 0.902564i \(-0.641682\pi\)
−0.430555 + 0.902564i \(0.641682\pi\)
\(90\) 3.37595 0.355857
\(91\) 0 0
\(92\) 20.1042 2.09600
\(93\) 5.59058 0.579716
\(94\) −7.68939 −0.793101
\(95\) −1.17955 −0.121019
\(96\) −5.07756 −0.518227
\(97\) −3.93035 −0.399066 −0.199533 0.979891i \(-0.563943\pi\)
−0.199533 + 0.979891i \(0.563943\pi\)
\(98\) −2.31147 −0.233493
\(99\) −0.0565977 −0.00568828
\(100\) −9.58358 −0.958358
\(101\) 6.75818 0.672464 0.336232 0.941779i \(-0.390847\pi\)
0.336232 + 0.941779i \(0.390847\pi\)
\(102\) 13.3007 1.31696
\(103\) −12.4083 −1.22262 −0.611312 0.791390i \(-0.709358\pi\)
−0.611312 + 0.791390i \(0.709358\pi\)
\(104\) 0 0
\(105\) −1.46052 −0.142533
\(106\) 22.0224 2.13901
\(107\) 18.1781 1.75734 0.878672 0.477425i \(-0.158430\pi\)
0.878672 + 0.477425i \(0.158430\pi\)
\(108\) −3.34288 −0.321668
\(109\) 9.12019 0.873556 0.436778 0.899569i \(-0.356120\pi\)
0.436778 + 0.899569i \(0.356120\pi\)
\(110\) −0.191071 −0.0182179
\(111\) 0.780896 0.0741193
\(112\) −0.489065 −0.0462123
\(113\) −14.7050 −1.38333 −0.691664 0.722220i \(-0.743122\pi\)
−0.691664 + 0.722220i \(0.743122\pi\)
\(114\) 1.86679 0.174840
\(115\) −8.78364 −0.819079
\(116\) 10.7682 0.999801
\(117\) 0 0
\(118\) 23.8699 2.19740
\(119\) −5.75421 −0.527488
\(120\) −4.53348 −0.413849
\(121\) −10.9968 −0.999709
\(122\) −20.5313 −1.85882
\(123\) −5.30154 −0.478023
\(124\) −18.6886 −1.67829
\(125\) 11.4898 1.02767
\(126\) 2.31147 0.205922
\(127\) −10.5900 −0.939714 −0.469857 0.882743i \(-0.655694\pi\)
−0.469857 + 0.882743i \(0.655694\pi\)
\(128\) 19.2346 1.70011
\(129\) −2.38217 −0.209738
\(130\) 0 0
\(131\) −9.31173 −0.813570 −0.406785 0.913524i \(-0.633350\pi\)
−0.406785 + 0.913524i \(0.633350\pi\)
\(132\) 0.189199 0.0164677
\(133\) −0.807619 −0.0700295
\(134\) 18.0466 1.55899
\(135\) 1.46052 0.125702
\(136\) −17.8611 −1.53158
\(137\) −4.10255 −0.350505 −0.175252 0.984524i \(-0.556074\pi\)
−0.175252 + 0.984524i \(0.556074\pi\)
\(138\) 13.9012 1.18335
\(139\) 16.2754 1.38046 0.690231 0.723589i \(-0.257509\pi\)
0.690231 + 0.723589i \(0.257509\pi\)
\(140\) 4.88235 0.412634
\(141\) −3.32663 −0.280153
\(142\) −26.5140 −2.22500
\(143\) 0 0
\(144\) 0.489065 0.0407554
\(145\) −4.70469 −0.390704
\(146\) 30.3830 2.51452
\(147\) −1.00000 −0.0824786
\(148\) −2.61044 −0.214577
\(149\) 2.11348 0.173143 0.0865717 0.996246i \(-0.472409\pi\)
0.0865717 + 0.996246i \(0.472409\pi\)
\(150\) −6.62667 −0.541065
\(151\) 17.2235 1.40163 0.700814 0.713344i \(-0.252820\pi\)
0.700814 + 0.713344i \(0.252820\pi\)
\(152\) −2.50686 −0.203333
\(153\) 5.75421 0.465201
\(154\) −0.130824 −0.0105421
\(155\) 8.16518 0.655843
\(156\) 0 0
\(157\) −20.5730 −1.64190 −0.820951 0.570998i \(-0.806556\pi\)
−0.820951 + 0.570998i \(0.806556\pi\)
\(158\) −25.0944 −1.99641
\(159\) 9.52747 0.755578
\(160\) −7.41591 −0.586279
\(161\) −6.01403 −0.473972
\(162\) −2.31147 −0.181606
\(163\) 8.77011 0.686928 0.343464 0.939166i \(-0.388400\pi\)
0.343464 + 0.939166i \(0.388400\pi\)
\(164\) 17.7224 1.38389
\(165\) −0.0826623 −0.00643525
\(166\) −17.8039 −1.38185
\(167\) −16.9542 −1.31195 −0.655976 0.754782i \(-0.727743\pi\)
−0.655976 + 0.754782i \(0.727743\pi\)
\(168\) −3.10401 −0.239480
\(169\) 0 0
\(170\) 19.4260 1.48990
\(171\) 0.807619 0.0617602
\(172\) 7.96330 0.607196
\(173\) 1.91338 0.145472 0.0727360 0.997351i \(-0.476827\pi\)
0.0727360 + 0.997351i \(0.476827\pi\)
\(174\) 7.44578 0.564463
\(175\) 2.86687 0.216715
\(176\) −0.0276800 −0.00208646
\(177\) 10.3267 0.776206
\(178\) 18.7776 1.40744
\(179\) −26.1240 −1.95260 −0.976300 0.216421i \(-0.930562\pi\)
−0.976300 + 0.216421i \(0.930562\pi\)
\(180\) −4.88235 −0.363909
\(181\) −1.98010 −0.147180 −0.0735899 0.997289i \(-0.523446\pi\)
−0.0735899 + 0.997289i \(0.523446\pi\)
\(182\) 0 0
\(183\) −8.88239 −0.656605
\(184\) −18.6676 −1.37620
\(185\) 1.14052 0.0838525
\(186\) −12.9224 −0.947520
\(187\) −0.325675 −0.0238157
\(188\) 11.1205 0.811047
\(189\) 1.00000 0.0727393
\(190\) 2.72649 0.197800
\(191\) −20.6851 −1.49672 −0.748359 0.663294i \(-0.769158\pi\)
−0.748359 + 0.663294i \(0.769158\pi\)
\(192\) 12.7147 0.917608
\(193\) −2.88929 −0.207976 −0.103988 0.994579i \(-0.533160\pi\)
−0.103988 + 0.994579i \(0.533160\pi\)
\(194\) 9.08487 0.652256
\(195\) 0 0
\(196\) 3.34288 0.238777
\(197\) −3.01713 −0.214962 −0.107481 0.994207i \(-0.534278\pi\)
−0.107481 + 0.994207i \(0.534278\pi\)
\(198\) 0.130824 0.00929723
\(199\) 24.5542 1.74060 0.870301 0.492520i \(-0.163924\pi\)
0.870301 + 0.492520i \(0.163924\pi\)
\(200\) 8.89879 0.629240
\(201\) 7.80744 0.550694
\(202\) −15.6213 −1.09911
\(203\) −3.22124 −0.226086
\(204\) −19.2356 −1.34676
\(205\) −7.74302 −0.540796
\(206\) 28.6813 1.99832
\(207\) 6.01403 0.418004
\(208\) 0 0
\(209\) −0.0457094 −0.00316179
\(210\) 3.37595 0.232963
\(211\) 15.2596 1.05052 0.525259 0.850943i \(-0.323969\pi\)
0.525259 + 0.850943i \(0.323969\pi\)
\(212\) −31.8492 −2.18741
\(213\) −11.4706 −0.785955
\(214\) −42.0181 −2.87230
\(215\) −3.47922 −0.237281
\(216\) 3.10401 0.211201
\(217\) 5.59058 0.379514
\(218\) −21.0810 −1.42779
\(219\) 13.1445 0.888222
\(220\) 0.276330 0.0186302
\(221\) 0 0
\(222\) −1.80501 −0.121145
\(223\) 3.41178 0.228470 0.114235 0.993454i \(-0.463558\pi\)
0.114235 + 0.993454i \(0.463558\pi\)
\(224\) −5.07756 −0.339259
\(225\) −2.86687 −0.191125
\(226\) 33.9900 2.26098
\(227\) 1.36962 0.0909046 0.0454523 0.998967i \(-0.485527\pi\)
0.0454523 + 0.998967i \(0.485527\pi\)
\(228\) −2.69977 −0.178797
\(229\) 17.3194 1.14450 0.572249 0.820080i \(-0.306071\pi\)
0.572249 + 0.820080i \(0.306071\pi\)
\(230\) 20.3031 1.33875
\(231\) −0.0565977 −0.00372386
\(232\) −9.99875 −0.656450
\(233\) 5.77054 0.378041 0.189020 0.981973i \(-0.439469\pi\)
0.189020 + 0.981973i \(0.439469\pi\)
\(234\) 0 0
\(235\) −4.85863 −0.316942
\(236\) −34.5210 −2.24713
\(237\) −10.8565 −0.705206
\(238\) 13.3007 0.862154
\(239\) 2.80755 0.181605 0.0908027 0.995869i \(-0.471057\pi\)
0.0908027 + 0.995869i \(0.471057\pi\)
\(240\) 0.714292 0.0461073
\(241\) 7.55528 0.486678 0.243339 0.969941i \(-0.421757\pi\)
0.243339 + 0.969941i \(0.421757\pi\)
\(242\) 25.4187 1.63398
\(243\) −1.00000 −0.0641500
\(244\) 29.6927 1.90088
\(245\) −1.46052 −0.0933095
\(246\) 12.2543 0.781307
\(247\) 0 0
\(248\) 17.3532 1.10193
\(249\) −7.70243 −0.488122
\(250\) −26.5582 −1.67969
\(251\) 26.2186 1.65491 0.827453 0.561535i \(-0.189789\pi\)
0.827453 + 0.561535i \(0.189789\pi\)
\(252\) −3.34288 −0.210581
\(253\) −0.340380 −0.0213995
\(254\) 24.4785 1.53592
\(255\) 8.40417 0.526290
\(256\) −19.0306 −1.18941
\(257\) −3.58179 −0.223426 −0.111713 0.993741i \(-0.535634\pi\)
−0.111713 + 0.993741i \(0.535634\pi\)
\(258\) 5.50631 0.342808
\(259\) 0.780896 0.0485225
\(260\) 0 0
\(261\) 3.22124 0.199389
\(262\) 21.5237 1.32974
\(263\) 26.7600 1.65009 0.825046 0.565066i \(-0.191149\pi\)
0.825046 + 0.565066i \(0.191149\pi\)
\(264\) −0.175680 −0.0108123
\(265\) 13.9151 0.854798
\(266\) 1.86679 0.114460
\(267\) 8.12369 0.497162
\(268\) −26.0993 −1.59427
\(269\) 14.7193 0.897454 0.448727 0.893669i \(-0.351878\pi\)
0.448727 + 0.893669i \(0.351878\pi\)
\(270\) −3.37595 −0.205454
\(271\) −13.1874 −0.801075 −0.400537 0.916280i \(-0.631176\pi\)
−0.400537 + 0.916280i \(0.631176\pi\)
\(272\) 2.81419 0.170635
\(273\) 0 0
\(274\) 9.48291 0.572884
\(275\) 0.162258 0.00978454
\(276\) −20.1042 −1.21013
\(277\) 21.5726 1.29617 0.648087 0.761566i \(-0.275569\pi\)
0.648087 + 0.761566i \(0.275569\pi\)
\(278\) −37.6200 −2.25630
\(279\) −5.59058 −0.334699
\(280\) −4.53348 −0.270927
\(281\) 0.186485 0.0111248 0.00556238 0.999985i \(-0.498229\pi\)
0.00556238 + 0.999985i \(0.498229\pi\)
\(282\) 7.68939 0.457897
\(283\) −14.0208 −0.833452 −0.416726 0.909032i \(-0.636823\pi\)
−0.416726 + 0.909032i \(0.636823\pi\)
\(284\) 38.3449 2.27535
\(285\) 1.17955 0.0698704
\(286\) 0 0
\(287\) −5.30154 −0.312940
\(288\) 5.07756 0.299198
\(289\) 16.1110 0.947705
\(290\) 10.8747 0.638587
\(291\) 3.93035 0.230401
\(292\) −43.9404 −2.57142
\(293\) 15.8832 0.927907 0.463953 0.885860i \(-0.346430\pi\)
0.463953 + 0.885860i \(0.346430\pi\)
\(294\) 2.31147 0.134807
\(295\) 15.0825 0.878135
\(296\) 2.42391 0.140887
\(297\) 0.0565977 0.00328413
\(298\) −4.88525 −0.282995
\(299\) 0 0
\(300\) 9.58358 0.553309
\(301\) −2.38217 −0.137306
\(302\) −39.8115 −2.29090
\(303\) −6.75818 −0.388247
\(304\) 0.394979 0.0226536
\(305\) −12.9729 −0.742829
\(306\) −13.3007 −0.760349
\(307\) −12.3994 −0.707669 −0.353834 0.935308i \(-0.615122\pi\)
−0.353834 + 0.935308i \(0.615122\pi\)
\(308\) 0.189199 0.0107806
\(309\) 12.4083 0.705882
\(310\) −18.8735 −1.07195
\(311\) 7.17624 0.406927 0.203463 0.979083i \(-0.434780\pi\)
0.203463 + 0.979083i \(0.434780\pi\)
\(312\) 0 0
\(313\) −21.8602 −1.23561 −0.617806 0.786330i \(-0.711978\pi\)
−0.617806 + 0.786330i \(0.711978\pi\)
\(314\) 47.5537 2.68361
\(315\) 1.46052 0.0822912
\(316\) 36.2919 2.04158
\(317\) 26.2740 1.47570 0.737848 0.674967i \(-0.235842\pi\)
0.737848 + 0.674967i \(0.235842\pi\)
\(318\) −22.0224 −1.23496
\(319\) −0.182315 −0.0102077
\(320\) 18.5702 1.03811
\(321\) −18.1781 −1.01460
\(322\) 13.9012 0.774686
\(323\) 4.64722 0.258578
\(324\) 3.34288 0.185715
\(325\) 0 0
\(326\) −20.2718 −1.12275
\(327\) −9.12019 −0.504348
\(328\) −16.4560 −0.908632
\(329\) −3.32663 −0.183403
\(330\) 0.191071 0.0105181
\(331\) 27.3837 1.50515 0.752573 0.658509i \(-0.228812\pi\)
0.752573 + 0.658509i \(0.228812\pi\)
\(332\) 25.7483 1.41312
\(333\) −0.780896 −0.0427928
\(334\) 39.1889 2.14432
\(335\) 11.4030 0.623010
\(336\) 0.489065 0.0266807
\(337\) −20.0655 −1.09304 −0.546520 0.837446i \(-0.684048\pi\)
−0.546520 + 0.837446i \(0.684048\pi\)
\(338\) 0 0
\(339\) 14.7050 0.798664
\(340\) −28.0941 −1.52362
\(341\) 0.316414 0.0171348
\(342\) −1.86679 −0.100944
\(343\) −1.00000 −0.0539949
\(344\) −7.39428 −0.398673
\(345\) 8.78364 0.472895
\(346\) −4.42272 −0.237767
\(347\) 17.6754 0.948865 0.474432 0.880292i \(-0.342653\pi\)
0.474432 + 0.880292i \(0.342653\pi\)
\(348\) −10.7682 −0.577236
\(349\) 11.8130 0.632336 0.316168 0.948703i \(-0.397604\pi\)
0.316168 + 0.948703i \(0.397604\pi\)
\(350\) −6.62667 −0.354210
\(351\) 0 0
\(352\) −0.287378 −0.0153173
\(353\) 28.9315 1.53987 0.769935 0.638122i \(-0.220288\pi\)
0.769935 + 0.638122i \(0.220288\pi\)
\(354\) −23.8699 −1.26867
\(355\) −16.7531 −0.889164
\(356\) −27.1565 −1.43929
\(357\) 5.75421 0.304545
\(358\) 60.3848 3.19143
\(359\) −1.69739 −0.0895850 −0.0447925 0.998996i \(-0.514263\pi\)
−0.0447925 + 0.998996i \(0.514263\pi\)
\(360\) 4.53348 0.238936
\(361\) −18.3478 −0.965671
\(362\) 4.57694 0.240559
\(363\) 10.9968 0.577182
\(364\) 0 0
\(365\) 19.1978 1.00486
\(366\) 20.5313 1.07319
\(367\) −30.9753 −1.61690 −0.808448 0.588567i \(-0.799692\pi\)
−0.808448 + 0.588567i \(0.799692\pi\)
\(368\) 2.94126 0.153324
\(369\) 5.30154 0.275987
\(370\) −2.63627 −0.137053
\(371\) 9.52747 0.494642
\(372\) 18.6886 0.968960
\(373\) −10.6807 −0.553026 −0.276513 0.961010i \(-0.589179\pi\)
−0.276513 + 0.961010i \(0.589179\pi\)
\(374\) 0.752787 0.0389257
\(375\) −11.4898 −0.593328
\(376\) −10.3259 −0.532518
\(377\) 0 0
\(378\) −2.31147 −0.118889
\(379\) 28.1251 1.44469 0.722344 0.691534i \(-0.243065\pi\)
0.722344 + 0.691534i \(0.243065\pi\)
\(380\) −3.94308 −0.202276
\(381\) 10.5900 0.542544
\(382\) 47.8128 2.44632
\(383\) −12.2466 −0.625772 −0.312886 0.949791i \(-0.601296\pi\)
−0.312886 + 0.949791i \(0.601296\pi\)
\(384\) −19.2346 −0.981561
\(385\) −0.0826623 −0.00421286
\(386\) 6.67849 0.339926
\(387\) 2.38217 0.121093
\(388\) −13.1387 −0.667015
\(389\) −13.6432 −0.691738 −0.345869 0.938283i \(-0.612416\pi\)
−0.345869 + 0.938283i \(0.612416\pi\)
\(390\) 0 0
\(391\) 34.6060 1.75010
\(392\) −3.10401 −0.156776
\(393\) 9.31173 0.469715
\(394\) 6.97399 0.351345
\(395\) −15.8562 −0.797811
\(396\) −0.189199 −0.00950761
\(397\) −12.4375 −0.624219 −0.312109 0.950046i \(-0.601036\pi\)
−0.312109 + 0.950046i \(0.601036\pi\)
\(398\) −56.7562 −2.84493
\(399\) 0.807619 0.0404315
\(400\) −1.40209 −0.0701043
\(401\) 25.0321 1.25004 0.625021 0.780608i \(-0.285090\pi\)
0.625021 + 0.780608i \(0.285090\pi\)
\(402\) −18.0466 −0.900084
\(403\) 0 0
\(404\) 22.5918 1.12398
\(405\) −1.46052 −0.0725740
\(406\) 7.44578 0.369528
\(407\) 0.0441969 0.00219076
\(408\) 17.8611 0.884258
\(409\) 35.3470 1.74780 0.873899 0.486108i \(-0.161584\pi\)
0.873899 + 0.486108i \(0.161584\pi\)
\(410\) 17.8977 0.883906
\(411\) 4.10255 0.202364
\(412\) −41.4793 −2.04354
\(413\) 10.3267 0.508146
\(414\) −13.9012 −0.683208
\(415\) −11.2496 −0.552221
\(416\) 0 0
\(417\) −16.2754 −0.797010
\(418\) 0.105656 0.00516779
\(419\) 26.0985 1.27499 0.637496 0.770453i \(-0.279970\pi\)
0.637496 + 0.770453i \(0.279970\pi\)
\(420\) −4.88235 −0.238234
\(421\) −0.465309 −0.0226778 −0.0113389 0.999936i \(-0.503609\pi\)
−0.0113389 + 0.999936i \(0.503609\pi\)
\(422\) −35.2722 −1.71702
\(423\) 3.32663 0.161746
\(424\) 29.5734 1.43621
\(425\) −16.4966 −0.800201
\(426\) 26.5140 1.28461
\(427\) −8.88239 −0.429849
\(428\) 60.7672 2.93729
\(429\) 0 0
\(430\) 8.04209 0.387824
\(431\) 26.8469 1.29317 0.646584 0.762843i \(-0.276197\pi\)
0.646584 + 0.762843i \(0.276197\pi\)
\(432\) −0.489065 −0.0235302
\(433\) 28.8450 1.38620 0.693101 0.720840i \(-0.256244\pi\)
0.693101 + 0.720840i \(0.256244\pi\)
\(434\) −12.9224 −0.620297
\(435\) 4.70469 0.225573
\(436\) 30.4877 1.46009
\(437\) 4.85705 0.232344
\(438\) −30.3830 −1.45176
\(439\) −19.1983 −0.916286 −0.458143 0.888879i \(-0.651485\pi\)
−0.458143 + 0.888879i \(0.651485\pi\)
\(440\) −0.256585 −0.0122322
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 23.9117 1.13608 0.568040 0.823001i \(-0.307702\pi\)
0.568040 + 0.823001i \(0.307702\pi\)
\(444\) 2.61044 0.123886
\(445\) 11.8648 0.562448
\(446\) −7.88621 −0.373423
\(447\) −2.11348 −0.0999644
\(448\) 12.7147 0.600715
\(449\) 31.8784 1.50444 0.752218 0.658914i \(-0.228984\pi\)
0.752218 + 0.658914i \(0.228984\pi\)
\(450\) 6.62667 0.312384
\(451\) −0.300055 −0.0141290
\(452\) −49.1569 −2.31215
\(453\) −17.2235 −0.809231
\(454\) −3.16582 −0.148579
\(455\) 0 0
\(456\) 2.50686 0.117394
\(457\) 31.4570 1.47149 0.735747 0.677256i \(-0.236831\pi\)
0.735747 + 0.677256i \(0.236831\pi\)
\(458\) −40.0332 −1.87063
\(459\) −5.75421 −0.268584
\(460\) −29.3626 −1.36904
\(461\) 25.1219 1.17004 0.585021 0.811018i \(-0.301086\pi\)
0.585021 + 0.811018i \(0.301086\pi\)
\(462\) 0.130824 0.00608647
\(463\) 20.4492 0.950354 0.475177 0.879890i \(-0.342384\pi\)
0.475177 + 0.879890i \(0.342384\pi\)
\(464\) 1.57539 0.0731359
\(465\) −8.16518 −0.378651
\(466\) −13.3384 −0.617890
\(467\) 22.0746 1.02149 0.510745 0.859732i \(-0.329370\pi\)
0.510745 + 0.859732i \(0.329370\pi\)
\(468\) 0 0
\(469\) 7.80744 0.360514
\(470\) 11.2305 0.518027
\(471\) 20.5730 0.947953
\(472\) 32.0543 1.47542
\(473\) −0.134825 −0.00619928
\(474\) 25.0944 1.15263
\(475\) −2.31534 −0.106235
\(476\) −19.2356 −0.881663
\(477\) −9.52747 −0.436233
\(478\) −6.48956 −0.296825
\(479\) 12.1574 0.555486 0.277743 0.960655i \(-0.410414\pi\)
0.277743 + 0.960655i \(0.410414\pi\)
\(480\) 7.41591 0.338488
\(481\) 0 0
\(482\) −17.4638 −0.795453
\(483\) 6.01403 0.273648
\(484\) −36.7609 −1.67095
\(485\) 5.74037 0.260657
\(486\) 2.31147 0.104850
\(487\) 18.6677 0.845914 0.422957 0.906150i \(-0.360992\pi\)
0.422957 + 0.906150i \(0.360992\pi\)
\(488\) −27.5710 −1.24808
\(489\) −8.77011 −0.396598
\(490\) 3.37595 0.152510
\(491\) 18.8532 0.850833 0.425416 0.904998i \(-0.360128\pi\)
0.425416 + 0.904998i \(0.360128\pi\)
\(492\) −17.7224 −0.798986
\(493\) 18.5357 0.834805
\(494\) 0 0
\(495\) 0.0826623 0.00371539
\(496\) −2.73416 −0.122767
\(497\) −11.4706 −0.514528
\(498\) 17.8039 0.797813
\(499\) 23.7688 1.06404 0.532018 0.846733i \(-0.321434\pi\)
0.532018 + 0.846733i \(0.321434\pi\)
\(500\) 38.4088 1.71769
\(501\) 16.9542 0.757456
\(502\) −60.6035 −2.70487
\(503\) 8.31234 0.370629 0.185314 0.982679i \(-0.440670\pi\)
0.185314 + 0.982679i \(0.440670\pi\)
\(504\) 3.10401 0.138264
\(505\) −9.87049 −0.439231
\(506\) 0.786778 0.0349765
\(507\) 0 0
\(508\) −35.4012 −1.57067
\(509\) −8.75231 −0.387939 −0.193970 0.981008i \(-0.562136\pi\)
−0.193970 + 0.981008i \(0.562136\pi\)
\(510\) −19.4260 −0.860196
\(511\) 13.1445 0.581478
\(512\) 5.51939 0.243925
\(513\) −0.807619 −0.0356573
\(514\) 8.27918 0.365179
\(515\) 18.1226 0.798577
\(516\) −7.96330 −0.350565
\(517\) −0.188280 −0.00828053
\(518\) −1.80501 −0.0793078
\(519\) −1.91338 −0.0839882
\(520\) 0 0
\(521\) −32.1915 −1.41033 −0.705167 0.709041i \(-0.749128\pi\)
−0.705167 + 0.709041i \(0.749128\pi\)
\(522\) −7.44578 −0.325893
\(523\) −13.3302 −0.582891 −0.291446 0.956587i \(-0.594136\pi\)
−0.291446 + 0.956587i \(0.594136\pi\)
\(524\) −31.1280 −1.35983
\(525\) −2.86687 −0.125120
\(526\) −61.8548 −2.69700
\(527\) −32.1694 −1.40132
\(528\) 0.0276800 0.00120462
\(529\) 13.1686 0.572548
\(530\) −32.1643 −1.39713
\(531\) −10.3267 −0.448143
\(532\) −2.69977 −0.117050
\(533\) 0 0
\(534\) −18.7776 −0.812588
\(535\) −26.5496 −1.14784
\(536\) 24.2344 1.04677
\(537\) 26.1240 1.12733
\(538\) −34.0232 −1.46685
\(539\) −0.0565977 −0.00243784
\(540\) 4.88235 0.210103
\(541\) 22.2023 0.954553 0.477277 0.878753i \(-0.341624\pi\)
0.477277 + 0.878753i \(0.341624\pi\)
\(542\) 30.4821 1.30932
\(543\) 1.98010 0.0849743
\(544\) 29.2174 1.25269
\(545\) −13.3203 −0.570577
\(546\) 0 0
\(547\) 36.3118 1.55258 0.776289 0.630377i \(-0.217100\pi\)
0.776289 + 0.630377i \(0.217100\pi\)
\(548\) −13.7143 −0.585847
\(549\) 8.88239 0.379091
\(550\) −0.375054 −0.0159924
\(551\) 2.60153 0.110829
\(552\) 18.6676 0.794547
\(553\) −10.8565 −0.461666
\(554\) −49.8644 −2.11854
\(555\) −1.14052 −0.0484123
\(556\) 54.4066 2.30736
\(557\) −42.7664 −1.81207 −0.906036 0.423200i \(-0.860907\pi\)
−0.906036 + 0.423200i \(0.860907\pi\)
\(558\) 12.9224 0.547051
\(559\) 0 0
\(560\) 0.714292 0.0301843
\(561\) 0.325675 0.0137500
\(562\) −0.431054 −0.0181829
\(563\) −13.8742 −0.584728 −0.292364 0.956307i \(-0.594442\pi\)
−0.292364 + 0.956307i \(0.594442\pi\)
\(564\) −11.1205 −0.468258
\(565\) 21.4770 0.903543
\(566\) 32.4087 1.36224
\(567\) −1.00000 −0.0419961
\(568\) −35.6050 −1.49395
\(569\) 7.44608 0.312156 0.156078 0.987745i \(-0.450115\pi\)
0.156078 + 0.987745i \(0.450115\pi\)
\(570\) −2.72649 −0.114200
\(571\) 24.7091 1.03404 0.517021 0.855973i \(-0.327041\pi\)
0.517021 + 0.855973i \(0.327041\pi\)
\(572\) 0 0
\(573\) 20.6851 0.864131
\(574\) 12.2543 0.511486
\(575\) −17.2414 −0.719018
\(576\) −12.7147 −0.529781
\(577\) 26.2593 1.09319 0.546595 0.837397i \(-0.315924\pi\)
0.546595 + 0.837397i \(0.315924\pi\)
\(578\) −37.2400 −1.54898
\(579\) 2.88929 0.120075
\(580\) −15.7272 −0.653037
\(581\) −7.70243 −0.319551
\(582\) −9.08487 −0.376580
\(583\) 0.539233 0.0223328
\(584\) 40.8006 1.68834
\(585\) 0 0
\(586\) −36.7135 −1.51662
\(587\) 36.7338 1.51617 0.758084 0.652157i \(-0.226136\pi\)
0.758084 + 0.652157i \(0.226136\pi\)
\(588\) −3.34288 −0.137858
\(589\) −4.51506 −0.186040
\(590\) −34.8626 −1.43527
\(591\) 3.01713 0.124108
\(592\) −0.381909 −0.0156964
\(593\) −8.94989 −0.367528 −0.183764 0.982970i \(-0.558828\pi\)
−0.183764 + 0.982970i \(0.558828\pi\)
\(594\) −0.130824 −0.00536776
\(595\) 8.40417 0.344537
\(596\) 7.06511 0.289398
\(597\) −24.5542 −1.00494
\(598\) 0 0
\(599\) −32.4529 −1.32599 −0.662995 0.748624i \(-0.730715\pi\)
−0.662995 + 0.748624i \(0.730715\pi\)
\(600\) −8.89879 −0.363292
\(601\) −30.4411 −1.24172 −0.620859 0.783922i \(-0.713216\pi\)
−0.620859 + 0.783922i \(0.713216\pi\)
\(602\) 5.50631 0.224420
\(603\) −7.80744 −0.317943
\(604\) 57.5760 2.34273
\(605\) 16.0611 0.652976
\(606\) 15.6213 0.634572
\(607\) −18.0074 −0.730899 −0.365449 0.930831i \(-0.619085\pi\)
−0.365449 + 0.930831i \(0.619085\pi\)
\(608\) 4.10074 0.166307
\(609\) 3.22124 0.130531
\(610\) 29.9865 1.21412
\(611\) 0 0
\(612\) 19.2356 0.777554
\(613\) −43.6064 −1.76125 −0.880623 0.473817i \(-0.842876\pi\)
−0.880623 + 0.473817i \(0.842876\pi\)
\(614\) 28.6607 1.15665
\(615\) 7.74302 0.312229
\(616\) −0.175680 −0.00707834
\(617\) −11.4509 −0.460997 −0.230499 0.973073i \(-0.574036\pi\)
−0.230499 + 0.973073i \(0.574036\pi\)
\(618\) −28.6813 −1.15373
\(619\) −33.0974 −1.33030 −0.665148 0.746712i \(-0.731631\pi\)
−0.665148 + 0.746712i \(0.731631\pi\)
\(620\) 27.2952 1.09620
\(621\) −6.01403 −0.241335
\(622\) −16.5876 −0.665103
\(623\) 8.12369 0.325469
\(624\) 0 0
\(625\) −2.44672 −0.0978689
\(626\) 50.5292 2.01955
\(627\) 0.0457094 0.00182546
\(628\) −68.7729 −2.74434
\(629\) −4.49344 −0.179165
\(630\) −3.37595 −0.134501
\(631\) −5.34538 −0.212796 −0.106398 0.994324i \(-0.533932\pi\)
−0.106398 + 0.994324i \(0.533932\pi\)
\(632\) −33.6987 −1.34046
\(633\) −15.2596 −0.606517
\(634\) −60.7315 −2.41196
\(635\) 15.4670 0.613789
\(636\) 31.8492 1.26290
\(637\) 0 0
\(638\) 0.421414 0.0166839
\(639\) 11.4706 0.453771
\(640\) −28.0926 −1.11046
\(641\) −18.3832 −0.726091 −0.363046 0.931771i \(-0.618263\pi\)
−0.363046 + 0.931771i \(0.618263\pi\)
\(642\) 42.0181 1.65832
\(643\) −3.77097 −0.148712 −0.0743562 0.997232i \(-0.523690\pi\)
−0.0743562 + 0.997232i \(0.523690\pi\)
\(644\) −20.1042 −0.792215
\(645\) 3.47922 0.136994
\(646\) −10.7419 −0.422634
\(647\) −1.95293 −0.0767775 −0.0383888 0.999263i \(-0.512223\pi\)
−0.0383888 + 0.999263i \(0.512223\pi\)
\(648\) −3.10401 −0.121937
\(649\) 0.584470 0.0229425
\(650\) 0 0
\(651\) −5.59058 −0.219112
\(652\) 29.3174 1.14816
\(653\) 21.9347 0.858372 0.429186 0.903216i \(-0.358801\pi\)
0.429186 + 0.903216i \(0.358801\pi\)
\(654\) 21.0810 0.824333
\(655\) 13.6000 0.531396
\(656\) 2.59280 0.101232
\(657\) −13.1445 −0.512815
\(658\) 7.68939 0.299764
\(659\) 34.8515 1.35762 0.678812 0.734312i \(-0.262495\pi\)
0.678812 + 0.734312i \(0.262495\pi\)
\(660\) −0.276330 −0.0107561
\(661\) −30.3342 −1.17986 −0.589931 0.807454i \(-0.700845\pi\)
−0.589931 + 0.807454i \(0.700845\pi\)
\(662\) −63.2966 −2.46009
\(663\) 0 0
\(664\) −23.9084 −0.927827
\(665\) 1.17955 0.0457409
\(666\) 1.80501 0.0699429
\(667\) 19.3726 0.750111
\(668\) −56.6756 −2.19285
\(669\) −3.41178 −0.131907
\(670\) −26.3575 −1.01828
\(671\) −0.502723 −0.0194074
\(672\) 5.07756 0.195871
\(673\) 42.8800 1.65290 0.826451 0.563009i \(-0.190356\pi\)
0.826451 + 0.563009i \(0.190356\pi\)
\(674\) 46.3808 1.78652
\(675\) 2.86687 0.110346
\(676\) 0 0
\(677\) −14.2890 −0.549171 −0.274586 0.961563i \(-0.588541\pi\)
−0.274586 + 0.961563i \(0.588541\pi\)
\(678\) −33.9900 −1.30538
\(679\) 3.93035 0.150833
\(680\) 26.0866 1.00038
\(681\) −1.36962 −0.0524838
\(682\) −0.731381 −0.0280060
\(683\) 24.5455 0.939209 0.469604 0.882877i \(-0.344397\pi\)
0.469604 + 0.882877i \(0.344397\pi\)
\(684\) 2.69977 0.103228
\(685\) 5.99188 0.228938
\(686\) 2.31147 0.0882522
\(687\) −17.3194 −0.660776
\(688\) 1.16504 0.0444166
\(689\) 0 0
\(690\) −20.3031 −0.772926
\(691\) 27.7763 1.05666 0.528331 0.849039i \(-0.322818\pi\)
0.528331 + 0.849039i \(0.322818\pi\)
\(692\) 6.39620 0.243147
\(693\) 0.0565977 0.00214997
\(694\) −40.8561 −1.55087
\(695\) −23.7706 −0.901671
\(696\) 9.99875 0.379002
\(697\) 30.5062 1.15550
\(698\) −27.3054 −1.03352
\(699\) −5.77054 −0.218262
\(700\) 9.58358 0.362225
\(701\) 37.2216 1.40584 0.702921 0.711268i \(-0.251879\pi\)
0.702921 + 0.711268i \(0.251879\pi\)
\(702\) 0 0
\(703\) −0.630667 −0.0237860
\(704\) 0.719625 0.0271219
\(705\) 4.85863 0.182986
\(706\) −66.8743 −2.51685
\(707\) −6.75818 −0.254168
\(708\) 34.5210 1.29738
\(709\) −40.3434 −1.51513 −0.757564 0.652760i \(-0.773611\pi\)
−0.757564 + 0.652760i \(0.773611\pi\)
\(710\) 38.7243 1.45330
\(711\) 10.8565 0.407151
\(712\) 25.2160 0.945010
\(713\) −33.6220 −1.25915
\(714\) −13.3007 −0.497765
\(715\) 0 0
\(716\) −87.3293 −3.26365
\(717\) −2.80755 −0.104850
\(718\) 3.92347 0.146423
\(719\) −5.37519 −0.200461 −0.100230 0.994964i \(-0.531958\pi\)
−0.100230 + 0.994964i \(0.531958\pi\)
\(720\) −0.714292 −0.0266201
\(721\) 12.4083 0.462108
\(722\) 42.4102 1.57834
\(723\) −7.55528 −0.280984
\(724\) −6.61924 −0.246002
\(725\) −9.23486 −0.342974
\(726\) −25.4187 −0.943377
\(727\) −9.42472 −0.349544 −0.174772 0.984609i \(-0.555919\pi\)
−0.174772 + 0.984609i \(0.555919\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −44.3752 −1.64240
\(731\) 13.7075 0.506991
\(732\) −29.6927 −1.09747
\(733\) 33.3006 1.22999 0.614994 0.788532i \(-0.289159\pi\)
0.614994 + 0.788532i \(0.289159\pi\)
\(734\) 71.5983 2.64274
\(735\) 1.46052 0.0538723
\(736\) 30.5366 1.12560
\(737\) 0.441883 0.0162770
\(738\) −12.2543 −0.451088
\(739\) 34.6898 1.27608 0.638042 0.770001i \(-0.279744\pi\)
0.638042 + 0.770001i \(0.279744\pi\)
\(740\) 3.81261 0.140154
\(741\) 0 0
\(742\) −22.0224 −0.808469
\(743\) −29.0170 −1.06453 −0.532264 0.846578i \(-0.678659\pi\)
−0.532264 + 0.846578i \(0.678659\pi\)
\(744\) −17.3532 −0.636200
\(745\) −3.08679 −0.113091
\(746\) 24.6881 0.903895
\(747\) 7.70243 0.281817
\(748\) −1.08869 −0.0398065
\(749\) −18.1781 −0.664214
\(750\) 26.5582 0.969767
\(751\) −22.3606 −0.815949 −0.407974 0.912993i \(-0.633765\pi\)
−0.407974 + 0.912993i \(0.633765\pi\)
\(752\) 1.62694 0.0593284
\(753\) −26.2186 −0.955460
\(754\) 0 0
\(755\) −25.1553 −0.915497
\(756\) 3.34288 0.121579
\(757\) −41.1339 −1.49504 −0.747519 0.664240i \(-0.768755\pi\)
−0.747519 + 0.664240i \(0.768755\pi\)
\(758\) −65.0102 −2.36128
\(759\) 0.340380 0.0123550
\(760\) 3.66133 0.132810
\(761\) −34.0410 −1.23398 −0.616992 0.786969i \(-0.711649\pi\)
−0.616992 + 0.786969i \(0.711649\pi\)
\(762\) −24.4785 −0.886763
\(763\) −9.12019 −0.330173
\(764\) −69.1476 −2.50167
\(765\) −8.40417 −0.303853
\(766\) 28.3076 1.02280
\(767\) 0 0
\(768\) 19.0306 0.686707
\(769\) −50.1326 −1.80783 −0.903914 0.427714i \(-0.859319\pi\)
−0.903914 + 0.427714i \(0.859319\pi\)
\(770\) 0.191071 0.00688573
\(771\) 3.58179 0.128995
\(772\) −9.65853 −0.347618
\(773\) −10.6809 −0.384167 −0.192083 0.981379i \(-0.561524\pi\)
−0.192083 + 0.981379i \(0.561524\pi\)
\(774\) −5.50631 −0.197920
\(775\) 16.0275 0.575724
\(776\) 12.1998 0.437949
\(777\) −0.780896 −0.0280145
\(778\) 31.5358 1.13061
\(779\) 4.28162 0.153405
\(780\) 0 0
\(781\) −0.649211 −0.0232306
\(782\) −79.9907 −2.86046
\(783\) −3.22124 −0.115118
\(784\) 0.489065 0.0174666
\(785\) 30.0473 1.07244
\(786\) −21.5237 −0.767727
\(787\) −8.44505 −0.301033 −0.150517 0.988607i \(-0.548094\pi\)
−0.150517 + 0.988607i \(0.548094\pi\)
\(788\) −10.0859 −0.359295
\(789\) −26.7600 −0.952681
\(790\) 36.6510 1.30399
\(791\) 14.7050 0.522849
\(792\) 0.175680 0.00624251
\(793\) 0 0
\(794\) 28.7488 1.02026
\(795\) −13.9151 −0.493518
\(796\) 82.0817 2.90931
\(797\) −8.37296 −0.296586 −0.148293 0.988944i \(-0.547378\pi\)
−0.148293 + 0.988944i \(0.547378\pi\)
\(798\) −1.86679 −0.0660835
\(799\) 19.1421 0.677201
\(800\) −14.5567 −0.514657
\(801\) −8.12369 −0.287036
\(802\) −57.8608 −2.04314
\(803\) 0.743948 0.0262534
\(804\) 26.0993 0.920451
\(805\) 8.78364 0.309583
\(806\) 0 0
\(807\) −14.7193 −0.518145
\(808\) −20.9775 −0.737985
\(809\) −4.04870 −0.142345 −0.0711723 0.997464i \(-0.522674\pi\)
−0.0711723 + 0.997464i \(0.522674\pi\)
\(810\) 3.37595 0.118619
\(811\) −40.7122 −1.42960 −0.714800 0.699329i \(-0.753482\pi\)
−0.714800 + 0.699329i \(0.753482\pi\)
\(812\) −10.7682 −0.377889
\(813\) 13.1874 0.462501
\(814\) −0.102160 −0.00358069
\(815\) −12.8090 −0.448678
\(816\) −2.81419 −0.0985162
\(817\) 1.92389 0.0673083
\(818\) −81.7035 −2.85669
\(819\) 0 0
\(820\) −25.8840 −0.903907
\(821\) −15.5618 −0.543110 −0.271555 0.962423i \(-0.587538\pi\)
−0.271555 + 0.962423i \(0.587538\pi\)
\(822\) −9.48291 −0.330755
\(823\) −4.81985 −0.168009 −0.0840046 0.996465i \(-0.526771\pi\)
−0.0840046 + 0.996465i \(0.526771\pi\)
\(824\) 38.5154 1.34175
\(825\) −0.162258 −0.00564910
\(826\) −23.8699 −0.830541
\(827\) −3.38418 −0.117680 −0.0588398 0.998267i \(-0.518740\pi\)
−0.0588398 + 0.998267i \(0.518740\pi\)
\(828\) 20.1042 0.698668
\(829\) −14.4519 −0.501937 −0.250968 0.967995i \(-0.580749\pi\)
−0.250968 + 0.967995i \(0.580749\pi\)
\(830\) 26.0031 0.902579
\(831\) −21.5726 −0.748347
\(832\) 0 0
\(833\) 5.75421 0.199372
\(834\) 37.6200 1.30268
\(835\) 24.7620 0.856923
\(836\) −0.152801 −0.00528473
\(837\) 5.59058 0.193239
\(838\) −60.3257 −2.08392
\(839\) −29.5887 −1.02152 −0.510758 0.859725i \(-0.670635\pi\)
−0.510758 + 0.859725i \(0.670635\pi\)
\(840\) 4.53348 0.156420
\(841\) −18.6236 −0.642194
\(842\) 1.07555 0.0370657
\(843\) −0.186485 −0.00642289
\(844\) 51.0111 1.75587
\(845\) 0 0
\(846\) −7.68939 −0.264367
\(847\) 10.9968 0.377854
\(848\) −4.65956 −0.160010
\(849\) 14.0208 0.481194
\(850\) 38.1313 1.30789
\(851\) −4.69633 −0.160988
\(852\) −38.3449 −1.31367
\(853\) −30.7580 −1.05313 −0.526567 0.850134i \(-0.676521\pi\)
−0.526567 + 0.850134i \(0.676521\pi\)
\(854\) 20.5313 0.702568
\(855\) −1.17955 −0.0403397
\(856\) −56.4251 −1.92857
\(857\) −15.7106 −0.536663 −0.268331 0.963327i \(-0.586472\pi\)
−0.268331 + 0.963327i \(0.586472\pi\)
\(858\) 0 0
\(859\) −23.2361 −0.792807 −0.396403 0.918076i \(-0.629742\pi\)
−0.396403 + 0.918076i \(0.629742\pi\)
\(860\) −11.6306 −0.396600
\(861\) 5.30154 0.180676
\(862\) −62.0556 −2.11362
\(863\) −29.7433 −1.01247 −0.506236 0.862395i \(-0.668964\pi\)
−0.506236 + 0.862395i \(0.668964\pi\)
\(864\) −5.07756 −0.172742
\(865\) −2.79454 −0.0950174
\(866\) −66.6743 −2.26568
\(867\) −16.1110 −0.547158
\(868\) 18.6886 0.634333
\(869\) −0.614453 −0.0208439
\(870\) −10.8747 −0.368688
\(871\) 0 0
\(872\) −28.3092 −0.958670
\(873\) −3.93035 −0.133022
\(874\) −11.2269 −0.379756
\(875\) −11.4898 −0.388425
\(876\) 43.9404 1.48461
\(877\) 12.7398 0.430193 0.215097 0.976593i \(-0.430993\pi\)
0.215097 + 0.976593i \(0.430993\pi\)
\(878\) 44.3763 1.49763
\(879\) −15.8832 −0.535727
\(880\) 0.0404273 0.00136280
\(881\) 10.9904 0.370277 0.185139 0.982712i \(-0.440727\pi\)
0.185139 + 0.982712i \(0.440727\pi\)
\(882\) −2.31147 −0.0778311
\(883\) 8.60222 0.289488 0.144744 0.989469i \(-0.453764\pi\)
0.144744 + 0.989469i \(0.453764\pi\)
\(884\) 0 0
\(885\) −15.0825 −0.506991
\(886\) −55.2711 −1.85687
\(887\) 21.0197 0.705773 0.352886 0.935666i \(-0.385200\pi\)
0.352886 + 0.935666i \(0.385200\pi\)
\(888\) −2.42391 −0.0813410
\(889\) 10.5900 0.355178
\(890\) −27.4252 −0.919295
\(891\) −0.0565977 −0.00189609
\(892\) 11.4052 0.381873
\(893\) 2.68665 0.0899054
\(894\) 4.88525 0.163387
\(895\) 38.1548 1.27537
\(896\) −19.2346 −0.642582
\(897\) 0 0
\(898\) −73.6859 −2.45893
\(899\) −18.0086 −0.600620
\(900\) −9.58358 −0.319453
\(901\) −54.8231 −1.82642
\(902\) 0.693566 0.0230932
\(903\) 2.38217 0.0792737
\(904\) 45.6444 1.51811
\(905\) 2.89199 0.0961329
\(906\) 39.8115 1.32265
\(907\) 4.64057 0.154087 0.0770437 0.997028i \(-0.475452\pi\)
0.0770437 + 0.997028i \(0.475452\pi\)
\(908\) 4.57845 0.151941
\(909\) 6.75818 0.224155
\(910\) 0 0
\(911\) 32.2392 1.06813 0.534067 0.845442i \(-0.320663\pi\)
0.534067 + 0.845442i \(0.320663\pi\)
\(912\) −0.394979 −0.0130790
\(913\) −0.435940 −0.0144275
\(914\) −72.7117 −2.40509
\(915\) 12.9729 0.428872
\(916\) 57.8965 1.91296
\(917\) 9.31173 0.307500
\(918\) 13.3007 0.438988
\(919\) 21.0489 0.694339 0.347169 0.937802i \(-0.387143\pi\)
0.347169 + 0.937802i \(0.387143\pi\)
\(920\) 27.2645 0.898885
\(921\) 12.3994 0.408573
\(922\) −58.0683 −1.91238
\(923\) 0 0
\(924\) −0.189199 −0.00622419
\(925\) 2.23873 0.0736088
\(926\) −47.2676 −1.55331
\(927\) −12.4083 −0.407541
\(928\) 16.3560 0.536913
\(929\) 36.3949 1.19408 0.597038 0.802213i \(-0.296344\pi\)
0.597038 + 0.802213i \(0.296344\pi\)
\(930\) 18.8735 0.618888
\(931\) 0.807619 0.0264687
\(932\) 19.2902 0.631871
\(933\) −7.17624 −0.234939
\(934\) −51.0246 −1.66958
\(935\) 0.475657 0.0155556
\(936\) 0 0
\(937\) 23.6753 0.773438 0.386719 0.922198i \(-0.373608\pi\)
0.386719 + 0.922198i \(0.373608\pi\)
\(938\) −18.0466 −0.589243
\(939\) 21.8602 0.713381
\(940\) −16.2418 −0.529748
\(941\) 15.2440 0.496940 0.248470 0.968640i \(-0.420072\pi\)
0.248470 + 0.968640i \(0.420072\pi\)
\(942\) −47.5537 −1.54938
\(943\) 31.8836 1.03827
\(944\) −5.05045 −0.164378
\(945\) −1.46052 −0.0475109
\(946\) 0.311644 0.0101324
\(947\) 5.38308 0.174926 0.0874632 0.996168i \(-0.472124\pi\)
0.0874632 + 0.996168i \(0.472124\pi\)
\(948\) −36.2919 −1.17871
\(949\) 0 0
\(950\) 5.35183 0.173636
\(951\) −26.2740 −0.851994
\(952\) 17.8611 0.578883
\(953\) 20.2342 0.655451 0.327725 0.944773i \(-0.393718\pi\)
0.327725 + 0.944773i \(0.393718\pi\)
\(954\) 22.0224 0.713003
\(955\) 30.2110 0.977606
\(956\) 9.38529 0.303542
\(957\) 0.182315 0.00589339
\(958\) −28.1014 −0.907916
\(959\) 4.10255 0.132478
\(960\) −18.5702 −0.599351
\(961\) 0.254620 0.00821356
\(962\) 0 0
\(963\) 18.1781 0.585782
\(964\) 25.2564 0.813453
\(965\) 4.21988 0.135843
\(966\) −13.9012 −0.447265
\(967\) 19.0150 0.611482 0.305741 0.952115i \(-0.401096\pi\)
0.305741 + 0.952115i \(0.401096\pi\)
\(968\) 34.1342 1.09711
\(969\) −4.64722 −0.149290
\(970\) −13.2687 −0.426031
\(971\) −25.4007 −0.815148 −0.407574 0.913172i \(-0.633625\pi\)
−0.407574 + 0.913172i \(0.633625\pi\)
\(972\) −3.34288 −0.107223
\(973\) −16.2754 −0.521765
\(974\) −43.1497 −1.38261
\(975\) 0 0
\(976\) 4.34407 0.139050
\(977\) −18.9933 −0.607650 −0.303825 0.952728i \(-0.598264\pi\)
−0.303825 + 0.952728i \(0.598264\pi\)
\(978\) 20.2718 0.648221
\(979\) 0.459782 0.0146947
\(980\) −4.88235 −0.155961
\(981\) 9.12019 0.291185
\(982\) −43.5785 −1.39065
\(983\) −40.4777 −1.29104 −0.645519 0.763744i \(-0.723359\pi\)
−0.645519 + 0.763744i \(0.723359\pi\)
\(984\) 16.4560 0.524599
\(985\) 4.40659 0.140406
\(986\) −42.8446 −1.36445
\(987\) 3.32663 0.105888
\(988\) 0 0
\(989\) 14.3265 0.455555
\(990\) −0.191071 −0.00607264
\(991\) 54.2021 1.72179 0.860893 0.508786i \(-0.169906\pi\)
0.860893 + 0.508786i \(0.169906\pi\)
\(992\) −28.3865 −0.901274
\(993\) −27.3837 −0.868997
\(994\) 26.5140 0.840972
\(995\) −35.8620 −1.13690
\(996\) −25.7483 −0.815865
\(997\) −36.0609 −1.14206 −0.571029 0.820930i \(-0.693456\pi\)
−0.571029 + 0.820930i \(0.693456\pi\)
\(998\) −54.9407 −1.73912
\(999\) 0.780896 0.0247064
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 3549.2.a.bf.1.1 yes 9
13.12 even 2 3549.2.a.be.1.9 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.be.1.9 9 13.12 even 2
3549.2.a.bf.1.1 yes 9 1.1 even 1 trivial