Properties

Label 6017.2.a.f.1.1
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.76609 q^{2} +1.72204 q^{3} +5.65124 q^{4} +1.59310 q^{5} -4.76331 q^{6} +4.82706 q^{7} -10.0996 q^{8} -0.0345853 q^{9} +O(q^{10})\) \(q-2.76609 q^{2} +1.72204 q^{3} +5.65124 q^{4} +1.59310 q^{5} -4.76331 q^{6} +4.82706 q^{7} -10.0996 q^{8} -0.0345853 q^{9} -4.40666 q^{10} -1.00000 q^{11} +9.73165 q^{12} -4.55724 q^{13} -13.3521 q^{14} +2.74338 q^{15} +16.6340 q^{16} -7.55927 q^{17} +0.0956660 q^{18} +3.61389 q^{19} +9.00300 q^{20} +8.31238 q^{21} +2.76609 q^{22} +7.11636 q^{23} -17.3920 q^{24} -2.46203 q^{25} +12.6057 q^{26} -5.22567 q^{27} +27.2789 q^{28} +4.19876 q^{29} -7.58843 q^{30} +5.25576 q^{31} -25.8119 q^{32} -1.72204 q^{33} +20.9096 q^{34} +7.69000 q^{35} -0.195450 q^{36} +3.75063 q^{37} -9.99634 q^{38} -7.84774 q^{39} -16.0898 q^{40} -4.11901 q^{41} -22.9928 q^{42} +7.79370 q^{43} -5.65124 q^{44} -0.0550979 q^{45} -19.6845 q^{46} +7.98049 q^{47} +28.6444 q^{48} +16.3005 q^{49} +6.81019 q^{50} -13.0174 q^{51} -25.7540 q^{52} +7.83066 q^{53} +14.4547 q^{54} -1.59310 q^{55} -48.7516 q^{56} +6.22326 q^{57} -11.6141 q^{58} -3.96160 q^{59} +15.5035 q^{60} -9.41072 q^{61} -14.5379 q^{62} -0.166945 q^{63} +38.1299 q^{64} -7.26014 q^{65} +4.76331 q^{66} -6.42278 q^{67} -42.7193 q^{68} +12.2546 q^{69} -21.2712 q^{70} -5.79611 q^{71} +0.349299 q^{72} +4.61959 q^{73} -10.3746 q^{74} -4.23971 q^{75} +20.4230 q^{76} -4.82706 q^{77} +21.7075 q^{78} +11.8018 q^{79} +26.4997 q^{80} -8.89505 q^{81} +11.3935 q^{82} +13.1657 q^{83} +46.9753 q^{84} -12.0427 q^{85} -21.5580 q^{86} +7.23042 q^{87} +10.0996 q^{88} +2.28499 q^{89} +0.152406 q^{90} -21.9981 q^{91} +40.2163 q^{92} +9.05062 q^{93} -22.0747 q^{94} +5.75730 q^{95} -44.4490 q^{96} -4.21485 q^{97} -45.0887 q^{98} +0.0345853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76609 −1.95592 −0.977960 0.208794i \(-0.933046\pi\)
−0.977960 + 0.208794i \(0.933046\pi\)
\(3\) 1.72204 0.994219 0.497110 0.867688i \(-0.334395\pi\)
0.497110 + 0.867688i \(0.334395\pi\)
\(4\) 5.65124 2.82562
\(5\) 1.59310 0.712457 0.356228 0.934399i \(-0.384063\pi\)
0.356228 + 0.934399i \(0.384063\pi\)
\(6\) −4.76331 −1.94461
\(7\) 4.82706 1.82446 0.912229 0.409681i \(-0.134360\pi\)
0.912229 + 0.409681i \(0.134360\pi\)
\(8\) −10.0996 −3.57076
\(9\) −0.0345853 −0.0115284
\(10\) −4.40666 −1.39351
\(11\) −1.00000 −0.301511
\(12\) 9.73165 2.80929
\(13\) −4.55724 −1.26395 −0.631975 0.774989i \(-0.717756\pi\)
−0.631975 + 0.774989i \(0.717756\pi\)
\(14\) −13.3521 −3.56849
\(15\) 2.74338 0.708338
\(16\) 16.6340 4.15851
\(17\) −7.55927 −1.83339 −0.916696 0.399584i \(-0.869154\pi\)
−0.916696 + 0.399584i \(0.869154\pi\)
\(18\) 0.0956660 0.0225487
\(19\) 3.61389 0.829084 0.414542 0.910030i \(-0.363942\pi\)
0.414542 + 0.910030i \(0.363942\pi\)
\(20\) 9.00300 2.01313
\(21\) 8.31238 1.81391
\(22\) 2.76609 0.589732
\(23\) 7.11636 1.48386 0.741932 0.670475i \(-0.233910\pi\)
0.741932 + 0.670475i \(0.233910\pi\)
\(24\) −17.3920 −3.55012
\(25\) −2.46203 −0.492406
\(26\) 12.6057 2.47218
\(27\) −5.22567 −1.00568
\(28\) 27.2789 5.15522
\(29\) 4.19876 0.779690 0.389845 0.920880i \(-0.372529\pi\)
0.389845 + 0.920880i \(0.372529\pi\)
\(30\) −7.58843 −1.38545
\(31\) 5.25576 0.943962 0.471981 0.881609i \(-0.343539\pi\)
0.471981 + 0.881609i \(0.343539\pi\)
\(32\) −25.8119 −4.56294
\(33\) −1.72204 −0.299768
\(34\) 20.9096 3.58597
\(35\) 7.69000 1.29985
\(36\) −0.195450 −0.0325750
\(37\) 3.75063 0.616600 0.308300 0.951289i \(-0.400240\pi\)
0.308300 + 0.951289i \(0.400240\pi\)
\(38\) −9.99634 −1.62162
\(39\) −7.84774 −1.25664
\(40\) −16.0898 −2.54401
\(41\) −4.11901 −0.643281 −0.321641 0.946862i \(-0.604234\pi\)
−0.321641 + 0.946862i \(0.604234\pi\)
\(42\) −22.9928 −3.54786
\(43\) 7.79370 1.18853 0.594264 0.804270i \(-0.297444\pi\)
0.594264 + 0.804270i \(0.297444\pi\)
\(44\) −5.65124 −0.851956
\(45\) −0.0550979 −0.00821351
\(46\) −19.6845 −2.90232
\(47\) 7.98049 1.16407 0.582037 0.813162i \(-0.302256\pi\)
0.582037 + 0.813162i \(0.302256\pi\)
\(48\) 28.6444 4.13447
\(49\) 16.3005 2.32865
\(50\) 6.81019 0.963106
\(51\) −13.0174 −1.82279
\(52\) −25.7540 −3.57144
\(53\) 7.83066 1.07562 0.537812 0.843065i \(-0.319251\pi\)
0.537812 + 0.843065i \(0.319251\pi\)
\(54\) 14.4547 1.96703
\(55\) −1.59310 −0.214814
\(56\) −48.7516 −6.51471
\(57\) 6.22326 0.824291
\(58\) −11.6141 −1.52501
\(59\) −3.96160 −0.515756 −0.257878 0.966177i \(-0.583023\pi\)
−0.257878 + 0.966177i \(0.583023\pi\)
\(60\) 15.5035 2.00149
\(61\) −9.41072 −1.20492 −0.602460 0.798149i \(-0.705813\pi\)
−0.602460 + 0.798149i \(0.705813\pi\)
\(62\) −14.5379 −1.84631
\(63\) −0.166945 −0.0210331
\(64\) 38.1299 4.76623
\(65\) −7.26014 −0.900510
\(66\) 4.76331 0.586323
\(67\) −6.42278 −0.784668 −0.392334 0.919823i \(-0.628332\pi\)
−0.392334 + 0.919823i \(0.628332\pi\)
\(68\) −42.7193 −5.18047
\(69\) 12.2546 1.47529
\(70\) −21.2712 −2.54240
\(71\) −5.79611 −0.687872 −0.343936 0.938993i \(-0.611760\pi\)
−0.343936 + 0.938993i \(0.611760\pi\)
\(72\) 0.349299 0.0411653
\(73\) 4.61959 0.540682 0.270341 0.962765i \(-0.412864\pi\)
0.270341 + 0.962765i \(0.412864\pi\)
\(74\) −10.3746 −1.20602
\(75\) −4.23971 −0.489559
\(76\) 20.4230 2.34268
\(77\) −4.82706 −0.550095
\(78\) 21.7075 2.45789
\(79\) 11.8018 1.32780 0.663902 0.747820i \(-0.268899\pi\)
0.663902 + 0.747820i \(0.268899\pi\)
\(80\) 26.4997 2.96276
\(81\) −8.89505 −0.988339
\(82\) 11.3935 1.25821
\(83\) 13.1657 1.44513 0.722563 0.691305i \(-0.242964\pi\)
0.722563 + 0.691305i \(0.242964\pi\)
\(84\) 46.9753 5.12542
\(85\) −12.0427 −1.30621
\(86\) −21.5580 −2.32466
\(87\) 7.23042 0.775183
\(88\) 10.0996 1.07663
\(89\) 2.28499 0.242208 0.121104 0.992640i \(-0.461356\pi\)
0.121104 + 0.992640i \(0.461356\pi\)
\(90\) 0.152406 0.0160650
\(91\) −21.9981 −2.30602
\(92\) 40.2163 4.19284
\(93\) 9.05062 0.938505
\(94\) −22.0747 −2.27684
\(95\) 5.75730 0.590686
\(96\) −44.4490 −4.53656
\(97\) −4.21485 −0.427953 −0.213977 0.976839i \(-0.568642\pi\)
−0.213977 + 0.976839i \(0.568642\pi\)
\(98\) −45.0887 −4.55464
\(99\) 0.0345853 0.00347595
\(100\) −13.9135 −1.39135
\(101\) 1.74584 0.173718 0.0868588 0.996221i \(-0.472317\pi\)
0.0868588 + 0.996221i \(0.472317\pi\)
\(102\) 36.0071 3.56524
\(103\) 8.98750 0.885565 0.442782 0.896629i \(-0.353991\pi\)
0.442782 + 0.896629i \(0.353991\pi\)
\(104\) 46.0265 4.51327
\(105\) 13.2425 1.29233
\(106\) −21.6603 −2.10383
\(107\) −19.0131 −1.83807 −0.919034 0.394178i \(-0.871029\pi\)
−0.919034 + 0.394178i \(0.871029\pi\)
\(108\) −29.5315 −2.84167
\(109\) 10.9149 1.04546 0.522728 0.852500i \(-0.324914\pi\)
0.522728 + 0.852500i \(0.324914\pi\)
\(110\) 4.40666 0.420158
\(111\) 6.45873 0.613036
\(112\) 80.2935 7.58702
\(113\) 9.81947 0.923738 0.461869 0.886948i \(-0.347179\pi\)
0.461869 + 0.886948i \(0.347179\pi\)
\(114\) −17.2141 −1.61225
\(115\) 11.3371 1.05719
\(116\) 23.7282 2.20311
\(117\) 0.157613 0.0145714
\(118\) 10.9581 1.00878
\(119\) −36.4891 −3.34495
\(120\) −27.7072 −2.52931
\(121\) 1.00000 0.0909091
\(122\) 26.0309 2.35672
\(123\) −7.09309 −0.639562
\(124\) 29.7016 2.66728
\(125\) −11.8878 −1.06327
\(126\) 0.461786 0.0411391
\(127\) 17.1760 1.52413 0.762063 0.647503i \(-0.224187\pi\)
0.762063 + 0.647503i \(0.224187\pi\)
\(128\) −53.8468 −4.75943
\(129\) 13.4210 1.18166
\(130\) 20.0822 1.76132
\(131\) 6.49876 0.567799 0.283900 0.958854i \(-0.408372\pi\)
0.283900 + 0.958854i \(0.408372\pi\)
\(132\) −9.73165 −0.847031
\(133\) 17.4445 1.51263
\(134\) 17.7660 1.53475
\(135\) −8.32502 −0.716504
\(136\) 76.3460 6.54661
\(137\) 10.1562 0.867703 0.433852 0.900984i \(-0.357154\pi\)
0.433852 + 0.900984i \(0.357154\pi\)
\(138\) −33.8974 −2.88554
\(139\) 12.0892 1.02540 0.512698 0.858569i \(-0.328646\pi\)
0.512698 + 0.858569i \(0.328646\pi\)
\(140\) 43.4580 3.67287
\(141\) 13.7427 1.15734
\(142\) 16.0326 1.34542
\(143\) 4.55724 0.381095
\(144\) −0.575293 −0.0479411
\(145\) 6.68905 0.555495
\(146\) −12.7782 −1.05753
\(147\) 28.0701 2.31518
\(148\) 21.1957 1.74228
\(149\) −17.4041 −1.42580 −0.712901 0.701264i \(-0.752619\pi\)
−0.712901 + 0.701264i \(0.752619\pi\)
\(150\) 11.7274 0.957538
\(151\) −17.3696 −1.41352 −0.706759 0.707455i \(-0.749843\pi\)
−0.706759 + 0.707455i \(0.749843\pi\)
\(152\) −36.4990 −2.96046
\(153\) 0.261440 0.0211361
\(154\) 13.3521 1.07594
\(155\) 8.37296 0.672532
\(156\) −44.3494 −3.55080
\(157\) 0.302820 0.0241677 0.0120839 0.999927i \(-0.496153\pi\)
0.0120839 + 0.999927i \(0.496153\pi\)
\(158\) −32.6447 −2.59708
\(159\) 13.4847 1.06941
\(160\) −41.1209 −3.25090
\(161\) 34.3511 2.70725
\(162\) 24.6045 1.93311
\(163\) 23.2004 1.81720 0.908599 0.417669i \(-0.137153\pi\)
0.908599 + 0.417669i \(0.137153\pi\)
\(164\) −23.2775 −1.81767
\(165\) −2.74338 −0.213572
\(166\) −36.4176 −2.82655
\(167\) −8.25517 −0.638804 −0.319402 0.947619i \(-0.603482\pi\)
−0.319402 + 0.947619i \(0.603482\pi\)
\(168\) −83.9521 −6.47705
\(169\) 7.76842 0.597571
\(170\) 33.3111 2.55485
\(171\) −0.124988 −0.00955804
\(172\) 44.0440 3.35833
\(173\) −12.3052 −0.935546 −0.467773 0.883849i \(-0.654944\pi\)
−0.467773 + 0.883849i \(0.654944\pi\)
\(174\) −20.0000 −1.51620
\(175\) −11.8844 −0.898373
\(176\) −16.6340 −1.25384
\(177\) −6.82202 −0.512774
\(178\) −6.32048 −0.473740
\(179\) −2.93838 −0.219625 −0.109812 0.993952i \(-0.535025\pi\)
−0.109812 + 0.993952i \(0.535025\pi\)
\(180\) −0.311371 −0.0232083
\(181\) 20.5463 1.52720 0.763599 0.645691i \(-0.223430\pi\)
0.763599 + 0.645691i \(0.223430\pi\)
\(182\) 60.8486 4.51040
\(183\) −16.2056 −1.19795
\(184\) −71.8727 −5.29853
\(185\) 5.97514 0.439301
\(186\) −25.0348 −1.83564
\(187\) 7.55927 0.552789
\(188\) 45.0997 3.28923
\(189\) −25.2246 −1.83482
\(190\) −15.9252 −1.15533
\(191\) −2.29237 −0.165870 −0.0829352 0.996555i \(-0.526429\pi\)
−0.0829352 + 0.996555i \(0.526429\pi\)
\(192\) 65.6611 4.73868
\(193\) 4.85074 0.349164 0.174582 0.984643i \(-0.444143\pi\)
0.174582 + 0.984643i \(0.444143\pi\)
\(194\) 11.6586 0.837042
\(195\) −12.5022 −0.895304
\(196\) 92.1181 6.57987
\(197\) 24.7690 1.76472 0.882360 0.470575i \(-0.155953\pi\)
0.882360 + 0.470575i \(0.155953\pi\)
\(198\) −0.0956660 −0.00679869
\(199\) −6.01960 −0.426718 −0.213359 0.976974i \(-0.568440\pi\)
−0.213359 + 0.976974i \(0.568440\pi\)
\(200\) 24.8656 1.75826
\(201\) −11.0603 −0.780132
\(202\) −4.82915 −0.339778
\(203\) 20.2677 1.42251
\(204\) −73.5642 −5.15052
\(205\) −6.56200 −0.458310
\(206\) −24.8602 −1.73209
\(207\) −0.246122 −0.0171066
\(208\) −75.8052 −5.25615
\(209\) −3.61389 −0.249978
\(210\) −36.6298 −2.52770
\(211\) −18.6808 −1.28604 −0.643021 0.765848i \(-0.722319\pi\)
−0.643021 + 0.765848i \(0.722319\pi\)
\(212\) 44.2530 3.03931
\(213\) −9.98113 −0.683895
\(214\) 52.5920 3.59511
\(215\) 12.4161 0.846774
\(216\) 52.7774 3.59105
\(217\) 25.3699 1.72222
\(218\) −30.1915 −2.04483
\(219\) 7.95511 0.537556
\(220\) −9.00300 −0.606982
\(221\) 34.4494 2.31732
\(222\) −17.8654 −1.19905
\(223\) 14.5378 0.973523 0.486762 0.873535i \(-0.338178\pi\)
0.486762 + 0.873535i \(0.338178\pi\)
\(224\) −124.596 −8.32489
\(225\) 0.0851500 0.00567667
\(226\) −27.1615 −1.80676
\(227\) 0.885115 0.0587472 0.0293736 0.999569i \(-0.490649\pi\)
0.0293736 + 0.999569i \(0.490649\pi\)
\(228\) 35.1691 2.32913
\(229\) −17.3684 −1.14774 −0.573868 0.818948i \(-0.694558\pi\)
−0.573868 + 0.818948i \(0.694558\pi\)
\(230\) −31.3594 −2.06778
\(231\) −8.31238 −0.546915
\(232\) −42.4060 −2.78409
\(233\) 12.8875 0.844287 0.422143 0.906529i \(-0.361278\pi\)
0.422143 + 0.906529i \(0.361278\pi\)
\(234\) −0.435973 −0.0285004
\(235\) 12.7137 0.829352
\(236\) −22.3879 −1.45733
\(237\) 20.3231 1.32013
\(238\) 100.932 6.54245
\(239\) 12.3926 0.801611 0.400805 0.916163i \(-0.368730\pi\)
0.400805 + 0.916163i \(0.368730\pi\)
\(240\) 45.6335 2.94563
\(241\) 20.5053 1.32086 0.660431 0.750887i \(-0.270374\pi\)
0.660431 + 0.750887i \(0.270374\pi\)
\(242\) −2.76609 −0.177811
\(243\) 0.359403 0.0230557
\(244\) −53.1822 −3.40464
\(245\) 25.9684 1.65906
\(246\) 19.6201 1.25093
\(247\) −16.4694 −1.04792
\(248\) −53.0813 −3.37067
\(249\) 22.6719 1.43677
\(250\) 32.8826 2.07968
\(251\) 21.9081 1.38283 0.691413 0.722460i \(-0.256989\pi\)
0.691413 + 0.722460i \(0.256989\pi\)
\(252\) −0.943448 −0.0594317
\(253\) −7.11636 −0.447402
\(254\) −47.5104 −2.98107
\(255\) −20.7380 −1.29866
\(256\) 72.6851 4.54282
\(257\) −8.39655 −0.523762 −0.261881 0.965100i \(-0.584343\pi\)
−0.261881 + 0.965100i \(0.584343\pi\)
\(258\) −37.1238 −2.31122
\(259\) 18.1045 1.12496
\(260\) −41.0288 −2.54450
\(261\) −0.145215 −0.00898861
\(262\) −17.9761 −1.11057
\(263\) 19.2483 1.18690 0.593449 0.804871i \(-0.297766\pi\)
0.593449 + 0.804871i \(0.297766\pi\)
\(264\) 17.3920 1.07040
\(265\) 12.4750 0.766336
\(266\) −48.2530 −2.95858
\(267\) 3.93484 0.240808
\(268\) −36.2967 −2.21717
\(269\) 5.16367 0.314834 0.157417 0.987532i \(-0.449683\pi\)
0.157417 + 0.987532i \(0.449683\pi\)
\(270\) 23.0277 1.40142
\(271\) 4.84737 0.294457 0.147228 0.989103i \(-0.452965\pi\)
0.147228 + 0.989103i \(0.452965\pi\)
\(272\) −125.741 −7.62418
\(273\) −37.8815 −2.29269
\(274\) −28.0929 −1.69716
\(275\) 2.46203 0.148466
\(276\) 69.2539 4.16860
\(277\) −7.08095 −0.425453 −0.212726 0.977112i \(-0.568234\pi\)
−0.212726 + 0.977112i \(0.568234\pi\)
\(278\) −33.4399 −2.00559
\(279\) −0.181772 −0.0108824
\(280\) −77.6663 −4.64145
\(281\) −1.78300 −0.106365 −0.0531826 0.998585i \(-0.516937\pi\)
−0.0531826 + 0.998585i \(0.516937\pi\)
\(282\) −38.0135 −2.26367
\(283\) −17.0872 −1.01573 −0.507863 0.861438i \(-0.669564\pi\)
−0.507863 + 0.861438i \(0.669564\pi\)
\(284\) −32.7552 −1.94366
\(285\) 9.91428 0.587271
\(286\) −12.6057 −0.745392
\(287\) −19.8827 −1.17364
\(288\) 0.892712 0.0526035
\(289\) 40.1426 2.36133
\(290\) −18.5025 −1.08650
\(291\) −7.25814 −0.425479
\(292\) 26.1064 1.52776
\(293\) −16.1209 −0.941791 −0.470896 0.882189i \(-0.656069\pi\)
−0.470896 + 0.882189i \(0.656069\pi\)
\(294\) −77.6444 −4.52831
\(295\) −6.31123 −0.367454
\(296\) −37.8801 −2.20173
\(297\) 5.22567 0.303224
\(298\) 48.1414 2.78876
\(299\) −32.4310 −1.87553
\(300\) −23.9596 −1.38331
\(301\) 37.6206 2.16842
\(302\) 48.0458 2.76473
\(303\) 3.00640 0.172713
\(304\) 60.1136 3.44775
\(305\) −14.9922 −0.858453
\(306\) −0.723165 −0.0413406
\(307\) −15.5729 −0.888790 −0.444395 0.895831i \(-0.646581\pi\)
−0.444395 + 0.895831i \(0.646581\pi\)
\(308\) −27.2789 −1.55436
\(309\) 15.4768 0.880445
\(310\) −23.1603 −1.31542
\(311\) −0.941881 −0.0534092 −0.0267046 0.999643i \(-0.508501\pi\)
−0.0267046 + 0.999643i \(0.508501\pi\)
\(312\) 79.2594 4.48718
\(313\) 2.75976 0.155991 0.0779955 0.996954i \(-0.475148\pi\)
0.0779955 + 0.996954i \(0.475148\pi\)
\(314\) −0.837628 −0.0472701
\(315\) −0.265961 −0.0149852
\(316\) 66.6946 3.75187
\(317\) 0.839880 0.0471724 0.0235862 0.999722i \(-0.492492\pi\)
0.0235862 + 0.999722i \(0.492492\pi\)
\(318\) −37.2999 −2.09167
\(319\) −4.19876 −0.235085
\(320\) 60.7447 3.39573
\(321\) −32.7413 −1.82744
\(322\) −95.0182 −5.29516
\(323\) −27.3184 −1.52004
\(324\) −50.2680 −2.79267
\(325\) 11.2200 0.622376
\(326\) −64.1744 −3.55429
\(327\) 18.7958 1.03941
\(328\) 41.6005 2.29701
\(329\) 38.5223 2.12380
\(330\) 7.58843 0.417729
\(331\) −33.7289 −1.85391 −0.926954 0.375176i \(-0.877582\pi\)
−0.926954 + 0.375176i \(0.877582\pi\)
\(332\) 74.4027 4.08338
\(333\) −0.129717 −0.00710843
\(334\) 22.8345 1.24945
\(335\) −10.2321 −0.559042
\(336\) 138.268 7.54316
\(337\) 20.7409 1.12983 0.564916 0.825149i \(-0.308909\pi\)
0.564916 + 0.825149i \(0.308909\pi\)
\(338\) −21.4881 −1.16880
\(339\) 16.9095 0.918398
\(340\) −68.0561 −3.69086
\(341\) −5.25576 −0.284615
\(342\) 0.345727 0.0186948
\(343\) 44.8942 2.42406
\(344\) −78.7136 −4.24395
\(345\) 19.5229 1.05108
\(346\) 34.0372 1.82985
\(347\) −16.8679 −0.905518 −0.452759 0.891633i \(-0.649560\pi\)
−0.452759 + 0.891633i \(0.649560\pi\)
\(348\) 40.8609 2.19037
\(349\) −3.92387 −0.210040 −0.105020 0.994470i \(-0.533491\pi\)
−0.105020 + 0.994470i \(0.533491\pi\)
\(350\) 32.8732 1.75715
\(351\) 23.8146 1.27113
\(352\) 25.8119 1.37578
\(353\) 14.1778 0.754611 0.377305 0.926089i \(-0.376851\pi\)
0.377305 + 0.926089i \(0.376851\pi\)
\(354\) 18.8703 1.00295
\(355\) −9.23379 −0.490079
\(356\) 12.9130 0.684389
\(357\) −62.8356 −3.32561
\(358\) 8.12780 0.429568
\(359\) −23.3064 −1.23007 −0.615033 0.788501i \(-0.710857\pi\)
−0.615033 + 0.788501i \(0.710857\pi\)
\(360\) 0.556469 0.0293285
\(361\) −5.93978 −0.312620
\(362\) −56.8330 −2.98708
\(363\) 1.72204 0.0903836
\(364\) −124.316 −6.51595
\(365\) 7.35947 0.385212
\(366\) 44.8262 2.34310
\(367\) −7.01716 −0.366293 −0.183146 0.983086i \(-0.558628\pi\)
−0.183146 + 0.983086i \(0.558628\pi\)
\(368\) 118.374 6.17066
\(369\) 0.142457 0.00741603
\(370\) −16.5278 −0.859237
\(371\) 37.7991 1.96243
\(372\) 51.1472 2.65186
\(373\) 8.36997 0.433381 0.216690 0.976240i \(-0.430474\pi\)
0.216690 + 0.976240i \(0.430474\pi\)
\(374\) −20.9096 −1.08121
\(375\) −20.4712 −1.05713
\(376\) −80.6002 −4.15664
\(377\) −19.1348 −0.985490
\(378\) 69.7735 3.58876
\(379\) −16.1453 −0.829330 −0.414665 0.909974i \(-0.636101\pi\)
−0.414665 + 0.909974i \(0.636101\pi\)
\(380\) 32.5359 1.66905
\(381\) 29.5778 1.51531
\(382\) 6.34090 0.324429
\(383\) 12.5513 0.641342 0.320671 0.947191i \(-0.396092\pi\)
0.320671 + 0.947191i \(0.396092\pi\)
\(384\) −92.7262 −4.73191
\(385\) −7.69000 −0.391919
\(386\) −13.4176 −0.682936
\(387\) −0.269547 −0.0137019
\(388\) −23.8191 −1.20923
\(389\) −11.2319 −0.569480 −0.284740 0.958605i \(-0.591907\pi\)
−0.284740 + 0.958605i \(0.591907\pi\)
\(390\) 34.5823 1.75114
\(391\) −53.7945 −2.72051
\(392\) −164.630 −8.31505
\(393\) 11.1911 0.564517
\(394\) −68.5133 −3.45165
\(395\) 18.8014 0.946002
\(396\) 0.195450 0.00982172
\(397\) −32.6597 −1.63914 −0.819572 0.572977i \(-0.805789\pi\)
−0.819572 + 0.572977i \(0.805789\pi\)
\(398\) 16.6507 0.834626
\(399\) 30.0401 1.50388
\(400\) −40.9534 −2.04767
\(401\) 30.0508 1.50066 0.750332 0.661062i \(-0.229894\pi\)
0.750332 + 0.661062i \(0.229894\pi\)
\(402\) 30.5937 1.52587
\(403\) −23.9517 −1.19312
\(404\) 9.86617 0.490860
\(405\) −14.1707 −0.704148
\(406\) −56.0622 −2.78232
\(407\) −3.75063 −0.185912
\(408\) 131.471 6.50877
\(409\) 18.3382 0.906764 0.453382 0.891316i \(-0.350217\pi\)
0.453382 + 0.891316i \(0.350217\pi\)
\(410\) 18.1511 0.896417
\(411\) 17.4894 0.862687
\(412\) 50.7905 2.50227
\(413\) −19.1229 −0.940975
\(414\) 0.680794 0.0334592
\(415\) 20.9743 1.02959
\(416\) 117.631 5.76733
\(417\) 20.8181 1.01947
\(418\) 9.99634 0.488937
\(419\) −12.5393 −0.612586 −0.306293 0.951937i \(-0.599089\pi\)
−0.306293 + 0.951937i \(0.599089\pi\)
\(420\) 74.8364 3.65164
\(421\) 17.8853 0.871676 0.435838 0.900025i \(-0.356452\pi\)
0.435838 + 0.900025i \(0.356452\pi\)
\(422\) 51.6729 2.51540
\(423\) −0.276008 −0.0134200
\(424\) −79.0869 −3.84080
\(425\) 18.6111 0.902773
\(426\) 27.6087 1.33764
\(427\) −45.4261 −2.19832
\(428\) −107.448 −5.19368
\(429\) 7.84774 0.378892
\(430\) −34.3441 −1.65622
\(431\) −35.0836 −1.68992 −0.844960 0.534830i \(-0.820376\pi\)
−0.844960 + 0.534830i \(0.820376\pi\)
\(432\) −86.9240 −4.18213
\(433\) −35.3433 −1.69849 −0.849244 0.528000i \(-0.822942\pi\)
−0.849244 + 0.528000i \(0.822942\pi\)
\(434\) −70.1753 −3.36852
\(435\) 11.5188 0.552284
\(436\) 61.6826 2.95406
\(437\) 25.7178 1.23025
\(438\) −22.0045 −1.05142
\(439\) −6.90256 −0.329441 −0.164721 0.986340i \(-0.552672\pi\)
−0.164721 + 0.986340i \(0.552672\pi\)
\(440\) 16.0898 0.767049
\(441\) −0.563759 −0.0268456
\(442\) −95.2901 −4.53249
\(443\) 15.7400 0.747830 0.373915 0.927463i \(-0.378015\pi\)
0.373915 + 0.927463i \(0.378015\pi\)
\(444\) 36.4998 1.73221
\(445\) 3.64022 0.172563
\(446\) −40.2128 −1.90413
\(447\) −29.9706 −1.41756
\(448\) 184.055 8.69579
\(449\) 15.5572 0.734188 0.367094 0.930184i \(-0.380353\pi\)
0.367094 + 0.930184i \(0.380353\pi\)
\(450\) −0.235532 −0.0111031
\(451\) 4.11901 0.193957
\(452\) 55.4922 2.61013
\(453\) −29.9111 −1.40535
\(454\) −2.44831 −0.114905
\(455\) −35.0452 −1.64294
\(456\) −62.8527 −2.94335
\(457\) −36.8348 −1.72306 −0.861530 0.507706i \(-0.830494\pi\)
−0.861530 + 0.507706i \(0.830494\pi\)
\(458\) 48.0425 2.24488
\(459\) 39.5023 1.84381
\(460\) 64.0686 2.98721
\(461\) −1.51664 −0.0706370 −0.0353185 0.999376i \(-0.511245\pi\)
−0.0353185 + 0.999376i \(0.511245\pi\)
\(462\) 22.9928 1.06972
\(463\) 14.1808 0.659038 0.329519 0.944149i \(-0.393113\pi\)
0.329519 + 0.944149i \(0.393113\pi\)
\(464\) 69.8423 3.24235
\(465\) 14.4185 0.668644
\(466\) −35.6479 −1.65136
\(467\) 16.6273 0.769418 0.384709 0.923038i \(-0.374302\pi\)
0.384709 + 0.923038i \(0.374302\pi\)
\(468\) 0.890712 0.0411732
\(469\) −31.0032 −1.43159
\(470\) −35.1673 −1.62215
\(471\) 0.521468 0.0240280
\(472\) 40.0107 1.84164
\(473\) −7.79370 −0.358355
\(474\) −56.2155 −2.58206
\(475\) −8.89751 −0.408246
\(476\) −206.208 −9.45155
\(477\) −0.270826 −0.0124003
\(478\) −34.2790 −1.56789
\(479\) 6.21708 0.284065 0.142033 0.989862i \(-0.454636\pi\)
0.142033 + 0.989862i \(0.454636\pi\)
\(480\) −70.8118 −3.23210
\(481\) −17.0925 −0.779352
\(482\) −56.7194 −2.58350
\(483\) 59.1539 2.69160
\(484\) 5.65124 0.256875
\(485\) −6.71469 −0.304898
\(486\) −0.994140 −0.0450951
\(487\) −28.6906 −1.30009 −0.650047 0.759894i \(-0.725251\pi\)
−0.650047 + 0.759894i \(0.725251\pi\)
\(488\) 95.0450 4.30248
\(489\) 39.9520 1.80669
\(490\) −71.8308 −3.24499
\(491\) 1.38426 0.0624706 0.0312353 0.999512i \(-0.490056\pi\)
0.0312353 + 0.999512i \(0.490056\pi\)
\(492\) −40.0848 −1.80716
\(493\) −31.7396 −1.42948
\(494\) 45.5557 2.04965
\(495\) 0.0550979 0.00247647
\(496\) 87.4244 3.92547
\(497\) −27.9782 −1.25499
\(498\) −62.7124 −2.81021
\(499\) 11.4918 0.514444 0.257222 0.966352i \(-0.417193\pi\)
0.257222 + 0.966352i \(0.417193\pi\)
\(500\) −67.1806 −3.00441
\(501\) −14.2157 −0.635111
\(502\) −60.5997 −2.70470
\(503\) −11.1348 −0.496478 −0.248239 0.968699i \(-0.579852\pi\)
−0.248239 + 0.968699i \(0.579852\pi\)
\(504\) 1.68609 0.0751044
\(505\) 2.78130 0.123766
\(506\) 19.6845 0.875082
\(507\) 13.3775 0.594116
\(508\) 97.0658 4.30660
\(509\) −9.78466 −0.433697 −0.216849 0.976205i \(-0.569578\pi\)
−0.216849 + 0.976205i \(0.569578\pi\)
\(510\) 57.3630 2.54008
\(511\) 22.2990 0.986452
\(512\) −93.3599 −4.12596
\(513\) −18.8850 −0.833794
\(514\) 23.2256 1.02444
\(515\) 14.3180 0.630926
\(516\) 75.8455 3.33891
\(517\) −7.98049 −0.350982
\(518\) −50.0787 −2.20033
\(519\) −21.1900 −0.930138
\(520\) 73.3249 3.21551
\(521\) −5.79636 −0.253943 −0.126972 0.991906i \(-0.540526\pi\)
−0.126972 + 0.991906i \(0.540526\pi\)
\(522\) 0.401679 0.0175810
\(523\) 17.1372 0.749358 0.374679 0.927155i \(-0.377753\pi\)
0.374679 + 0.927155i \(0.377753\pi\)
\(524\) 36.7261 1.60439
\(525\) −20.4653 −0.893180
\(526\) −53.2424 −2.32148
\(527\) −39.7297 −1.73065
\(528\) −28.6444 −1.24659
\(529\) 27.6426 1.20185
\(530\) −34.5070 −1.49889
\(531\) 0.137013 0.00594586
\(532\) 98.5829 4.27411
\(533\) 18.7713 0.813076
\(534\) −10.8841 −0.471001
\(535\) −30.2898 −1.30954
\(536\) 64.8678 2.80186
\(537\) −5.06000 −0.218355
\(538\) −14.2831 −0.615790
\(539\) −16.3005 −0.702113
\(540\) −47.0467 −2.02457
\(541\) 16.0419 0.689696 0.344848 0.938659i \(-0.387931\pi\)
0.344848 + 0.938659i \(0.387931\pi\)
\(542\) −13.4082 −0.575933
\(543\) 35.3816 1.51837
\(544\) 195.119 8.36566
\(545\) 17.3885 0.744841
\(546\) 104.784 4.48432
\(547\) 1.00000 0.0427569
\(548\) 57.3951 2.45180
\(549\) 0.325473 0.0138908
\(550\) −6.81019 −0.290387
\(551\) 15.1739 0.646429
\(552\) −123.768 −5.26790
\(553\) 56.9679 2.42252
\(554\) 19.5865 0.832151
\(555\) 10.2894 0.436761
\(556\) 68.3192 2.89738
\(557\) 19.7295 0.835967 0.417983 0.908455i \(-0.362737\pi\)
0.417983 + 0.908455i \(0.362737\pi\)
\(558\) 0.502797 0.0212851
\(559\) −35.5177 −1.50224
\(560\) 127.916 5.40542
\(561\) 13.0174 0.549593
\(562\) 4.93195 0.208042
\(563\) −26.2904 −1.10801 −0.554005 0.832513i \(-0.686901\pi\)
−0.554005 + 0.832513i \(0.686901\pi\)
\(564\) 77.6633 3.27022
\(565\) 15.6434 0.658123
\(566\) 47.2646 1.98668
\(567\) −42.9369 −1.80318
\(568\) 58.5387 2.45623
\(569\) −28.2588 −1.18467 −0.592336 0.805691i \(-0.701794\pi\)
−0.592336 + 0.805691i \(0.701794\pi\)
\(570\) −27.4238 −1.14866
\(571\) −5.14097 −0.215143 −0.107571 0.994197i \(-0.534307\pi\)
−0.107571 + 0.994197i \(0.534307\pi\)
\(572\) 25.7540 1.07683
\(573\) −3.94755 −0.164911
\(574\) 54.9973 2.29554
\(575\) −17.5207 −0.730663
\(576\) −1.31873 −0.0549472
\(577\) 21.2285 0.883754 0.441877 0.897076i \(-0.354313\pi\)
0.441877 + 0.897076i \(0.354313\pi\)
\(578\) −111.038 −4.61857
\(579\) 8.35315 0.347145
\(580\) 37.8014 1.56962
\(581\) 63.5518 2.63657
\(582\) 20.0766 0.832203
\(583\) −7.83066 −0.324313
\(584\) −46.6562 −1.93065
\(585\) 0.251094 0.0103815
\(586\) 44.5917 1.84207
\(587\) 41.4487 1.71077 0.855386 0.517992i \(-0.173320\pi\)
0.855386 + 0.517992i \(0.173320\pi\)
\(588\) 158.631 6.54183
\(589\) 18.9937 0.782624
\(590\) 17.4574 0.718710
\(591\) 42.6532 1.75452
\(592\) 62.3881 2.56414
\(593\) 12.9625 0.532308 0.266154 0.963931i \(-0.414247\pi\)
0.266154 + 0.963931i \(0.414247\pi\)
\(594\) −14.4547 −0.593082
\(595\) −58.1308 −2.38313
\(596\) −98.3550 −4.02878
\(597\) −10.3660 −0.424251
\(598\) 89.7069 3.66839
\(599\) −39.0427 −1.59524 −0.797621 0.603158i \(-0.793909\pi\)
−0.797621 + 0.603158i \(0.793909\pi\)
\(600\) 42.8195 1.74810
\(601\) −23.4330 −0.955850 −0.477925 0.878401i \(-0.658611\pi\)
−0.477925 + 0.878401i \(0.658611\pi\)
\(602\) −104.062 −4.24125
\(603\) 0.222134 0.00904599
\(604\) −98.1597 −3.99406
\(605\) 1.59310 0.0647688
\(606\) −8.31598 −0.337814
\(607\) 44.1869 1.79349 0.896746 0.442545i \(-0.145924\pi\)
0.896746 + 0.442545i \(0.145924\pi\)
\(608\) −93.2814 −3.78306
\(609\) 34.9017 1.41429
\(610\) 41.4698 1.67906
\(611\) −36.3690 −1.47133
\(612\) 1.47746 0.0597227
\(613\) −6.92238 −0.279592 −0.139796 0.990180i \(-0.544645\pi\)
−0.139796 + 0.990180i \(0.544645\pi\)
\(614\) 43.0759 1.73840
\(615\) −11.3000 −0.455660
\(616\) 48.7516 1.96426
\(617\) 8.10349 0.326234 0.163117 0.986607i \(-0.447845\pi\)
0.163117 + 0.986607i \(0.447845\pi\)
\(618\) −42.8102 −1.72208
\(619\) 1.83586 0.0737895 0.0368948 0.999319i \(-0.488253\pi\)
0.0368948 + 0.999319i \(0.488253\pi\)
\(620\) 47.3176 1.90032
\(621\) −37.1878 −1.49229
\(622\) 2.60533 0.104464
\(623\) 11.0298 0.441899
\(624\) −130.539 −5.22576
\(625\) −6.62828 −0.265131
\(626\) −7.63374 −0.305106
\(627\) −6.22326 −0.248533
\(628\) 1.71131 0.0682887
\(629\) −28.3520 −1.13047
\(630\) 0.735671 0.0293098
\(631\) −32.5986 −1.29773 −0.648864 0.760904i \(-0.724756\pi\)
−0.648864 + 0.760904i \(0.724756\pi\)
\(632\) −119.194 −4.74127
\(633\) −32.1691 −1.27861
\(634\) −2.32318 −0.0922653
\(635\) 27.3631 1.08587
\(636\) 76.2053 3.02174
\(637\) −74.2854 −2.94329
\(638\) 11.6141 0.459808
\(639\) 0.200460 0.00793009
\(640\) −85.7834 −3.39088
\(641\) 27.7925 1.09774 0.548868 0.835909i \(-0.315059\pi\)
0.548868 + 0.835909i \(0.315059\pi\)
\(642\) 90.5654 3.57433
\(643\) 15.5759 0.614252 0.307126 0.951669i \(-0.400633\pi\)
0.307126 + 0.951669i \(0.400633\pi\)
\(644\) 194.126 7.64965
\(645\) 21.3811 0.841879
\(646\) 75.5651 2.97307
\(647\) −44.8356 −1.76267 −0.881335 0.472492i \(-0.843355\pi\)
−0.881335 + 0.472492i \(0.843355\pi\)
\(648\) 89.8368 3.52912
\(649\) 3.96160 0.155506
\(650\) −31.0356 −1.21732
\(651\) 43.6879 1.71226
\(652\) 131.111 5.13471
\(653\) −33.8941 −1.32638 −0.663190 0.748451i \(-0.730798\pi\)
−0.663190 + 0.748451i \(0.730798\pi\)
\(654\) −51.9909 −2.03301
\(655\) 10.3532 0.404532
\(656\) −68.5157 −2.67509
\(657\) −0.159770 −0.00623322
\(658\) −106.556 −4.15399
\(659\) 22.7738 0.887140 0.443570 0.896240i \(-0.353712\pi\)
0.443570 + 0.896240i \(0.353712\pi\)
\(660\) −15.5035 −0.603473
\(661\) −8.05202 −0.313187 −0.156594 0.987663i \(-0.550051\pi\)
−0.156594 + 0.987663i \(0.550051\pi\)
\(662\) 93.2971 3.62609
\(663\) 59.3232 2.30392
\(664\) −132.969 −5.16021
\(665\) 27.7908 1.07768
\(666\) 0.358808 0.0139035
\(667\) 29.8799 1.15695
\(668\) −46.6520 −1.80502
\(669\) 25.0346 0.967895
\(670\) 28.3030 1.09344
\(671\) 9.41072 0.363297
\(672\) −214.558 −8.27676
\(673\) −12.2755 −0.473187 −0.236593 0.971609i \(-0.576031\pi\)
−0.236593 + 0.971609i \(0.576031\pi\)
\(674\) −57.3713 −2.20986
\(675\) 12.8657 0.495203
\(676\) 43.9012 1.68851
\(677\) 17.2430 0.662701 0.331350 0.943508i \(-0.392496\pi\)
0.331350 + 0.943508i \(0.392496\pi\)
\(678\) −46.7732 −1.79631
\(679\) −20.3453 −0.780783
\(680\) 121.627 4.66418
\(681\) 1.52420 0.0584075
\(682\) 14.5379 0.556684
\(683\) 3.01755 0.115464 0.0577318 0.998332i \(-0.481613\pi\)
0.0577318 + 0.998332i \(0.481613\pi\)
\(684\) −0.706335 −0.0270074
\(685\) 16.1799 0.618201
\(686\) −124.181 −4.74126
\(687\) −29.9090 −1.14110
\(688\) 129.641 4.94250
\(689\) −35.6862 −1.35954
\(690\) −54.0020 −2.05582
\(691\) −19.5725 −0.744572 −0.372286 0.928118i \(-0.621426\pi\)
−0.372286 + 0.928118i \(0.621426\pi\)
\(692\) −69.5396 −2.64350
\(693\) 0.166945 0.00634173
\(694\) 46.6582 1.77112
\(695\) 19.2594 0.730551
\(696\) −73.0247 −2.76800
\(697\) 31.1367 1.17939
\(698\) 10.8538 0.410821
\(699\) 22.1927 0.839406
\(700\) −67.1614 −2.53846
\(701\) 38.2218 1.44362 0.721810 0.692092i \(-0.243311\pi\)
0.721810 + 0.692092i \(0.243311\pi\)
\(702\) −65.8733 −2.48623
\(703\) 13.5544 0.511213
\(704\) −38.1299 −1.43707
\(705\) 21.8935 0.824558
\(706\) −39.2172 −1.47596
\(707\) 8.42728 0.316941
\(708\) −38.5529 −1.44891
\(709\) −46.0209 −1.72835 −0.864175 0.503191i \(-0.832159\pi\)
−0.864175 + 0.503191i \(0.832159\pi\)
\(710\) 25.5415 0.958555
\(711\) −0.408168 −0.0153075
\(712\) −23.0776 −0.864869
\(713\) 37.4019 1.40071
\(714\) 173.809 6.50463
\(715\) 7.26014 0.271514
\(716\) −16.6055 −0.620575
\(717\) 21.3405 0.796977
\(718\) 64.4676 2.40591
\(719\) 20.9429 0.781038 0.390519 0.920595i \(-0.372296\pi\)
0.390519 + 0.920595i \(0.372296\pi\)
\(720\) −0.916500 −0.0341559
\(721\) 43.3832 1.61568
\(722\) 16.4300 0.611460
\(723\) 35.3109 1.31323
\(724\) 116.112 4.31528
\(725\) −10.3375 −0.383924
\(726\) −4.76331 −0.176783
\(727\) −15.5958 −0.578416 −0.289208 0.957266i \(-0.593392\pi\)
−0.289208 + 0.957266i \(0.593392\pi\)
\(728\) 222.173 8.23427
\(729\) 27.3040 1.01126
\(730\) −20.3569 −0.753444
\(731\) −58.9147 −2.17904
\(732\) −91.5818 −3.38496
\(733\) 43.1501 1.59378 0.796892 0.604121i \(-0.206476\pi\)
0.796892 + 0.604121i \(0.206476\pi\)
\(734\) 19.4101 0.716439
\(735\) 44.7185 1.64947
\(736\) −183.687 −6.77078
\(737\) 6.42278 0.236586
\(738\) −0.394049 −0.0145051
\(739\) 4.44706 0.163588 0.0817939 0.996649i \(-0.473935\pi\)
0.0817939 + 0.996649i \(0.473935\pi\)
\(740\) 33.7669 1.24130
\(741\) −28.3609 −1.04186
\(742\) −104.556 −3.83836
\(743\) −13.6476 −0.500682 −0.250341 0.968158i \(-0.580543\pi\)
−0.250341 + 0.968158i \(0.580543\pi\)
\(744\) −91.4080 −3.35118
\(745\) −27.7266 −1.01582
\(746\) −23.1521 −0.847657
\(747\) −0.455341 −0.0166601
\(748\) 42.7193 1.56197
\(749\) −91.7775 −3.35348
\(750\) 56.6251 2.06766
\(751\) 30.8658 1.12631 0.563154 0.826352i \(-0.309588\pi\)
0.563154 + 0.826352i \(0.309588\pi\)
\(752\) 132.748 4.84081
\(753\) 37.7265 1.37483
\(754\) 52.9284 1.92754
\(755\) −27.6715 −1.00707
\(756\) −142.550 −5.18451
\(757\) 16.7802 0.609885 0.304942 0.952371i \(-0.401363\pi\)
0.304942 + 0.952371i \(0.401363\pi\)
\(758\) 44.6594 1.62210
\(759\) −12.2546 −0.444815
\(760\) −58.1467 −2.10920
\(761\) 16.6043 0.601904 0.300952 0.953639i \(-0.402696\pi\)
0.300952 + 0.953639i \(0.402696\pi\)
\(762\) −81.8147 −2.96383
\(763\) 52.6868 1.90739
\(764\) −12.9548 −0.468686
\(765\) 0.416500 0.0150586
\(766\) −34.7180 −1.25441
\(767\) 18.0539 0.651890
\(768\) 125.167 4.51656
\(769\) 42.5253 1.53350 0.766752 0.641944i \(-0.221872\pi\)
0.766752 + 0.641944i \(0.221872\pi\)
\(770\) 21.2712 0.766561
\(771\) −14.4592 −0.520734
\(772\) 27.4127 0.986604
\(773\) 5.04172 0.181338 0.0906691 0.995881i \(-0.471099\pi\)
0.0906691 + 0.995881i \(0.471099\pi\)
\(774\) 0.745592 0.0267997
\(775\) −12.9398 −0.464812
\(776\) 42.5685 1.52812
\(777\) 31.1767 1.11846
\(778\) 31.0684 1.11386
\(779\) −14.8857 −0.533334
\(780\) −70.6532 −2.52979
\(781\) 5.79611 0.207401
\(782\) 148.800 5.32109
\(783\) −21.9413 −0.784120
\(784\) 271.143 9.68369
\(785\) 0.482424 0.0172184
\(786\) −30.9556 −1.10415
\(787\) 0.739039 0.0263439 0.0131719 0.999913i \(-0.495807\pi\)
0.0131719 + 0.999913i \(0.495807\pi\)
\(788\) 139.976 4.98643
\(789\) 33.1462 1.18004
\(790\) −52.0064 −1.85030
\(791\) 47.3992 1.68532
\(792\) −0.349299 −0.0124118
\(793\) 42.8869 1.52296
\(794\) 90.3396 3.20603
\(795\) 21.4825 0.761905
\(796\) −34.0182 −1.20574
\(797\) 27.8065 0.984956 0.492478 0.870325i \(-0.336091\pi\)
0.492478 + 0.870325i \(0.336091\pi\)
\(798\) −83.0934 −2.94148
\(799\) −60.3267 −2.13421
\(800\) 63.5496 2.24682
\(801\) −0.0790271 −0.00279228
\(802\) −83.1230 −2.93518
\(803\) −4.61959 −0.163022
\(804\) −62.5043 −2.20436
\(805\) 54.7248 1.92880
\(806\) 66.2526 2.33365
\(807\) 8.89203 0.313014
\(808\) −17.6324 −0.620305
\(809\) 17.3056 0.608433 0.304216 0.952603i \(-0.401605\pi\)
0.304216 + 0.952603i \(0.401605\pi\)
\(810\) 39.1974 1.37726
\(811\) 15.6310 0.548879 0.274439 0.961604i \(-0.411508\pi\)
0.274439 + 0.961604i \(0.411508\pi\)
\(812\) 114.537 4.01948
\(813\) 8.34735 0.292754
\(814\) 10.3746 0.363629
\(815\) 36.9606 1.29467
\(816\) −216.531 −7.58010
\(817\) 28.1656 0.985389
\(818\) −50.7250 −1.77356
\(819\) 0.760810 0.0265849
\(820\) −37.0834 −1.29501
\(821\) −46.9309 −1.63790 −0.818950 0.573864i \(-0.805444\pi\)
−0.818950 + 0.573864i \(0.805444\pi\)
\(822\) −48.3771 −1.68735
\(823\) 40.1087 1.39810 0.699051 0.715072i \(-0.253606\pi\)
0.699051 + 0.715072i \(0.253606\pi\)
\(824\) −90.7706 −3.16214
\(825\) 4.23971 0.147608
\(826\) 52.8955 1.84047
\(827\) 9.72155 0.338051 0.169026 0.985612i \(-0.445938\pi\)
0.169026 + 0.985612i \(0.445938\pi\)
\(828\) −1.39089 −0.0483368
\(829\) 27.9566 0.970973 0.485487 0.874244i \(-0.338642\pi\)
0.485487 + 0.874244i \(0.338642\pi\)
\(830\) −58.0169 −2.01379
\(831\) −12.1937 −0.422993
\(832\) −173.767 −6.02428
\(833\) −123.220 −4.26932
\(834\) −57.5848 −1.99400
\(835\) −13.1513 −0.455120
\(836\) −20.4230 −0.706343
\(837\) −27.4649 −0.949325
\(838\) 34.6848 1.19817
\(839\) −49.4330 −1.70662 −0.853308 0.521407i \(-0.825407\pi\)
−0.853308 + 0.521407i \(0.825407\pi\)
\(840\) −133.744 −4.61462
\(841\) −11.3704 −0.392083
\(842\) −49.4723 −1.70493
\(843\) −3.07040 −0.105750
\(844\) −105.570 −3.63387
\(845\) 12.3759 0.425743
\(846\) 0.763462 0.0262483
\(847\) 4.82706 0.165860
\(848\) 130.255 4.47299
\(849\) −29.4247 −1.00985
\(850\) −51.4800 −1.76575
\(851\) 26.6909 0.914951
\(852\) −56.4057 −1.93243
\(853\) −15.2840 −0.523314 −0.261657 0.965161i \(-0.584269\pi\)
−0.261657 + 0.965161i \(0.584269\pi\)
\(854\) 125.653 4.29974
\(855\) −0.199118 −0.00680969
\(856\) 192.026 6.56331
\(857\) −53.8381 −1.83908 −0.919538 0.393001i \(-0.871437\pi\)
−0.919538 + 0.393001i \(0.871437\pi\)
\(858\) −21.7075 −0.741083
\(859\) −10.7928 −0.368245 −0.184123 0.982903i \(-0.558944\pi\)
−0.184123 + 0.982903i \(0.558944\pi\)
\(860\) 70.1666 2.39266
\(861\) −34.2388 −1.16685
\(862\) 97.0444 3.30535
\(863\) −54.4143 −1.85228 −0.926142 0.377174i \(-0.876896\pi\)
−0.926142 + 0.377174i \(0.876896\pi\)
\(864\) 134.884 4.58886
\(865\) −19.6034 −0.666536
\(866\) 97.7626 3.32211
\(867\) 69.1271 2.34768
\(868\) 143.371 4.86634
\(869\) −11.8018 −0.400348
\(870\) −31.8620 −1.08022
\(871\) 29.2701 0.991781
\(872\) −110.236 −3.73307
\(873\) 0.145772 0.00493363
\(874\) −71.1376 −2.40626
\(875\) −57.3830 −1.93990
\(876\) 44.9562 1.51893
\(877\) −14.2199 −0.480171 −0.240086 0.970752i \(-0.577176\pi\)
−0.240086 + 0.970752i \(0.577176\pi\)
\(878\) 19.0931 0.644361
\(879\) −27.7607 −0.936347
\(880\) −26.4997 −0.893304
\(881\) 7.21423 0.243054 0.121527 0.992588i \(-0.461221\pi\)
0.121527 + 0.992588i \(0.461221\pi\)
\(882\) 1.55941 0.0525079
\(883\) −39.1720 −1.31824 −0.659122 0.752036i \(-0.729072\pi\)
−0.659122 + 0.752036i \(0.729072\pi\)
\(884\) 194.682 6.54786
\(885\) −10.8682 −0.365330
\(886\) −43.5382 −1.46270
\(887\) 46.6889 1.56766 0.783829 0.620976i \(-0.213264\pi\)
0.783829 + 0.620976i \(0.213264\pi\)
\(888\) −65.2309 −2.18901
\(889\) 82.9097 2.78070
\(890\) −10.0692 −0.337519
\(891\) 8.89505 0.297995
\(892\) 82.1566 2.75081
\(893\) 28.8406 0.965115
\(894\) 82.9013 2.77263
\(895\) −4.68113 −0.156473
\(896\) −259.922 −8.68337
\(897\) −55.8473 −1.86469
\(898\) −43.0325 −1.43601
\(899\) 22.0677 0.735998
\(900\) 0.481203 0.0160401
\(901\) −59.1941 −1.97204
\(902\) −11.3935 −0.379363
\(903\) 64.7842 2.15588
\(904\) −99.1732 −3.29845
\(905\) 32.7324 1.08806
\(906\) 82.7367 2.74874
\(907\) 26.0115 0.863696 0.431848 0.901946i \(-0.357862\pi\)
0.431848 + 0.901946i \(0.357862\pi\)
\(908\) 5.00200 0.165997
\(909\) −0.0603804 −0.00200269
\(910\) 96.9380 3.21346
\(911\) 38.4828 1.27499 0.637496 0.770454i \(-0.279970\pi\)
0.637496 + 0.770454i \(0.279970\pi\)
\(912\) 103.518 3.42782
\(913\) −13.1657 −0.435722
\(914\) 101.888 3.37017
\(915\) −25.8172 −0.853490
\(916\) −98.1529 −3.24306
\(917\) 31.3699 1.03593
\(918\) −109.267 −3.60634
\(919\) −30.2143 −0.996679 −0.498339 0.866982i \(-0.666057\pi\)
−0.498339 + 0.866982i \(0.666057\pi\)
\(920\) −114.501 −3.77497
\(921\) −26.8170 −0.883652
\(922\) 4.19516 0.138160
\(923\) 26.4143 0.869436
\(924\) −46.9753 −1.54537
\(925\) −9.23416 −0.303617
\(926\) −39.2254 −1.28903
\(927\) −0.310835 −0.0102092
\(928\) −108.378 −3.55768
\(929\) −44.5084 −1.46027 −0.730137 0.683301i \(-0.760544\pi\)
−0.730137 + 0.683301i \(0.760544\pi\)
\(930\) −39.8830 −1.30781
\(931\) 58.9083 1.93064
\(932\) 72.8302 2.38563
\(933\) −1.62196 −0.0531004
\(934\) −45.9925 −1.50492
\(935\) 12.0427 0.393838
\(936\) −1.59184 −0.0520309
\(937\) −35.5029 −1.15983 −0.579915 0.814677i \(-0.696914\pi\)
−0.579915 + 0.814677i \(0.696914\pi\)
\(938\) 85.7575 2.80008
\(939\) 4.75241 0.155089
\(940\) 71.8483 2.34343
\(941\) −7.83018 −0.255256 −0.127628 0.991822i \(-0.540736\pi\)
−0.127628 + 0.991822i \(0.540736\pi\)
\(942\) −1.44243 −0.0469968
\(943\) −29.3124 −0.954542
\(944\) −65.8973 −2.14477
\(945\) −40.1854 −1.30723
\(946\) 21.5580 0.700912
\(947\) 18.2581 0.593309 0.296654 0.954985i \(-0.404129\pi\)
0.296654 + 0.954985i \(0.404129\pi\)
\(948\) 114.851 3.73018
\(949\) −21.0526 −0.683395
\(950\) 24.6113 0.798495
\(951\) 1.44631 0.0468997
\(952\) 368.527 11.9440
\(953\) 8.61510 0.279070 0.139535 0.990217i \(-0.455439\pi\)
0.139535 + 0.990217i \(0.455439\pi\)
\(954\) 0.749128 0.0242539
\(955\) −3.65198 −0.118175
\(956\) 70.0336 2.26505
\(957\) −7.23042 −0.233726
\(958\) −17.1970 −0.555609
\(959\) 49.0246 1.58309
\(960\) 104.605 3.37610
\(961\) −3.37700 −0.108936
\(962\) 47.2794 1.52435
\(963\) 0.657575 0.0211901
\(964\) 115.880 3.73225
\(965\) 7.72771 0.248764
\(966\) −163.625 −5.26455
\(967\) −15.1217 −0.486280 −0.243140 0.969991i \(-0.578177\pi\)
−0.243140 + 0.969991i \(0.578177\pi\)
\(968\) −10.0996 −0.324615
\(969\) −47.0433 −1.51125
\(970\) 18.5734 0.596356
\(971\) −18.3217 −0.587972 −0.293986 0.955810i \(-0.594982\pi\)
−0.293986 + 0.955810i \(0.594982\pi\)
\(972\) 2.03107 0.0651467
\(973\) 58.3555 1.87079
\(974\) 79.3606 2.54288
\(975\) 19.3214 0.618778
\(976\) −156.538 −5.01066
\(977\) 25.9350 0.829734 0.414867 0.909882i \(-0.363828\pi\)
0.414867 + 0.909882i \(0.363828\pi\)
\(978\) −110.511 −3.53375
\(979\) −2.28499 −0.0730286
\(980\) 146.754 4.68787
\(981\) −0.377494 −0.0120525
\(982\) −3.82898 −0.122188
\(983\) −32.8735 −1.04850 −0.524251 0.851564i \(-0.675655\pi\)
−0.524251 + 0.851564i \(0.675655\pi\)
\(984\) 71.6377 2.28373
\(985\) 39.4596 1.25729
\(986\) 87.7944 2.79594
\(987\) 66.3369 2.11153
\(988\) −93.0723 −2.96103
\(989\) 55.4628 1.76361
\(990\) −0.152406 −0.00484377
\(991\) −48.3428 −1.53566 −0.767829 0.640655i \(-0.778663\pi\)
−0.767829 + 0.640655i \(0.778663\pi\)
\(992\) −135.661 −4.30724
\(993\) −58.0824 −1.84319
\(994\) 77.3901 2.45467
\(995\) −9.58983 −0.304018
\(996\) 128.124 4.05977
\(997\) 27.9591 0.885473 0.442736 0.896652i \(-0.354008\pi\)
0.442736 + 0.896652i \(0.354008\pi\)
\(998\) −31.7874 −1.00621
\(999\) −19.5996 −0.620103
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 6017.2.a.f.1.1 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.1 121 1.1 even 1 trivial