Properties

Label 4010.2.a.i.1.7
Level 4010
Weight 2
Character 4010.1
Self dual yes
Analytic conductor 32.020
Analytic rank 1
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-2.65028\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.675556 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.675556 q^{6} -1.96617 q^{7} -1.00000 q^{8} -2.54362 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.675556 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.675556 q^{6} -1.96617 q^{7} -1.00000 q^{8} -2.54362 q^{9} -1.00000 q^{10} -0.702842 q^{11} +0.675556 q^{12} +3.63999 q^{13} +1.96617 q^{14} +0.675556 q^{15} +1.00000 q^{16} -0.463370 q^{17} +2.54362 q^{18} +1.64115 q^{19} +1.00000 q^{20} -1.32826 q^{21} +0.702842 q^{22} -3.53333 q^{23} -0.675556 q^{24} +1.00000 q^{25} -3.63999 q^{26} -3.74503 q^{27} -1.96617 q^{28} +2.53753 q^{29} -0.675556 q^{30} -6.10965 q^{31} -1.00000 q^{32} -0.474809 q^{33} +0.463370 q^{34} -1.96617 q^{35} -2.54362 q^{36} +5.76322 q^{37} -1.64115 q^{38} +2.45902 q^{39} -1.00000 q^{40} +7.14911 q^{41} +1.32826 q^{42} -6.31705 q^{43} -0.702842 q^{44} -2.54362 q^{45} +3.53333 q^{46} +5.97612 q^{47} +0.675556 q^{48} -3.13418 q^{49} -1.00000 q^{50} -0.313032 q^{51} +3.63999 q^{52} -4.57721 q^{53} +3.74503 q^{54} -0.702842 q^{55} +1.96617 q^{56} +1.10869 q^{57} -2.53753 q^{58} -2.56548 q^{59} +0.675556 q^{60} -9.20668 q^{61} +6.10965 q^{62} +5.00120 q^{63} +1.00000 q^{64} +3.63999 q^{65} +0.474809 q^{66} +2.71402 q^{67} -0.463370 q^{68} -2.38696 q^{69} +1.96617 q^{70} -3.57818 q^{71} +2.54362 q^{72} -1.05604 q^{73} -5.76322 q^{74} +0.675556 q^{75} +1.64115 q^{76} +1.38191 q^{77} -2.45902 q^{78} -7.77888 q^{79} +1.00000 q^{80} +5.10089 q^{81} -7.14911 q^{82} -5.64286 q^{83} -1.32826 q^{84} -0.463370 q^{85} +6.31705 q^{86} +1.71424 q^{87} +0.702842 q^{88} +2.42510 q^{89} +2.54362 q^{90} -7.15683 q^{91} -3.53333 q^{92} -4.12741 q^{93} -5.97612 q^{94} +1.64115 q^{95} -0.675556 q^{96} +14.3124 q^{97} +3.13418 q^{98} +1.78776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} - 10q^{10} - 11q^{11} - 4q^{12} + 6q^{13} + 3q^{14} - 4q^{15} + 10q^{16} + 9q^{17} - 6q^{18} - 13q^{19} + 10q^{20} - 24q^{21} + 11q^{22} - 3q^{23} + 4q^{24} + 10q^{25} - 6q^{26} - 10q^{27} - 3q^{28} - 4q^{29} + 4q^{30} - 17q^{31} - 10q^{32} - 2q^{33} - 9q^{34} - 3q^{35} + 6q^{36} - 15q^{37} + 13q^{38} - 6q^{39} - 10q^{40} - 11q^{41} + 24q^{42} - 11q^{43} - 11q^{44} + 6q^{45} + 3q^{46} + 3q^{47} - 4q^{48} - 5q^{49} - 10q^{50} - 21q^{51} + 6q^{52} + 25q^{53} + 10q^{54} - 11q^{55} + 3q^{56} + 31q^{57} + 4q^{58} - 46q^{59} - 4q^{60} - 54q^{61} + 17q^{62} - 6q^{63} + 10q^{64} + 6q^{65} + 2q^{66} - 26q^{67} + 9q^{68} - 9q^{69} + 3q^{70} - 16q^{71} - 6q^{72} + 4q^{73} + 15q^{74} - 4q^{75} - 13q^{76} + 11q^{77} + 6q^{78} - 19q^{79} + 10q^{80} - 6q^{81} + 11q^{82} + 19q^{83} - 24q^{84} + 9q^{85} + 11q^{86} + 28q^{87} + 11q^{88} - 30q^{89} - 6q^{90} - 38q^{91} - 3q^{92} - 18q^{93} - 3q^{94} - 13q^{95} + 4q^{96} - 16q^{97} + 5q^{98} - 59q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.675556 0.390033 0.195016 0.980800i \(-0.437524\pi\)
0.195016 + 0.980800i \(0.437524\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −0.675556 −0.275795
\(7\) −1.96617 −0.743142 −0.371571 0.928404i \(-0.621181\pi\)
−0.371571 + 0.928404i \(0.621181\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.54362 −0.847875
\(10\) −1.00000 −0.316228
\(11\) −0.702842 −0.211915 −0.105957 0.994371i \(-0.533791\pi\)
−0.105957 + 0.994371i \(0.533791\pi\)
\(12\) 0.675556 0.195016
\(13\) 3.63999 1.00955 0.504775 0.863251i \(-0.331575\pi\)
0.504775 + 0.863251i \(0.331575\pi\)
\(14\) 1.96617 0.525481
\(15\) 0.675556 0.174428
\(16\) 1.00000 0.250000
\(17\) −0.463370 −0.112384 −0.0561919 0.998420i \(-0.517896\pi\)
−0.0561919 + 0.998420i \(0.517896\pi\)
\(18\) 2.54362 0.599538
\(19\) 1.64115 0.376505 0.188252 0.982121i \(-0.439718\pi\)
0.188252 + 0.982121i \(0.439718\pi\)
\(20\) 1.00000 0.223607
\(21\) −1.32826 −0.289850
\(22\) 0.702842 0.149846
\(23\) −3.53333 −0.736750 −0.368375 0.929677i \(-0.620086\pi\)
−0.368375 + 0.929677i \(0.620086\pi\)
\(24\) −0.675556 −0.137897
\(25\) 1.00000 0.200000
\(26\) −3.63999 −0.713860
\(27\) −3.74503 −0.720731
\(28\) −1.96617 −0.371571
\(29\) 2.53753 0.471208 0.235604 0.971849i \(-0.424293\pi\)
0.235604 + 0.971849i \(0.424293\pi\)
\(30\) −0.675556 −0.123339
\(31\) −6.10965 −1.09733 −0.548663 0.836044i \(-0.684863\pi\)
−0.548663 + 0.836044i \(0.684863\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.474809 −0.0826537
\(34\) 0.463370 0.0794673
\(35\) −1.96617 −0.332343
\(36\) −2.54362 −0.423937
\(37\) 5.76322 0.947468 0.473734 0.880668i \(-0.342906\pi\)
0.473734 + 0.880668i \(0.342906\pi\)
\(38\) −1.64115 −0.266229
\(39\) 2.45902 0.393758
\(40\) −1.00000 −0.158114
\(41\) 7.14911 1.11650 0.558251 0.829672i \(-0.311472\pi\)
0.558251 + 0.829672i \(0.311472\pi\)
\(42\) 1.32826 0.204955
\(43\) −6.31705 −0.963342 −0.481671 0.876352i \(-0.659970\pi\)
−0.481671 + 0.876352i \(0.659970\pi\)
\(44\) −0.702842 −0.105957
\(45\) −2.54362 −0.379181
\(46\) 3.53333 0.520961
\(47\) 5.97612 0.871707 0.435854 0.900018i \(-0.356447\pi\)
0.435854 + 0.900018i \(0.356447\pi\)
\(48\) 0.675556 0.0975082
\(49\) −3.13418 −0.447739
\(50\) −1.00000 −0.141421
\(51\) −0.313032 −0.0438333
\(52\) 3.63999 0.504775
\(53\) −4.57721 −0.628729 −0.314364 0.949302i \(-0.601791\pi\)
−0.314364 + 0.949302i \(0.601791\pi\)
\(54\) 3.74503 0.509634
\(55\) −0.702842 −0.0947711
\(56\) 1.96617 0.262741
\(57\) 1.10869 0.146849
\(58\) −2.53753 −0.333194
\(59\) −2.56548 −0.333997 −0.166998 0.985957i \(-0.553407\pi\)
−0.166998 + 0.985957i \(0.553407\pi\)
\(60\) 0.675556 0.0872139
\(61\) −9.20668 −1.17879 −0.589397 0.807843i \(-0.700635\pi\)
−0.589397 + 0.807843i \(0.700635\pi\)
\(62\) 6.10965 0.775926
\(63\) 5.00120 0.630092
\(64\) 1.00000 0.125000
\(65\) 3.63999 0.451485
\(66\) 0.474809 0.0584450
\(67\) 2.71402 0.331570 0.165785 0.986162i \(-0.446984\pi\)
0.165785 + 0.986162i \(0.446984\pi\)
\(68\) −0.463370 −0.0561919
\(69\) −2.38696 −0.287357
\(70\) 1.96617 0.235002
\(71\) −3.57818 −0.424651 −0.212326 0.977199i \(-0.568104\pi\)
−0.212326 + 0.977199i \(0.568104\pi\)
\(72\) 2.54362 0.299769
\(73\) −1.05604 −0.123600 −0.0617999 0.998089i \(-0.519684\pi\)
−0.0617999 + 0.998089i \(0.519684\pi\)
\(74\) −5.76322 −0.669961
\(75\) 0.675556 0.0780065
\(76\) 1.64115 0.188252
\(77\) 1.38191 0.157483
\(78\) −2.45902 −0.278429
\(79\) −7.77888 −0.875192 −0.437596 0.899172i \(-0.644170\pi\)
−0.437596 + 0.899172i \(0.644170\pi\)
\(80\) 1.00000 0.111803
\(81\) 5.10089 0.566766
\(82\) −7.14911 −0.789487
\(83\) −5.64286 −0.619384 −0.309692 0.950837i \(-0.600226\pi\)
−0.309692 + 0.950837i \(0.600226\pi\)
\(84\) −1.32826 −0.144925
\(85\) −0.463370 −0.0502595
\(86\) 6.31705 0.681186
\(87\) 1.71424 0.183786
\(88\) 0.702842 0.0749232
\(89\) 2.42510 0.257060 0.128530 0.991706i \(-0.458974\pi\)
0.128530 + 0.991706i \(0.458974\pi\)
\(90\) 2.54362 0.268121
\(91\) −7.15683 −0.750240
\(92\) −3.53333 −0.368375
\(93\) −4.12741 −0.427993
\(94\) −5.97612 −0.616390
\(95\) 1.64115 0.168378
\(96\) −0.675556 −0.0689487
\(97\) 14.3124 1.45321 0.726604 0.687057i \(-0.241098\pi\)
0.726604 + 0.687057i \(0.241098\pi\)
\(98\) 3.13418 0.316599
\(99\) 1.78776 0.179677
\(100\) 1.00000 0.100000
\(101\) 11.1101 1.10549 0.552747 0.833349i \(-0.313580\pi\)
0.552747 + 0.833349i \(0.313580\pi\)
\(102\) 0.313032 0.0309948
\(103\) −13.5007 −1.33026 −0.665130 0.746727i \(-0.731624\pi\)
−0.665130 + 0.746727i \(0.731624\pi\)
\(104\) −3.63999 −0.356930
\(105\) −1.32826 −0.129625
\(106\) 4.57721 0.444578
\(107\) −9.98140 −0.964939 −0.482469 0.875913i \(-0.660260\pi\)
−0.482469 + 0.875913i \(0.660260\pi\)
\(108\) −3.74503 −0.360366
\(109\) −17.3033 −1.65736 −0.828678 0.559725i \(-0.810907\pi\)
−0.828678 + 0.559725i \(0.810907\pi\)
\(110\) 0.702842 0.0670133
\(111\) 3.89338 0.369543
\(112\) −1.96617 −0.185786
\(113\) −15.8435 −1.49043 −0.745215 0.666824i \(-0.767653\pi\)
−0.745215 + 0.666824i \(0.767653\pi\)
\(114\) −1.10869 −0.103838
\(115\) −3.53333 −0.329485
\(116\) 2.53753 0.235604
\(117\) −9.25876 −0.855972
\(118\) 2.56548 0.236171
\(119\) 0.911064 0.0835171
\(120\) −0.675556 −0.0616696
\(121\) −10.5060 −0.955092
\(122\) 9.20668 0.833534
\(123\) 4.82962 0.435472
\(124\) −6.10965 −0.548663
\(125\) 1.00000 0.0894427
\(126\) −5.00120 −0.445542
\(127\) −2.46196 −0.218463 −0.109232 0.994016i \(-0.534839\pi\)
−0.109232 + 0.994016i \(0.534839\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.26753 −0.375735
\(130\) −3.63999 −0.319248
\(131\) −12.1540 −1.06190 −0.530950 0.847403i \(-0.678165\pi\)
−0.530950 + 0.847403i \(0.678165\pi\)
\(132\) −0.474809 −0.0413268
\(133\) −3.22677 −0.279797
\(134\) −2.71402 −0.234456
\(135\) −3.74503 −0.322321
\(136\) 0.463370 0.0397336
\(137\) −14.9534 −1.27755 −0.638777 0.769392i \(-0.720559\pi\)
−0.638777 + 0.769392i \(0.720559\pi\)
\(138\) 2.38696 0.203192
\(139\) −21.8514 −1.85341 −0.926704 0.375792i \(-0.877371\pi\)
−0.926704 + 0.375792i \(0.877371\pi\)
\(140\) −1.96617 −0.166172
\(141\) 4.03721 0.339994
\(142\) 3.57818 0.300274
\(143\) −2.55833 −0.213939
\(144\) −2.54362 −0.211969
\(145\) 2.53753 0.210730
\(146\) 1.05604 0.0873982
\(147\) −2.11731 −0.174633
\(148\) 5.76322 0.473734
\(149\) 3.79711 0.311071 0.155536 0.987830i \(-0.450290\pi\)
0.155536 + 0.987830i \(0.450290\pi\)
\(150\) −0.675556 −0.0551589
\(151\) −5.98467 −0.487026 −0.243513 0.969898i \(-0.578300\pi\)
−0.243513 + 0.969898i \(0.578300\pi\)
\(152\) −1.64115 −0.133114
\(153\) 1.17864 0.0952873
\(154\) −1.38191 −0.111357
\(155\) −6.10965 −0.490739
\(156\) 2.45902 0.196879
\(157\) 18.7300 1.49482 0.747409 0.664364i \(-0.231297\pi\)
0.747409 + 0.664364i \(0.231297\pi\)
\(158\) 7.77888 0.618854
\(159\) −3.09217 −0.245225
\(160\) −1.00000 −0.0790569
\(161\) 6.94712 0.547510
\(162\) −5.10089 −0.400764
\(163\) 24.0979 1.88750 0.943748 0.330666i \(-0.107273\pi\)
0.943748 + 0.330666i \(0.107273\pi\)
\(164\) 7.14911 0.558251
\(165\) −0.474809 −0.0369638
\(166\) 5.64286 0.437971
\(167\) −6.60551 −0.511150 −0.255575 0.966789i \(-0.582265\pi\)
−0.255575 + 0.966789i \(0.582265\pi\)
\(168\) 1.32826 0.102477
\(169\) 0.249501 0.0191924
\(170\) 0.463370 0.0355389
\(171\) −4.17446 −0.319229
\(172\) −6.31705 −0.481671
\(173\) −15.0557 −1.14466 −0.572332 0.820022i \(-0.693961\pi\)
−0.572332 + 0.820022i \(0.693961\pi\)
\(174\) −1.71424 −0.129957
\(175\) −1.96617 −0.148628
\(176\) −0.702842 −0.0529787
\(177\) −1.73312 −0.130270
\(178\) −2.42510 −0.181769
\(179\) 12.5215 0.935904 0.467952 0.883754i \(-0.344992\pi\)
0.467952 + 0.883754i \(0.344992\pi\)
\(180\) −2.54362 −0.189591
\(181\) −23.0329 −1.71202 −0.856012 0.516956i \(-0.827065\pi\)
−0.856012 + 0.516956i \(0.827065\pi\)
\(182\) 7.15683 0.530500
\(183\) −6.21963 −0.459768
\(184\) 3.53333 0.260480
\(185\) 5.76322 0.423721
\(186\) 4.12741 0.302637
\(187\) 0.325676 0.0238158
\(188\) 5.97612 0.435854
\(189\) 7.36337 0.535606
\(190\) −1.64115 −0.119061
\(191\) 15.0467 1.08874 0.544371 0.838844i \(-0.316768\pi\)
0.544371 + 0.838844i \(0.316768\pi\)
\(192\) 0.675556 0.0487541
\(193\) −19.7068 −1.41852 −0.709262 0.704945i \(-0.750972\pi\)
−0.709262 + 0.704945i \(0.750972\pi\)
\(194\) −14.3124 −1.02757
\(195\) 2.45902 0.176094
\(196\) −3.13418 −0.223870
\(197\) 15.6305 1.11363 0.556813 0.830638i \(-0.312024\pi\)
0.556813 + 0.830638i \(0.312024\pi\)
\(198\) −1.78776 −0.127051
\(199\) −6.63045 −0.470020 −0.235010 0.971993i \(-0.575512\pi\)
−0.235010 + 0.971993i \(0.575512\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 1.83347 0.129323
\(202\) −11.1101 −0.781703
\(203\) −4.98922 −0.350174
\(204\) −0.313032 −0.0219167
\(205\) 7.14911 0.499315
\(206\) 13.5007 0.940636
\(207\) 8.98746 0.624671
\(208\) 3.63999 0.252388
\(209\) −1.15347 −0.0797869
\(210\) 1.32826 0.0916586
\(211\) 18.7194 1.28870 0.644350 0.764731i \(-0.277128\pi\)
0.644350 + 0.764731i \(0.277128\pi\)
\(212\) −4.57721 −0.314364
\(213\) −2.41726 −0.165628
\(214\) 9.98140 0.682315
\(215\) −6.31705 −0.430820
\(216\) 3.74503 0.254817
\(217\) 12.0126 0.815469
\(218\) 17.3033 1.17193
\(219\) −0.713412 −0.0482079
\(220\) −0.702842 −0.0473856
\(221\) −1.68666 −0.113457
\(222\) −3.89338 −0.261307
\(223\) −7.21360 −0.483059 −0.241529 0.970394i \(-0.577649\pi\)
−0.241529 + 0.970394i \(0.577649\pi\)
\(224\) 1.96617 0.131370
\(225\) −2.54362 −0.169575
\(226\) 15.8435 1.05389
\(227\) 19.4540 1.29120 0.645602 0.763674i \(-0.276606\pi\)
0.645602 + 0.763674i \(0.276606\pi\)
\(228\) 1.10869 0.0734245
\(229\) 11.2055 0.740479 0.370239 0.928936i \(-0.379276\pi\)
0.370239 + 0.928936i \(0.379276\pi\)
\(230\) 3.53333 0.232981
\(231\) 0.933555 0.0614234
\(232\) −2.53753 −0.166597
\(233\) 17.7284 1.16143 0.580714 0.814108i \(-0.302773\pi\)
0.580714 + 0.814108i \(0.302773\pi\)
\(234\) 9.25876 0.605264
\(235\) 5.97612 0.389839
\(236\) −2.56548 −0.166998
\(237\) −5.25507 −0.341353
\(238\) −0.911064 −0.0590555
\(239\) −13.2487 −0.856990 −0.428495 0.903544i \(-0.640956\pi\)
−0.428495 + 0.903544i \(0.640956\pi\)
\(240\) 0.675556 0.0436070
\(241\) 6.61312 0.425989 0.212994 0.977053i \(-0.431678\pi\)
0.212994 + 0.977053i \(0.431678\pi\)
\(242\) 10.5060 0.675352
\(243\) 14.6810 0.941789
\(244\) −9.20668 −0.589397
\(245\) −3.13418 −0.200235
\(246\) −4.82962 −0.307926
\(247\) 5.97375 0.380100
\(248\) 6.10965 0.387963
\(249\) −3.81207 −0.241580
\(250\) −1.00000 −0.0632456
\(251\) −26.0274 −1.64283 −0.821417 0.570329i \(-0.806816\pi\)
−0.821417 + 0.570329i \(0.806816\pi\)
\(252\) 5.00120 0.315046
\(253\) 2.48337 0.156128
\(254\) 2.46196 0.154477
\(255\) −0.313032 −0.0196029
\(256\) 1.00000 0.0625000
\(257\) −8.14027 −0.507776 −0.253888 0.967234i \(-0.581710\pi\)
−0.253888 + 0.967234i \(0.581710\pi\)
\(258\) 4.26753 0.265685
\(259\) −11.3315 −0.704104
\(260\) 3.63999 0.225742
\(261\) −6.45452 −0.399525
\(262\) 12.1540 0.750877
\(263\) 2.11090 0.130164 0.0650820 0.997880i \(-0.479269\pi\)
0.0650820 + 0.997880i \(0.479269\pi\)
\(264\) 0.474809 0.0292225
\(265\) −4.57721 −0.281176
\(266\) 3.22677 0.197846
\(267\) 1.63829 0.100262
\(268\) 2.71402 0.165785
\(269\) −19.0580 −1.16199 −0.580993 0.813909i \(-0.697336\pi\)
−0.580993 + 0.813909i \(0.697336\pi\)
\(270\) 3.74503 0.227915
\(271\) −5.04991 −0.306760 −0.153380 0.988167i \(-0.549016\pi\)
−0.153380 + 0.988167i \(0.549016\pi\)
\(272\) −0.463370 −0.0280959
\(273\) −4.83484 −0.292618
\(274\) 14.9534 0.903367
\(275\) −0.702842 −0.0423829
\(276\) −2.38696 −0.143678
\(277\) −9.21670 −0.553778 −0.276889 0.960902i \(-0.589303\pi\)
−0.276889 + 0.960902i \(0.589303\pi\)
\(278\) 21.8514 1.31056
\(279\) 15.5407 0.930394
\(280\) 1.96617 0.117501
\(281\) −6.57568 −0.392272 −0.196136 0.980577i \(-0.562839\pi\)
−0.196136 + 0.980577i \(0.562839\pi\)
\(282\) −4.03721 −0.240412
\(283\) 18.7413 1.11406 0.557028 0.830494i \(-0.311942\pi\)
0.557028 + 0.830494i \(0.311942\pi\)
\(284\) −3.57818 −0.212326
\(285\) 1.10869 0.0656729
\(286\) 2.55833 0.151277
\(287\) −14.0564 −0.829721
\(288\) 2.54362 0.149884
\(289\) −16.7853 −0.987370
\(290\) −2.53753 −0.149009
\(291\) 9.66886 0.566798
\(292\) −1.05604 −0.0617999
\(293\) 20.3420 1.18839 0.594195 0.804321i \(-0.297471\pi\)
0.594195 + 0.804321i \(0.297471\pi\)
\(294\) 2.11731 0.123484
\(295\) −2.56548 −0.149368
\(296\) −5.76322 −0.334981
\(297\) 2.63216 0.152734
\(298\) −3.79711 −0.219961
\(299\) −12.8613 −0.743786
\(300\) 0.675556 0.0390033
\(301\) 12.4204 0.715900
\(302\) 5.98467 0.344379
\(303\) 7.50548 0.431179
\(304\) 1.64115 0.0941261
\(305\) −9.20668 −0.527173
\(306\) −1.17864 −0.0673783
\(307\) −9.26421 −0.528737 −0.264368 0.964422i \(-0.585163\pi\)
−0.264368 + 0.964422i \(0.585163\pi\)
\(308\) 1.38191 0.0787414
\(309\) −9.12046 −0.518845
\(310\) 6.10965 0.347005
\(311\) −10.3280 −0.585650 −0.292825 0.956166i \(-0.594595\pi\)
−0.292825 + 0.956166i \(0.594595\pi\)
\(312\) −2.45902 −0.139214
\(313\) −24.1184 −1.36325 −0.681626 0.731701i \(-0.738727\pi\)
−0.681626 + 0.731701i \(0.738727\pi\)
\(314\) −18.7300 −1.05700
\(315\) 5.00120 0.281786
\(316\) −7.77888 −0.437596
\(317\) 19.8911 1.11720 0.558598 0.829438i \(-0.311339\pi\)
0.558598 + 0.829438i \(0.311339\pi\)
\(318\) 3.09217 0.173400
\(319\) −1.78348 −0.0998558
\(320\) 1.00000 0.0559017
\(321\) −6.74300 −0.376358
\(322\) −6.94712 −0.387148
\(323\) −0.760457 −0.0423130
\(324\) 5.10089 0.283383
\(325\) 3.63999 0.201910
\(326\) −24.0979 −1.33466
\(327\) −11.6894 −0.646423
\(328\) −7.14911 −0.394743
\(329\) −11.7501 −0.647803
\(330\) 0.474809 0.0261374
\(331\) −25.8891 −1.42299 −0.711496 0.702691i \(-0.751982\pi\)
−0.711496 + 0.702691i \(0.751982\pi\)
\(332\) −5.64286 −0.309692
\(333\) −14.6595 −0.803334
\(334\) 6.60551 0.361437
\(335\) 2.71402 0.148283
\(336\) −1.32826 −0.0724625
\(337\) 14.9572 0.814770 0.407385 0.913257i \(-0.366441\pi\)
0.407385 + 0.913257i \(0.366441\pi\)
\(338\) −0.249501 −0.0135711
\(339\) −10.7032 −0.581317
\(340\) −0.463370 −0.0251298
\(341\) 4.29412 0.232539
\(342\) 4.17446 0.225729
\(343\) 19.9255 1.07588
\(344\) 6.31705 0.340593
\(345\) −2.38696 −0.128510
\(346\) 15.0557 0.809400
\(347\) 27.7319 1.48873 0.744363 0.667776i \(-0.232753\pi\)
0.744363 + 0.667776i \(0.232753\pi\)
\(348\) 1.71424 0.0918932
\(349\) 2.15312 0.115254 0.0576270 0.998338i \(-0.481647\pi\)
0.0576270 + 0.998338i \(0.481647\pi\)
\(350\) 1.96617 0.105096
\(351\) −13.6319 −0.727615
\(352\) 0.702842 0.0374616
\(353\) 6.05838 0.322455 0.161228 0.986917i \(-0.448455\pi\)
0.161228 + 0.986917i \(0.448455\pi\)
\(354\) 1.73312 0.0921145
\(355\) −3.57818 −0.189910
\(356\) 2.42510 0.128530
\(357\) 0.615475 0.0325744
\(358\) −12.5215 −0.661784
\(359\) −26.0891 −1.37693 −0.688465 0.725270i \(-0.741715\pi\)
−0.688465 + 0.725270i \(0.741715\pi\)
\(360\) 2.54362 0.134061
\(361\) −16.3066 −0.858244
\(362\) 23.0329 1.21058
\(363\) −7.09740 −0.372517
\(364\) −7.15683 −0.375120
\(365\) −1.05604 −0.0552755
\(366\) 6.21963 0.325105
\(367\) 2.08709 0.108945 0.0544725 0.998515i \(-0.482652\pi\)
0.0544725 + 0.998515i \(0.482652\pi\)
\(368\) −3.53333 −0.184187
\(369\) −18.1846 −0.946654
\(370\) −5.76322 −0.299616
\(371\) 8.99958 0.467235
\(372\) −4.12741 −0.213996
\(373\) −28.8649 −1.49457 −0.747284 0.664504i \(-0.768643\pi\)
−0.747284 + 0.664504i \(0.768643\pi\)
\(374\) −0.325676 −0.0168403
\(375\) 0.675556 0.0348856
\(376\) −5.97612 −0.308195
\(377\) 9.23658 0.475708
\(378\) −7.36337 −0.378731
\(379\) 7.44485 0.382416 0.191208 0.981550i \(-0.438759\pi\)
0.191208 + 0.981550i \(0.438759\pi\)
\(380\) 1.64115 0.0841890
\(381\) −1.66319 −0.0852079
\(382\) −15.0467 −0.769858
\(383\) −18.3001 −0.935092 −0.467546 0.883969i \(-0.654862\pi\)
−0.467546 + 0.883969i \(0.654862\pi\)
\(384\) −0.675556 −0.0344743
\(385\) 1.38191 0.0704285
\(386\) 19.7068 1.00305
\(387\) 16.0682 0.816793
\(388\) 14.3124 0.726604
\(389\) 22.2317 1.12719 0.563597 0.826050i \(-0.309417\pi\)
0.563597 + 0.826050i \(0.309417\pi\)
\(390\) −2.45902 −0.124517
\(391\) 1.63724 0.0827987
\(392\) 3.13418 0.158300
\(393\) −8.21071 −0.414176
\(394\) −15.6305 −0.787452
\(395\) −7.77888 −0.391398
\(396\) 1.78776 0.0898385
\(397\) 3.83234 0.192340 0.0961699 0.995365i \(-0.469341\pi\)
0.0961699 + 0.995365i \(0.469341\pi\)
\(398\) 6.63045 0.332354
\(399\) −2.17987 −0.109130
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) −1.83347 −0.0914453
\(403\) −22.2390 −1.10781
\(404\) 11.1101 0.552747
\(405\) 5.10089 0.253465
\(406\) 4.98922 0.247611
\(407\) −4.05063 −0.200782
\(408\) 0.313032 0.0154974
\(409\) 20.3572 1.00660 0.503300 0.864112i \(-0.332119\pi\)
0.503300 + 0.864112i \(0.332119\pi\)
\(410\) −7.14911 −0.353069
\(411\) −10.1019 −0.498288
\(412\) −13.5007 −0.665130
\(413\) 5.04416 0.248207
\(414\) −8.98746 −0.441709
\(415\) −5.64286 −0.276997
\(416\) −3.63999 −0.178465
\(417\) −14.7618 −0.722890
\(418\) 1.15347 0.0564178
\(419\) 20.8407 1.01814 0.509068 0.860726i \(-0.329990\pi\)
0.509068 + 0.860726i \(0.329990\pi\)
\(420\) −1.32826 −0.0648124
\(421\) 23.1118 1.12640 0.563200 0.826321i \(-0.309570\pi\)
0.563200 + 0.826321i \(0.309570\pi\)
\(422\) −18.7194 −0.911248
\(423\) −15.2010 −0.739098
\(424\) 4.57721 0.222289
\(425\) −0.463370 −0.0224767
\(426\) 2.41726 0.117117
\(427\) 18.1019 0.876012
\(428\) −9.98140 −0.482469
\(429\) −1.72830 −0.0834430
\(430\) 6.31705 0.304635
\(431\) −26.9560 −1.29842 −0.649212 0.760608i \(-0.724901\pi\)
−0.649212 + 0.760608i \(0.724901\pi\)
\(432\) −3.74503 −0.180183
\(433\) 1.05846 0.0508662 0.0254331 0.999677i \(-0.491904\pi\)
0.0254331 + 0.999677i \(0.491904\pi\)
\(434\) −12.0126 −0.576624
\(435\) 1.71424 0.0821917
\(436\) −17.3033 −0.828678
\(437\) −5.79871 −0.277390
\(438\) 0.713412 0.0340882
\(439\) −26.9332 −1.28545 −0.642725 0.766097i \(-0.722196\pi\)
−0.642725 + 0.766097i \(0.722196\pi\)
\(440\) 0.702842 0.0335067
\(441\) 7.97216 0.379627
\(442\) 1.68666 0.0802262
\(443\) 3.79606 0.180356 0.0901782 0.995926i \(-0.471256\pi\)
0.0901782 + 0.995926i \(0.471256\pi\)
\(444\) 3.89338 0.184772
\(445\) 2.42510 0.114961
\(446\) 7.21360 0.341574
\(447\) 2.56516 0.121328
\(448\) −1.96617 −0.0928928
\(449\) −19.9784 −0.942841 −0.471420 0.881909i \(-0.656258\pi\)
−0.471420 + 0.881909i \(0.656258\pi\)
\(450\) 2.54362 0.119908
\(451\) −5.02469 −0.236603
\(452\) −15.8435 −0.745215
\(453\) −4.04298 −0.189956
\(454\) −19.4540 −0.913020
\(455\) −7.15683 −0.335517
\(456\) −1.10869 −0.0519190
\(457\) −12.0619 −0.564231 −0.282115 0.959380i \(-0.591036\pi\)
−0.282115 + 0.959380i \(0.591036\pi\)
\(458\) −11.2055 −0.523598
\(459\) 1.73533 0.0809985
\(460\) −3.53333 −0.164742
\(461\) −23.7685 −1.10701 −0.553504 0.832847i \(-0.686710\pi\)
−0.553504 + 0.832847i \(0.686710\pi\)
\(462\) −0.933555 −0.0434329
\(463\) −25.5650 −1.18810 −0.594052 0.804426i \(-0.702473\pi\)
−0.594052 + 0.804426i \(0.702473\pi\)
\(464\) 2.53753 0.117802
\(465\) −4.12741 −0.191404
\(466\) −17.7284 −0.821254
\(467\) 1.38486 0.0640835 0.0320418 0.999487i \(-0.489799\pi\)
0.0320418 + 0.999487i \(0.489799\pi\)
\(468\) −9.25876 −0.427986
\(469\) −5.33623 −0.246404
\(470\) −5.97612 −0.275658
\(471\) 12.6532 0.583028
\(472\) 2.56548 0.118086
\(473\) 4.43989 0.204146
\(474\) 5.25507 0.241373
\(475\) 1.64115 0.0753009
\(476\) 0.911064 0.0417586
\(477\) 11.6427 0.533083
\(478\) 13.2487 0.605983
\(479\) −9.15088 −0.418114 −0.209057 0.977903i \(-0.567039\pi\)
−0.209057 + 0.977903i \(0.567039\pi\)
\(480\) −0.675556 −0.0308348
\(481\) 20.9781 0.956517
\(482\) −6.61312 −0.301219
\(483\) 4.69317 0.213547
\(484\) −10.5060 −0.477546
\(485\) 14.3124 0.649894
\(486\) −14.6810 −0.665945
\(487\) 9.41697 0.426724 0.213362 0.976973i \(-0.431559\pi\)
0.213362 + 0.976973i \(0.431559\pi\)
\(488\) 9.20668 0.416767
\(489\) 16.2795 0.736185
\(490\) 3.13418 0.141588
\(491\) 21.6913 0.978917 0.489458 0.872027i \(-0.337195\pi\)
0.489458 + 0.872027i \(0.337195\pi\)
\(492\) 4.82962 0.217736
\(493\) −1.17582 −0.0529561
\(494\) −5.97375 −0.268772
\(495\) 1.78776 0.0803540
\(496\) −6.10965 −0.274331
\(497\) 7.03530 0.315577
\(498\) 3.81207 0.170823
\(499\) −38.4965 −1.72334 −0.861670 0.507468i \(-0.830581\pi\)
−0.861670 + 0.507468i \(0.830581\pi\)
\(500\) 1.00000 0.0447214
\(501\) −4.46239 −0.199365
\(502\) 26.0274 1.16166
\(503\) −18.5035 −0.825029 −0.412515 0.910951i \(-0.635349\pi\)
−0.412515 + 0.910951i \(0.635349\pi\)
\(504\) −5.00120 −0.222771
\(505\) 11.1101 0.494392
\(506\) −2.48337 −0.110399
\(507\) 0.168552 0.00748566
\(508\) −2.46196 −0.109232
\(509\) 29.3133 1.29929 0.649644 0.760239i \(-0.274918\pi\)
0.649644 + 0.760239i \(0.274918\pi\)
\(510\) 0.313032 0.0138613
\(511\) 2.07635 0.0918522
\(512\) −1.00000 −0.0441942
\(513\) −6.14614 −0.271359
\(514\) 8.14027 0.359052
\(515\) −13.5007 −0.594910
\(516\) −4.26753 −0.187867
\(517\) −4.20027 −0.184728
\(518\) 11.3315 0.497877
\(519\) −10.1710 −0.446456
\(520\) −3.63999 −0.159624
\(521\) −28.6667 −1.25591 −0.627956 0.778249i \(-0.716108\pi\)
−0.627956 + 0.778249i \(0.716108\pi\)
\(522\) 6.45452 0.282507
\(523\) 35.7366 1.56265 0.781326 0.624123i \(-0.214543\pi\)
0.781326 + 0.624123i \(0.214543\pi\)
\(524\) −12.1540 −0.530950
\(525\) −1.32826 −0.0579700
\(526\) −2.11090 −0.0920398
\(527\) 2.83103 0.123322
\(528\) −0.474809 −0.0206634
\(529\) −10.5156 −0.457200
\(530\) 4.57721 0.198821
\(531\) 6.52561 0.283187
\(532\) −3.22677 −0.139898
\(533\) 26.0226 1.12717
\(534\) −1.63829 −0.0708959
\(535\) −9.98140 −0.431534
\(536\) −2.71402 −0.117228
\(537\) 8.45900 0.365033
\(538\) 19.0580 0.821648
\(539\) 2.20283 0.0948826
\(540\) −3.74503 −0.161160
\(541\) 34.4528 1.48124 0.740620 0.671924i \(-0.234532\pi\)
0.740620 + 0.671924i \(0.234532\pi\)
\(542\) 5.04991 0.216912
\(543\) −15.5600 −0.667745
\(544\) 0.463370 0.0198668
\(545\) −17.3033 −0.741192
\(546\) 4.83484 0.206912
\(547\) −23.5201 −1.00565 −0.502824 0.864389i \(-0.667705\pi\)
−0.502824 + 0.864389i \(0.667705\pi\)
\(548\) −14.9534 −0.638777
\(549\) 23.4183 0.999470
\(550\) 0.702842 0.0299693
\(551\) 4.16446 0.177412
\(552\) 2.38696 0.101596
\(553\) 15.2946 0.650392
\(554\) 9.21670 0.391580
\(555\) 3.89338 0.165265
\(556\) −21.8514 −0.926704
\(557\) 7.16891 0.303757 0.151878 0.988399i \(-0.451468\pi\)
0.151878 + 0.988399i \(0.451468\pi\)
\(558\) −15.5407 −0.657888
\(559\) −22.9940 −0.972542
\(560\) −1.96617 −0.0830859
\(561\) 0.220012 0.00928893
\(562\) 6.57568 0.277378
\(563\) −6.13281 −0.258467 −0.129234 0.991614i \(-0.541252\pi\)
−0.129234 + 0.991614i \(0.541252\pi\)
\(564\) 4.03721 0.169997
\(565\) −15.8435 −0.666541
\(566\) −18.7413 −0.787757
\(567\) −10.0292 −0.421188
\(568\) 3.57818 0.150137
\(569\) −36.2932 −1.52149 −0.760745 0.649050i \(-0.775166\pi\)
−0.760745 + 0.649050i \(0.775166\pi\)
\(570\) −1.10869 −0.0464378
\(571\) −4.27540 −0.178920 −0.0894600 0.995990i \(-0.528514\pi\)
−0.0894600 + 0.995990i \(0.528514\pi\)
\(572\) −2.55833 −0.106969
\(573\) 10.1649 0.424645
\(574\) 14.0564 0.586701
\(575\) −3.53333 −0.147350
\(576\) −2.54362 −0.105984
\(577\) 13.9229 0.579616 0.289808 0.957085i \(-0.406408\pi\)
0.289808 + 0.957085i \(0.406408\pi\)
\(578\) 16.7853 0.698176
\(579\) −13.3130 −0.553271
\(580\) 2.53753 0.105365
\(581\) 11.0948 0.460291
\(582\) −9.66886 −0.400787
\(583\) 3.21706 0.133237
\(584\) 1.05604 0.0436991
\(585\) −9.25876 −0.382802
\(586\) −20.3420 −0.840319
\(587\) −30.9970 −1.27938 −0.639692 0.768631i \(-0.720938\pi\)
−0.639692 + 0.768631i \(0.720938\pi\)
\(588\) −2.11731 −0.0873165
\(589\) −10.0268 −0.413148
\(590\) 2.56548 0.105619
\(591\) 10.5593 0.434350
\(592\) 5.76322 0.236867
\(593\) 29.1063 1.19525 0.597625 0.801775i \(-0.296111\pi\)
0.597625 + 0.801775i \(0.296111\pi\)
\(594\) −2.63216 −0.107999
\(595\) 0.911064 0.0373500
\(596\) 3.79711 0.155536
\(597\) −4.47924 −0.183323
\(598\) 12.8613 0.525936
\(599\) 34.1254 1.39433 0.697163 0.716912i \(-0.254445\pi\)
0.697163 + 0.716912i \(0.254445\pi\)
\(600\) −0.675556 −0.0275795
\(601\) 34.7085 1.41579 0.707895 0.706318i \(-0.249645\pi\)
0.707895 + 0.706318i \(0.249645\pi\)
\(602\) −12.4204 −0.506218
\(603\) −6.90345 −0.281130
\(604\) −5.98467 −0.243513
\(605\) −10.5060 −0.427130
\(606\) −7.50548 −0.304889
\(607\) 3.38718 0.137481 0.0687407 0.997635i \(-0.478102\pi\)
0.0687407 + 0.997635i \(0.478102\pi\)
\(608\) −1.64115 −0.0665572
\(609\) −3.37050 −0.136579
\(610\) 9.20668 0.372768
\(611\) 21.7530 0.880032
\(612\) 1.17864 0.0476436
\(613\) −44.1473 −1.78309 −0.891547 0.452928i \(-0.850379\pi\)
−0.891547 + 0.452928i \(0.850379\pi\)
\(614\) 9.26421 0.373873
\(615\) 4.82962 0.194749
\(616\) −1.38191 −0.0556786
\(617\) 24.2323 0.975555 0.487777 0.872968i \(-0.337808\pi\)
0.487777 + 0.872968i \(0.337808\pi\)
\(618\) 9.12046 0.366879
\(619\) −32.1593 −1.29259 −0.646295 0.763088i \(-0.723682\pi\)
−0.646295 + 0.763088i \(0.723682\pi\)
\(620\) −6.10965 −0.245369
\(621\) 13.2324 0.530999
\(622\) 10.3280 0.414117
\(623\) −4.76816 −0.191032
\(624\) 2.45902 0.0984394
\(625\) 1.00000 0.0400000
\(626\) 24.1184 0.963965
\(627\) −0.779231 −0.0311195
\(628\) 18.7300 0.747409
\(629\) −2.67050 −0.106480
\(630\) −5.00120 −0.199252
\(631\) −39.2786 −1.56366 −0.781829 0.623493i \(-0.785713\pi\)
−0.781829 + 0.623493i \(0.785713\pi\)
\(632\) 7.77888 0.309427
\(633\) 12.6460 0.502635
\(634\) −19.8911 −0.789977
\(635\) −2.46196 −0.0976998
\(636\) −3.09217 −0.122612
\(637\) −11.4084 −0.452015
\(638\) 1.78348 0.0706087
\(639\) 9.10154 0.360051
\(640\) −1.00000 −0.0395285
\(641\) 31.9114 1.26042 0.630212 0.776423i \(-0.282968\pi\)
0.630212 + 0.776423i \(0.282968\pi\)
\(642\) 6.74300 0.266125
\(643\) 28.2686 1.11480 0.557402 0.830243i \(-0.311798\pi\)
0.557402 + 0.830243i \(0.311798\pi\)
\(644\) 6.94712 0.273755
\(645\) −4.26753 −0.168034
\(646\) 0.760457 0.0299198
\(647\) 5.22465 0.205402 0.102701 0.994712i \(-0.467251\pi\)
0.102701 + 0.994712i \(0.467251\pi\)
\(648\) −5.10089 −0.200382
\(649\) 1.80312 0.0707788
\(650\) −3.63999 −0.142772
\(651\) 8.11520 0.318060
\(652\) 24.0979 0.943748
\(653\) 9.99605 0.391176 0.195588 0.980686i \(-0.437339\pi\)
0.195588 + 0.980686i \(0.437339\pi\)
\(654\) 11.6894 0.457090
\(655\) −12.1540 −0.474896
\(656\) 7.14911 0.279126
\(657\) 2.68616 0.104797
\(658\) 11.7501 0.458066
\(659\) 31.5145 1.22763 0.613816 0.789449i \(-0.289634\pi\)
0.613816 + 0.789449i \(0.289634\pi\)
\(660\) −0.474809 −0.0184819
\(661\) 43.0557 1.67467 0.837336 0.546688i \(-0.184112\pi\)
0.837336 + 0.546688i \(0.184112\pi\)
\(662\) 25.8891 1.00621
\(663\) −1.13943 −0.0442520
\(664\) 5.64286 0.218985
\(665\) −3.22677 −0.125129
\(666\) 14.6595 0.568043
\(667\) −8.96593 −0.347162
\(668\) −6.60551 −0.255575
\(669\) −4.87320 −0.188409
\(670\) −2.71402 −0.104852
\(671\) 6.47084 0.249804
\(672\) 1.32826 0.0512387
\(673\) 19.2058 0.740331 0.370165 0.928966i \(-0.379301\pi\)
0.370165 + 0.928966i \(0.379301\pi\)
\(674\) −14.9572 −0.576129
\(675\) −3.74503 −0.144146
\(676\) 0.249501 0.00959619
\(677\) 29.2520 1.12425 0.562123 0.827054i \(-0.309985\pi\)
0.562123 + 0.827054i \(0.309985\pi\)
\(678\) 10.7032 0.411053
\(679\) −28.1407 −1.07994
\(680\) 0.463370 0.0177694
\(681\) 13.1422 0.503612
\(682\) −4.29412 −0.164430
\(683\) 19.8552 0.759737 0.379869 0.925040i \(-0.375969\pi\)
0.379869 + 0.925040i \(0.375969\pi\)
\(684\) −4.17446 −0.159614
\(685\) −14.9534 −0.571339
\(686\) −19.9255 −0.760760
\(687\) 7.56993 0.288811
\(688\) −6.31705 −0.240835
\(689\) −16.6610 −0.634733
\(690\) 2.38696 0.0908701
\(691\) −31.8422 −1.21133 −0.605667 0.795718i \(-0.707094\pi\)
−0.605667 + 0.795718i \(0.707094\pi\)
\(692\) −15.0557 −0.572332
\(693\) −3.51505 −0.133526
\(694\) −27.7319 −1.05269
\(695\) −21.8514 −0.828869
\(696\) −1.71424 −0.0649783
\(697\) −3.31268 −0.125477
\(698\) −2.15312 −0.0814969
\(699\) 11.9766 0.452995
\(700\) −1.96617 −0.0743142
\(701\) 31.8457 1.20280 0.601398 0.798950i \(-0.294611\pi\)
0.601398 + 0.798950i \(0.294611\pi\)
\(702\) 13.6319 0.514501
\(703\) 9.45829 0.356726
\(704\) −0.702842 −0.0264893
\(705\) 4.03721 0.152050
\(706\) −6.05838 −0.228010
\(707\) −21.8443 −0.821540
\(708\) −1.73312 −0.0651348
\(709\) −39.1770 −1.47132 −0.735661 0.677350i \(-0.763128\pi\)
−0.735661 + 0.677350i \(0.763128\pi\)
\(710\) 3.57818 0.134287
\(711\) 19.7865 0.742053
\(712\) −2.42510 −0.0908845
\(713\) 21.5874 0.808454
\(714\) −0.615475 −0.0230336
\(715\) −2.55833 −0.0956763
\(716\) 12.5215 0.467952
\(717\) −8.95027 −0.334254
\(718\) 26.0891 0.973636
\(719\) −10.4263 −0.388836 −0.194418 0.980919i \(-0.562282\pi\)
−0.194418 + 0.980919i \(0.562282\pi\)
\(720\) −2.54362 −0.0947953
\(721\) 26.5446 0.988573
\(722\) 16.3066 0.606870
\(723\) 4.46754 0.166149
\(724\) −23.0329 −0.856012
\(725\) 2.53753 0.0942415
\(726\) 7.09740 0.263409
\(727\) 18.9553 0.703014 0.351507 0.936185i \(-0.385669\pi\)
0.351507 + 0.936185i \(0.385669\pi\)
\(728\) 7.15683 0.265250
\(729\) −5.38481 −0.199438
\(730\) 1.05604 0.0390857
\(731\) 2.92713 0.108264
\(732\) −6.21963 −0.229884
\(733\) −31.9555 −1.18030 −0.590151 0.807293i \(-0.700932\pi\)
−0.590151 + 0.807293i \(0.700932\pi\)
\(734\) −2.08709 −0.0770358
\(735\) −2.11731 −0.0780982
\(736\) 3.53333 0.130240
\(737\) −1.90753 −0.0702646
\(738\) 18.1846 0.669386
\(739\) 52.0858 1.91601 0.958004 0.286755i \(-0.0925766\pi\)
0.958004 + 0.286755i \(0.0925766\pi\)
\(740\) 5.76322 0.211860
\(741\) 4.03560 0.148252
\(742\) −8.99958 −0.330385
\(743\) 38.5288 1.41349 0.706743 0.707470i \(-0.250164\pi\)
0.706743 + 0.707470i \(0.250164\pi\)
\(744\) 4.12741 0.151318
\(745\) 3.79711 0.139115
\(746\) 28.8649 1.05682
\(747\) 14.3533 0.525160
\(748\) 0.325676 0.0119079
\(749\) 19.6251 0.717087
\(750\) −0.675556 −0.0246678
\(751\) 11.6188 0.423977 0.211988 0.977272i \(-0.432006\pi\)
0.211988 + 0.977272i \(0.432006\pi\)
\(752\) 5.97612 0.217927
\(753\) −17.5830 −0.640759
\(754\) −9.23658 −0.336376
\(755\) −5.98467 −0.217805
\(756\) 7.36337 0.267803
\(757\) −1.94600 −0.0707286 −0.0353643 0.999374i \(-0.511259\pi\)
−0.0353643 + 0.999374i \(0.511259\pi\)
\(758\) −7.44485 −0.270409
\(759\) 1.67766 0.0608951
\(760\) −1.64115 −0.0595306
\(761\) −41.4858 −1.50386 −0.751930 0.659243i \(-0.770877\pi\)
−0.751930 + 0.659243i \(0.770877\pi\)
\(762\) 1.66319 0.0602511
\(763\) 34.0212 1.23165
\(764\) 15.0467 0.544371
\(765\) 1.17864 0.0426138
\(766\) 18.3001 0.661210
\(767\) −9.33830 −0.337186
\(768\) 0.675556 0.0243770
\(769\) −29.7575 −1.07308 −0.536541 0.843874i \(-0.680269\pi\)
−0.536541 + 0.843874i \(0.680269\pi\)
\(770\) −1.38191 −0.0498004
\(771\) −5.49921 −0.198049
\(772\) −19.7068 −0.709262
\(773\) 19.3525 0.696061 0.348030 0.937483i \(-0.386851\pi\)
0.348030 + 0.937483i \(0.386851\pi\)
\(774\) −16.0682 −0.577560
\(775\) −6.10965 −0.219465
\(776\) −14.3124 −0.513786
\(777\) −7.65505 −0.274623
\(778\) −22.2317 −0.797046
\(779\) 11.7327 0.420368
\(780\) 2.45902 0.0880469
\(781\) 2.51489 0.0899899
\(782\) −1.63724 −0.0585475
\(783\) −9.50313 −0.339614
\(784\) −3.13418 −0.111935
\(785\) 18.7300 0.668503
\(786\) 8.21071 0.292866
\(787\) 20.6864 0.737390 0.368695 0.929550i \(-0.379805\pi\)
0.368695 + 0.929550i \(0.379805\pi\)
\(788\) 15.6305 0.556813
\(789\) 1.42604 0.0507682
\(790\) 7.77888 0.276760
\(791\) 31.1510 1.10760
\(792\) −1.78776 −0.0635254
\(793\) −33.5122 −1.19005
\(794\) −3.83234 −0.136005
\(795\) −3.09217 −0.109668
\(796\) −6.63045 −0.235010
\(797\) 35.4361 1.25521 0.627606 0.778531i \(-0.284035\pi\)
0.627606 + 0.778531i \(0.284035\pi\)
\(798\) 2.17987 0.0771664
\(799\) −2.76916 −0.0979657
\(800\) −1.00000 −0.0353553
\(801\) −6.16855 −0.217955
\(802\) −1.00000 −0.0353112
\(803\) 0.742227 0.0261926
\(804\) 1.83347 0.0646616
\(805\) 6.94712 0.244854
\(806\) 22.2390 0.783337
\(807\) −12.8747 −0.453213
\(808\) −11.1101 −0.390851
\(809\) 27.9959 0.984283 0.492142 0.870515i \(-0.336214\pi\)
0.492142 + 0.870515i \(0.336214\pi\)
\(810\) −5.10089 −0.179227
\(811\) 22.3971 0.786469 0.393234 0.919438i \(-0.371356\pi\)
0.393234 + 0.919438i \(0.371356\pi\)
\(812\) −4.98922 −0.175087
\(813\) −3.41150 −0.119647
\(814\) 4.05063 0.141975
\(815\) 24.0979 0.844114
\(816\) −0.313032 −0.0109583
\(817\) −10.3672 −0.362703
\(818\) −20.3572 −0.711774
\(819\) 18.2043 0.636109
\(820\) 7.14911 0.249658
\(821\) 20.9374 0.730722 0.365361 0.930866i \(-0.380946\pi\)
0.365361 + 0.930866i \(0.380946\pi\)
\(822\) 10.1019 0.352343
\(823\) 47.8076 1.66647 0.833234 0.552921i \(-0.186487\pi\)
0.833234 + 0.552921i \(0.186487\pi\)
\(824\) 13.5007 0.470318
\(825\) −0.474809 −0.0165307
\(826\) −5.04416 −0.175509
\(827\) −14.9690 −0.520522 −0.260261 0.965538i \(-0.583809\pi\)
−0.260261 + 0.965538i \(0.583809\pi\)
\(828\) 8.98746 0.312336
\(829\) −21.5059 −0.746929 −0.373465 0.927644i \(-0.621830\pi\)
−0.373465 + 0.927644i \(0.621830\pi\)
\(830\) 5.64286 0.195866
\(831\) −6.22640 −0.215991
\(832\) 3.63999 0.126194
\(833\) 1.45228 0.0503186
\(834\) 14.7618 0.511160
\(835\) −6.60551 −0.228593
\(836\) −1.15347 −0.0398934
\(837\) 22.8808 0.790877
\(838\) −20.8407 −0.719931
\(839\) 13.8121 0.476846 0.238423 0.971161i \(-0.423370\pi\)
0.238423 + 0.971161i \(0.423370\pi\)
\(840\) 1.32826 0.0458293
\(841\) −22.5609 −0.777963
\(842\) −23.1118 −0.796485
\(843\) −4.44224 −0.152999
\(844\) 18.7194 0.644350
\(845\) 0.249501 0.00858310
\(846\) 15.2010 0.522621
\(847\) 20.6566 0.709770
\(848\) −4.57721 −0.157182
\(849\) 12.6608 0.434518
\(850\) 0.463370 0.0158935
\(851\) −20.3634 −0.698047
\(852\) −2.41726 −0.0828140
\(853\) −9.04546 −0.309711 −0.154855 0.987937i \(-0.549491\pi\)
−0.154855 + 0.987937i \(0.549491\pi\)
\(854\) −18.1019 −0.619434
\(855\) −4.17446 −0.142763
\(856\) 9.98140 0.341157
\(857\) −1.35948 −0.0464389 −0.0232194 0.999730i \(-0.507392\pi\)
−0.0232194 + 0.999730i \(0.507392\pi\)
\(858\) 1.72830 0.0590031
\(859\) −6.15779 −0.210101 −0.105051 0.994467i \(-0.533500\pi\)
−0.105051 + 0.994467i \(0.533500\pi\)
\(860\) −6.31705 −0.215410
\(861\) −9.49586 −0.323618
\(862\) 26.9560 0.918124
\(863\) 6.62312 0.225454 0.112727 0.993626i \(-0.464041\pi\)
0.112727 + 0.993626i \(0.464041\pi\)
\(864\) 3.74503 0.127409
\(865\) −15.0557 −0.511909
\(866\) −1.05846 −0.0359678
\(867\) −11.3394 −0.385106
\(868\) 12.0126 0.407735
\(869\) 5.46732 0.185466
\(870\) −1.71424 −0.0581183
\(871\) 9.87900 0.334737
\(872\) 17.3033 0.585964
\(873\) −36.4054 −1.23214
\(874\) 5.79871 0.196144
\(875\) −1.96617 −0.0664687
\(876\) −0.713412 −0.0241040
\(877\) −25.9471 −0.876170 −0.438085 0.898934i \(-0.644343\pi\)
−0.438085 + 0.898934i \(0.644343\pi\)
\(878\) 26.9332 0.908950
\(879\) 13.7421 0.463511
\(880\) −0.702842 −0.0236928
\(881\) −32.5527 −1.09673 −0.548365 0.836239i \(-0.684749\pi\)
−0.548365 + 0.836239i \(0.684749\pi\)
\(882\) −7.97216 −0.268437
\(883\) −17.9716 −0.604793 −0.302396 0.953182i \(-0.597787\pi\)
−0.302396 + 0.953182i \(0.597787\pi\)
\(884\) −1.68666 −0.0567285
\(885\) −1.73312 −0.0582583
\(886\) −3.79606 −0.127531
\(887\) 22.3570 0.750674 0.375337 0.926889i \(-0.377527\pi\)
0.375337 + 0.926889i \(0.377527\pi\)
\(888\) −3.89338 −0.130653
\(889\) 4.84063 0.162349
\(890\) −2.42510 −0.0812896
\(891\) −3.58512 −0.120106
\(892\) −7.21360 −0.241529
\(893\) 9.80769 0.328202
\(894\) −2.56516 −0.0857919
\(895\) 12.5215 0.418549
\(896\) 1.96617 0.0656851
\(897\) −8.68851 −0.290101
\(898\) 19.9784 0.666689
\(899\) −15.5034 −0.517068
\(900\) −2.54362 −0.0847875
\(901\) 2.12094 0.0706589
\(902\) 5.02469 0.167304
\(903\) 8.39068 0.279224
\(904\) 15.8435 0.526947
\(905\) −23.0329 −0.765641
\(906\) 4.04298 0.134319
\(907\) 1.71251 0.0568629 0.0284315 0.999596i \(-0.490949\pi\)
0.0284315 + 0.999596i \(0.490949\pi\)
\(908\) 19.4540 0.645602
\(909\) −28.2599 −0.937320
\(910\) 7.15683 0.237247
\(911\) 48.8985 1.62008 0.810040 0.586374i \(-0.199445\pi\)
0.810040 + 0.586374i \(0.199445\pi\)
\(912\) 1.10869 0.0367123
\(913\) 3.96603 0.131257
\(914\) 12.0619 0.398971
\(915\) −6.21963 −0.205615
\(916\) 11.2055 0.370239
\(917\) 23.8968 0.789143
\(918\) −1.73533 −0.0572746
\(919\) −22.4082 −0.739177 −0.369589 0.929195i \(-0.620501\pi\)
−0.369589 + 0.929195i \(0.620501\pi\)
\(920\) 3.53333 0.116490
\(921\) −6.25850 −0.206225
\(922\) 23.7685 0.782773
\(923\) −13.0245 −0.428707
\(924\) 0.933555 0.0307117
\(925\) 5.76322 0.189494
\(926\) 25.5650 0.840117
\(927\) 34.3406 1.12789
\(928\) −2.53753 −0.0832985
\(929\) −8.82972 −0.289694 −0.144847 0.989454i \(-0.546269\pi\)
−0.144847 + 0.989454i \(0.546269\pi\)
\(930\) 4.12741 0.135343
\(931\) −5.14364 −0.168576
\(932\) 17.7284 0.580714
\(933\) −6.97718 −0.228423
\(934\) −1.38486 −0.0453139
\(935\) 0.325676 0.0106507
\(936\) 9.25876 0.302632
\(937\) −39.4540 −1.28891 −0.644453 0.764644i \(-0.722915\pi\)
−0.644453 + 0.764644i \(0.722915\pi\)
\(938\) 5.33623 0.174234
\(939\) −16.2933 −0.531713
\(940\) 5.97612 0.194920
\(941\) 36.8693 1.20190 0.600952 0.799285i \(-0.294788\pi\)
0.600952 + 0.799285i \(0.294788\pi\)
\(942\) −12.6532 −0.412263
\(943\) −25.2601 −0.822583
\(944\) −2.56548 −0.0834991
\(945\) 7.36337 0.239530
\(946\) −4.43989 −0.144353
\(947\) 33.8844 1.10110 0.550548 0.834804i \(-0.314419\pi\)
0.550548 + 0.834804i \(0.314419\pi\)
\(948\) −5.25507 −0.170677
\(949\) −3.84396 −0.124780
\(950\) −1.64115 −0.0532458
\(951\) 13.4376 0.435743
\(952\) −0.911064 −0.0295278
\(953\) 12.8001 0.414635 0.207317 0.978274i \(-0.433527\pi\)
0.207317 + 0.978274i \(0.433527\pi\)
\(954\) −11.6427 −0.376947
\(955\) 15.0467 0.486901
\(956\) −13.2487 −0.428495
\(957\) −1.20484 −0.0389470
\(958\) 9.15088 0.295651
\(959\) 29.4009 0.949405
\(960\) 0.675556 0.0218035
\(961\) 6.32782 0.204123
\(962\) −20.9781 −0.676360
\(963\) 25.3889 0.818147
\(964\) 6.61312 0.212994
\(965\) −19.7068 −0.634383
\(966\) −4.69317 −0.151000
\(967\) −16.6147 −0.534293 −0.267147 0.963656i \(-0.586081\pi\)
−0.267147 + 0.963656i \(0.586081\pi\)
\(968\) 10.5060 0.337676
\(969\) −0.513732 −0.0165034
\(970\) −14.3124 −0.459545
\(971\) −38.9312 −1.24936 −0.624681 0.780880i \(-0.714771\pi\)
−0.624681 + 0.780880i \(0.714771\pi\)
\(972\) 14.6810 0.470894
\(973\) 42.9635 1.37735
\(974\) −9.41697 −0.301739
\(975\) 2.45902 0.0787515
\(976\) −9.20668 −0.294699
\(977\) −11.9325 −0.381755 −0.190878 0.981614i \(-0.561133\pi\)
−0.190878 + 0.981614i \(0.561133\pi\)
\(978\) −16.2795 −0.520561
\(979\) −1.70446 −0.0544749
\(980\) −3.13418 −0.100118
\(981\) 44.0131 1.40523
\(982\) −21.6913 −0.692199
\(983\) 13.2389 0.422254 0.211127 0.977459i \(-0.432287\pi\)
0.211127 + 0.977459i \(0.432287\pi\)
\(984\) −4.82962 −0.153963
\(985\) 15.6305 0.498029
\(986\) 1.17582 0.0374456
\(987\) −7.93784 −0.252664
\(988\) 5.97375 0.190050
\(989\) 22.3202 0.709742
\(990\) −1.78776 −0.0568189
\(991\) 25.3896 0.806526 0.403263 0.915084i \(-0.367876\pi\)
0.403263 + 0.915084i \(0.367876\pi\)
\(992\) 6.10965 0.193982
\(993\) −17.4895 −0.555013
\(994\) −7.03530 −0.223146
\(995\) −6.63045 −0.210199
\(996\) −3.81207 −0.120790
\(997\) −13.2384 −0.419263 −0.209632 0.977780i \(-0.567226\pi\)
−0.209632 + 0.977780i \(0.567226\pi\)
\(998\) 38.4965 1.21859
\(999\) −21.5834 −0.682870
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 4010.2.a.i.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.i.1.7 10 1.1 even 1 trivial