Properties

Label 8003.2.a.b.1.14
Level $8003$
Weight $2$
Character 8003.1
Self dual yes
Analytic conductor $63.904$
Analytic rank $1$
Dimension $153$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.41716 q^{2} -1.38399 q^{3} +3.84266 q^{4} +1.63498 q^{5} +3.34533 q^{6} -3.98295 q^{7} -4.45401 q^{8} -1.08457 q^{9} +O(q^{10})\) \(q-2.41716 q^{2} -1.38399 q^{3} +3.84266 q^{4} +1.63498 q^{5} +3.34533 q^{6} -3.98295 q^{7} -4.45401 q^{8} -1.08457 q^{9} -3.95202 q^{10} +3.77197 q^{11} -5.31821 q^{12} -0.915163 q^{13} +9.62743 q^{14} -2.26280 q^{15} +3.08073 q^{16} +2.97669 q^{17} +2.62157 q^{18} +5.78926 q^{19} +6.28269 q^{20} +5.51237 q^{21} -9.11745 q^{22} -4.09109 q^{23} +6.16431 q^{24} -2.32683 q^{25} +2.21209 q^{26} +5.65301 q^{27} -15.3051 q^{28} -2.59173 q^{29} +5.46956 q^{30} +8.51302 q^{31} +1.46140 q^{32} -5.22038 q^{33} -7.19513 q^{34} -6.51206 q^{35} -4.16762 q^{36} -1.46789 q^{37} -13.9936 q^{38} +1.26658 q^{39} -7.28223 q^{40} +2.34134 q^{41} -13.3243 q^{42} -11.1388 q^{43} +14.4944 q^{44} -1.77325 q^{45} +9.88882 q^{46} -12.8765 q^{47} -4.26370 q^{48} +8.86389 q^{49} +5.62432 q^{50} -4.11971 q^{51} -3.51666 q^{52} -1.00000 q^{53} -13.6642 q^{54} +6.16711 q^{55} +17.7401 q^{56} -8.01229 q^{57} +6.26462 q^{58} -9.03203 q^{59} -8.69519 q^{60} +1.34872 q^{61} -20.5773 q^{62} +4.31977 q^{63} -9.69391 q^{64} -1.49628 q^{65} +12.6185 q^{66} +4.57214 q^{67} +11.4384 q^{68} +5.66203 q^{69} +15.7407 q^{70} +3.64013 q^{71} +4.83067 q^{72} -5.63539 q^{73} +3.54812 q^{74} +3.22031 q^{75} +22.2462 q^{76} -15.0236 q^{77} -3.06152 q^{78} +15.6324 q^{79} +5.03694 q^{80} -4.57002 q^{81} -5.65939 q^{82} -4.47647 q^{83} +21.1822 q^{84} +4.86684 q^{85} +26.9243 q^{86} +3.58693 q^{87} -16.8004 q^{88} +6.18881 q^{89} +4.28622 q^{90} +3.64505 q^{91} -15.7207 q^{92} -11.7820 q^{93} +31.1245 q^{94} +9.46535 q^{95} -2.02257 q^{96} +7.86088 q^{97} -21.4254 q^{98} -4.09095 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41716 −1.70919 −0.854595 0.519295i \(-0.826195\pi\)
−0.854595 + 0.519295i \(0.826195\pi\)
\(3\) −1.38399 −0.799048 −0.399524 0.916723i \(-0.630825\pi\)
−0.399524 + 0.916723i \(0.630825\pi\)
\(4\) 3.84266 1.92133
\(5\) 1.63498 0.731187 0.365593 0.930775i \(-0.380866\pi\)
0.365593 + 0.930775i \(0.380866\pi\)
\(6\) 3.34533 1.36573
\(7\) −3.98295 −1.50541 −0.752707 0.658356i \(-0.771252\pi\)
−0.752707 + 0.658356i \(0.771252\pi\)
\(8\) −4.45401 −1.57473
\(9\) −1.08457 −0.361522
\(10\) −3.95202 −1.24974
\(11\) 3.77197 1.13729 0.568646 0.822582i \(-0.307468\pi\)
0.568646 + 0.822582i \(0.307468\pi\)
\(12\) −5.31821 −1.53524
\(13\) −0.915163 −0.253820 −0.126910 0.991914i \(-0.540506\pi\)
−0.126910 + 0.991914i \(0.540506\pi\)
\(14\) 9.62743 2.57304
\(15\) −2.26280 −0.584254
\(16\) 3.08073 0.770182
\(17\) 2.97669 0.721953 0.360976 0.932575i \(-0.382443\pi\)
0.360976 + 0.932575i \(0.382443\pi\)
\(18\) 2.62157 0.617910
\(19\) 5.78926 1.32815 0.664074 0.747667i \(-0.268826\pi\)
0.664074 + 0.747667i \(0.268826\pi\)
\(20\) 6.28269 1.40485
\(21\) 5.51237 1.20290
\(22\) −9.11745 −1.94385
\(23\) −4.09109 −0.853051 −0.426526 0.904476i \(-0.640263\pi\)
−0.426526 + 0.904476i \(0.640263\pi\)
\(24\) 6.16431 1.25829
\(25\) −2.32683 −0.465366
\(26\) 2.21209 0.433827
\(27\) 5.65301 1.08792
\(28\) −15.3051 −2.89240
\(29\) −2.59173 −0.481272 −0.240636 0.970615i \(-0.577356\pi\)
−0.240636 + 0.970615i \(0.577356\pi\)
\(30\) 5.46956 0.998600
\(31\) 8.51302 1.52898 0.764492 0.644633i \(-0.222990\pi\)
0.764492 + 0.644633i \(0.222990\pi\)
\(32\) 1.46140 0.258342
\(33\) −5.22038 −0.908751
\(34\) −7.19513 −1.23395
\(35\) −6.51206 −1.10074
\(36\) −4.16762 −0.694604
\(37\) −1.46789 −0.241319 −0.120660 0.992694i \(-0.538501\pi\)
−0.120660 + 0.992694i \(0.538501\pi\)
\(38\) −13.9936 −2.27006
\(39\) 1.26658 0.202815
\(40\) −7.28223 −1.15142
\(41\) 2.34134 0.365656 0.182828 0.983145i \(-0.441475\pi\)
0.182828 + 0.983145i \(0.441475\pi\)
\(42\) −13.3243 −2.05598
\(43\) −11.1388 −1.69865 −0.849327 0.527867i \(-0.822992\pi\)
−0.849327 + 0.527867i \(0.822992\pi\)
\(44\) 14.4944 2.18511
\(45\) −1.77325 −0.264340
\(46\) 9.88882 1.45803
\(47\) −12.8765 −1.87822 −0.939112 0.343610i \(-0.888350\pi\)
−0.939112 + 0.343610i \(0.888350\pi\)
\(48\) −4.26370 −0.615413
\(49\) 8.86389 1.26627
\(50\) 5.62432 0.795398
\(51\) −4.11971 −0.576875
\(52\) −3.51666 −0.487673
\(53\) −1.00000 −0.137361
\(54\) −13.6642 −1.85947
\(55\) 6.16711 0.831573
\(56\) 17.7401 2.37062
\(57\) −8.01229 −1.06125
\(58\) 6.26462 0.822585
\(59\) −9.03203 −1.17587 −0.587935 0.808908i \(-0.700059\pi\)
−0.587935 + 0.808908i \(0.700059\pi\)
\(60\) −8.69519 −1.12254
\(61\) 1.34872 0.172686 0.0863431 0.996265i \(-0.472482\pi\)
0.0863431 + 0.996265i \(0.472482\pi\)
\(62\) −20.5773 −2.61332
\(63\) 4.31977 0.544240
\(64\) −9.69391 −1.21174
\(65\) −1.49628 −0.185590
\(66\) 12.6185 1.55323
\(67\) 4.57214 0.558575 0.279288 0.960207i \(-0.409902\pi\)
0.279288 + 0.960207i \(0.409902\pi\)
\(68\) 11.4384 1.38711
\(69\) 5.66203 0.681629
\(70\) 15.7407 1.88137
\(71\) 3.64013 0.432003 0.216002 0.976393i \(-0.430698\pi\)
0.216002 + 0.976393i \(0.430698\pi\)
\(72\) 4.83067 0.569300
\(73\) −5.63539 −0.659573 −0.329786 0.944056i \(-0.606977\pi\)
−0.329786 + 0.944056i \(0.606977\pi\)
\(74\) 3.54812 0.412460
\(75\) 3.22031 0.371850
\(76\) 22.2462 2.55181
\(77\) −15.0236 −1.71209
\(78\) −3.06152 −0.346649
\(79\) 15.6324 1.75878 0.879389 0.476104i \(-0.157951\pi\)
0.879389 + 0.476104i \(0.157951\pi\)
\(80\) 5.03694 0.563147
\(81\) −4.57002 −0.507780
\(82\) −5.65939 −0.624975
\(83\) −4.47647 −0.491357 −0.245678 0.969351i \(-0.579011\pi\)
−0.245678 + 0.969351i \(0.579011\pi\)
\(84\) 21.1822 2.31116
\(85\) 4.86684 0.527882
\(86\) 26.9243 2.90332
\(87\) 3.58693 0.384559
\(88\) −16.8004 −1.79093
\(89\) 6.18881 0.656013 0.328006 0.944676i \(-0.393623\pi\)
0.328006 + 0.944676i \(0.393623\pi\)
\(90\) 4.28622 0.451808
\(91\) 3.64505 0.382105
\(92\) −15.7207 −1.63899
\(93\) −11.7820 −1.22173
\(94\) 31.1245 3.21024
\(95\) 9.46535 0.971124
\(96\) −2.02257 −0.206428
\(97\) 7.86088 0.798151 0.399076 0.916918i \(-0.369331\pi\)
0.399076 + 0.916918i \(0.369331\pi\)
\(98\) −21.4254 −2.16430
\(99\) −4.09095 −0.411156
\(100\) −8.94122 −0.894122
\(101\) −0.368282 −0.0366455 −0.0183227 0.999832i \(-0.505833\pi\)
−0.0183227 + 0.999832i \(0.505833\pi\)
\(102\) 9.95800 0.985989
\(103\) 6.21988 0.612862 0.306431 0.951893i \(-0.400865\pi\)
0.306431 + 0.951893i \(0.400865\pi\)
\(104\) 4.07614 0.399699
\(105\) 9.01263 0.879543
\(106\) 2.41716 0.234775
\(107\) 0.700217 0.0676926 0.0338463 0.999427i \(-0.489224\pi\)
0.0338463 + 0.999427i \(0.489224\pi\)
\(108\) 21.7226 2.09026
\(109\) 2.42746 0.232509 0.116254 0.993219i \(-0.462911\pi\)
0.116254 + 0.993219i \(0.462911\pi\)
\(110\) −14.9069 −1.42132
\(111\) 2.03154 0.192826
\(112\) −12.2704 −1.15944
\(113\) 7.25651 0.682635 0.341318 0.939948i \(-0.389127\pi\)
0.341318 + 0.939948i \(0.389127\pi\)
\(114\) 19.3670 1.81388
\(115\) −6.68886 −0.623740
\(116\) −9.95914 −0.924683
\(117\) 0.992555 0.0917617
\(118\) 21.8319 2.00979
\(119\) −11.8560 −1.08684
\(120\) 10.0786 0.920042
\(121\) 3.22775 0.293432
\(122\) −3.26008 −0.295154
\(123\) −3.24039 −0.292176
\(124\) 32.7127 2.93768
\(125\) −11.9792 −1.07146
\(126\) −10.4416 −0.930210
\(127\) −13.3065 −1.18076 −0.590381 0.807125i \(-0.701022\pi\)
−0.590381 + 0.807125i \(0.701022\pi\)
\(128\) 20.5089 1.81275
\(129\) 15.4160 1.35731
\(130\) 3.61674 0.317209
\(131\) −3.05257 −0.266704 −0.133352 0.991069i \(-0.542574\pi\)
−0.133352 + 0.991069i \(0.542574\pi\)
\(132\) −20.0601 −1.74601
\(133\) −23.0583 −1.99941
\(134\) −11.0516 −0.954712
\(135\) 9.24257 0.795474
\(136\) −13.2582 −1.13688
\(137\) 4.02836 0.344166 0.172083 0.985082i \(-0.444950\pi\)
0.172083 + 0.985082i \(0.444950\pi\)
\(138\) −13.6860 −1.16503
\(139\) −8.78329 −0.744989 −0.372495 0.928034i \(-0.621497\pi\)
−0.372495 + 0.928034i \(0.621497\pi\)
\(140\) −25.0236 −2.11488
\(141\) 17.8209 1.50079
\(142\) −8.79876 −0.738376
\(143\) −3.45197 −0.288668
\(144\) −3.34125 −0.278438
\(145\) −4.23743 −0.351900
\(146\) 13.6216 1.12734
\(147\) −12.2675 −1.01181
\(148\) −5.64059 −0.463654
\(149\) −10.7964 −0.884478 −0.442239 0.896897i \(-0.645816\pi\)
−0.442239 + 0.896897i \(0.645816\pi\)
\(150\) −7.78401 −0.635562
\(151\) −1.00000 −0.0813788
\(152\) −25.7854 −2.09147
\(153\) −3.22842 −0.261002
\(154\) 36.3144 2.92629
\(155\) 13.9186 1.11797
\(156\) 4.86703 0.389674
\(157\) 22.4632 1.79276 0.896379 0.443289i \(-0.146188\pi\)
0.896379 + 0.443289i \(0.146188\pi\)
\(158\) −37.7859 −3.00609
\(159\) 1.38399 0.109758
\(160\) 2.38937 0.188896
\(161\) 16.2946 1.28419
\(162\) 11.0465 0.867892
\(163\) −6.05993 −0.474650 −0.237325 0.971430i \(-0.576271\pi\)
−0.237325 + 0.971430i \(0.576271\pi\)
\(164\) 8.99697 0.702546
\(165\) −8.53523 −0.664467
\(166\) 10.8203 0.839822
\(167\) 25.7728 1.99436 0.997181 0.0750270i \(-0.0239043\pi\)
0.997181 + 0.0750270i \(0.0239043\pi\)
\(168\) −24.5521 −1.89424
\(169\) −12.1625 −0.935575
\(170\) −11.7639 −0.902251
\(171\) −6.27884 −0.480155
\(172\) −42.8027 −3.26368
\(173\) −4.00816 −0.304735 −0.152368 0.988324i \(-0.548690\pi\)
−0.152368 + 0.988324i \(0.548690\pi\)
\(174\) −8.67019 −0.657285
\(175\) 9.26764 0.700568
\(176\) 11.6204 0.875922
\(177\) 12.5003 0.939577
\(178\) −14.9593 −1.12125
\(179\) −3.22255 −0.240865 −0.120432 0.992722i \(-0.538428\pi\)
−0.120432 + 0.992722i \(0.538428\pi\)
\(180\) −6.81399 −0.507885
\(181\) −5.83918 −0.434023 −0.217012 0.976169i \(-0.569631\pi\)
−0.217012 + 0.976169i \(0.569631\pi\)
\(182\) −8.81066 −0.653090
\(183\) −1.86662 −0.137985
\(184\) 18.2218 1.34333
\(185\) −2.39997 −0.176449
\(186\) 28.4789 2.08817
\(187\) 11.2280 0.821071
\(188\) −49.4799 −3.60869
\(189\) −22.5156 −1.63777
\(190\) −22.8793 −1.65984
\(191\) 9.71456 0.702921 0.351460 0.936203i \(-0.385685\pi\)
0.351460 + 0.936203i \(0.385685\pi\)
\(192\) 13.4163 0.968237
\(193\) 10.6698 0.768028 0.384014 0.923327i \(-0.374541\pi\)
0.384014 + 0.923327i \(0.374541\pi\)
\(194\) −19.0010 −1.36419
\(195\) 2.07083 0.148295
\(196\) 34.0609 2.43292
\(197\) −16.3821 −1.16717 −0.583587 0.812051i \(-0.698351\pi\)
−0.583587 + 0.812051i \(0.698351\pi\)
\(198\) 9.88848 0.702744
\(199\) 2.20043 0.155984 0.0779921 0.996954i \(-0.475149\pi\)
0.0779921 + 0.996954i \(0.475149\pi\)
\(200\) 10.3637 0.732825
\(201\) −6.32780 −0.446329
\(202\) 0.890198 0.0626341
\(203\) 10.3227 0.724513
\(204\) −15.8307 −1.10837
\(205\) 3.82805 0.267363
\(206\) −15.0344 −1.04750
\(207\) 4.43706 0.308397
\(208\) −2.81937 −0.195488
\(209\) 21.8369 1.51049
\(210\) −21.7850 −1.50331
\(211\) −17.4754 −1.20306 −0.601529 0.798851i \(-0.705441\pi\)
−0.601529 + 0.798851i \(0.705441\pi\)
\(212\) −3.84266 −0.263915
\(213\) −5.03790 −0.345191
\(214\) −1.69254 −0.115699
\(215\) −18.2118 −1.24203
\(216\) −25.1785 −1.71318
\(217\) −33.9069 −2.30175
\(218\) −5.86757 −0.397402
\(219\) 7.79934 0.527030
\(220\) 23.6981 1.59773
\(221\) −2.72415 −0.183246
\(222\) −4.91056 −0.329575
\(223\) 8.61755 0.577074 0.288537 0.957469i \(-0.406831\pi\)
0.288537 + 0.957469i \(0.406831\pi\)
\(224\) −5.82070 −0.388912
\(225\) 2.52360 0.168240
\(226\) −17.5401 −1.16675
\(227\) 22.0292 1.46213 0.731065 0.682307i \(-0.239023\pi\)
0.731065 + 0.682307i \(0.239023\pi\)
\(228\) −30.7885 −2.03902
\(229\) 7.83327 0.517637 0.258818 0.965926i \(-0.416667\pi\)
0.258818 + 0.965926i \(0.416667\pi\)
\(230\) 16.1681 1.06609
\(231\) 20.7925 1.36805
\(232\) 11.5436 0.757873
\(233\) −9.62780 −0.630738 −0.315369 0.948969i \(-0.602128\pi\)
−0.315369 + 0.948969i \(0.602128\pi\)
\(234\) −2.39916 −0.156838
\(235\) −21.0528 −1.37333
\(236\) −34.7070 −2.25924
\(237\) −21.6351 −1.40535
\(238\) 28.6578 1.85761
\(239\) −9.11876 −0.589844 −0.294922 0.955521i \(-0.595294\pi\)
−0.294922 + 0.955521i \(0.595294\pi\)
\(240\) −6.97109 −0.449982
\(241\) 6.53291 0.420822 0.210411 0.977613i \(-0.432520\pi\)
0.210411 + 0.977613i \(0.432520\pi\)
\(242\) −7.80200 −0.501531
\(243\) −10.6342 −0.682181
\(244\) 5.18269 0.331788
\(245\) 14.4923 0.925880
\(246\) 7.83255 0.499385
\(247\) −5.29811 −0.337111
\(248\) −37.9171 −2.40774
\(249\) 6.19540 0.392618
\(250\) 28.9558 1.83132
\(251\) 17.3455 1.09484 0.547420 0.836858i \(-0.315610\pi\)
0.547420 + 0.836858i \(0.315610\pi\)
\(252\) 16.5994 1.04567
\(253\) −15.4315 −0.970168
\(254\) 32.1639 2.01815
\(255\) −6.73566 −0.421803
\(256\) −30.1855 −1.88659
\(257\) −5.01817 −0.313025 −0.156512 0.987676i \(-0.550025\pi\)
−0.156512 + 0.987676i \(0.550025\pi\)
\(258\) −37.2630 −2.31989
\(259\) 5.84652 0.363285
\(260\) −5.74968 −0.356580
\(261\) 2.81090 0.173990
\(262\) 7.37855 0.455848
\(263\) 25.2743 1.55848 0.779241 0.626724i \(-0.215605\pi\)
0.779241 + 0.626724i \(0.215605\pi\)
\(264\) 23.2516 1.43104
\(265\) −1.63498 −0.100436
\(266\) 55.7357 3.41737
\(267\) −8.56526 −0.524186
\(268\) 17.5692 1.07321
\(269\) −12.5595 −0.765766 −0.382883 0.923797i \(-0.625069\pi\)
−0.382883 + 0.923797i \(0.625069\pi\)
\(270\) −22.3408 −1.35962
\(271\) −3.00930 −0.182802 −0.0914011 0.995814i \(-0.529135\pi\)
−0.0914011 + 0.995814i \(0.529135\pi\)
\(272\) 9.17037 0.556035
\(273\) −5.04472 −0.305320
\(274\) −9.73718 −0.588245
\(275\) −8.77673 −0.529256
\(276\) 21.7573 1.30963
\(277\) −25.0390 −1.50445 −0.752225 0.658906i \(-0.771019\pi\)
−0.752225 + 0.658906i \(0.771019\pi\)
\(278\) 21.2306 1.27333
\(279\) −9.23293 −0.552761
\(280\) 29.0048 1.73337
\(281\) 4.59917 0.274364 0.137182 0.990546i \(-0.456196\pi\)
0.137182 + 0.990546i \(0.456196\pi\)
\(282\) −43.0760 −2.56514
\(283\) 28.6117 1.70079 0.850395 0.526145i \(-0.176363\pi\)
0.850395 + 0.526145i \(0.176363\pi\)
\(284\) 13.9878 0.830022
\(285\) −13.1000 −0.775975
\(286\) 8.34395 0.493388
\(287\) −9.32543 −0.550463
\(288\) −1.58499 −0.0933964
\(289\) −8.13933 −0.478784
\(290\) 10.2426 0.601464
\(291\) −10.8794 −0.637761
\(292\) −21.6549 −1.26726
\(293\) −3.64687 −0.213052 −0.106526 0.994310i \(-0.533973\pi\)
−0.106526 + 0.994310i \(0.533973\pi\)
\(294\) 29.6526 1.72938
\(295\) −14.7672 −0.859781
\(296\) 6.53798 0.380012
\(297\) 21.3230 1.23728
\(298\) 26.0967 1.51174
\(299\) 3.74401 0.216522
\(300\) 12.3746 0.714446
\(301\) 44.3654 2.55718
\(302\) 2.41716 0.139092
\(303\) 0.509700 0.0292815
\(304\) 17.8351 1.02292
\(305\) 2.20514 0.126266
\(306\) 7.80360 0.446102
\(307\) −3.22369 −0.183986 −0.0919929 0.995760i \(-0.529324\pi\)
−0.0919929 + 0.995760i \(0.529324\pi\)
\(308\) −57.7305 −3.28950
\(309\) −8.60826 −0.489707
\(310\) −33.6436 −1.91083
\(311\) −13.5724 −0.769621 −0.384811 0.922996i \(-0.625733\pi\)
−0.384811 + 0.922996i \(0.625733\pi\)
\(312\) −5.64135 −0.319379
\(313\) −13.3008 −0.751807 −0.375904 0.926659i \(-0.622668\pi\)
−0.375904 + 0.926659i \(0.622668\pi\)
\(314\) −54.2971 −3.06416
\(315\) 7.06276 0.397941
\(316\) 60.0699 3.37919
\(317\) 15.9615 0.896488 0.448244 0.893911i \(-0.352050\pi\)
0.448244 + 0.893911i \(0.352050\pi\)
\(318\) −3.34533 −0.187597
\(319\) −9.77592 −0.547346
\(320\) −15.8494 −0.886007
\(321\) −0.969095 −0.0540896
\(322\) −39.3867 −2.19493
\(323\) 17.2328 0.958860
\(324\) −17.5610 −0.975613
\(325\) 2.12943 0.118119
\(326\) 14.6478 0.811267
\(327\) −3.35959 −0.185786
\(328\) −10.4283 −0.575809
\(329\) 51.2863 2.82750
\(330\) 20.6310 1.13570
\(331\) −9.78829 −0.538013 −0.269007 0.963138i \(-0.586695\pi\)
−0.269007 + 0.963138i \(0.586695\pi\)
\(332\) −17.2016 −0.944059
\(333\) 1.59202 0.0872422
\(334\) −62.2971 −3.40875
\(335\) 7.47537 0.408423
\(336\) 16.9821 0.926450
\(337\) −15.9058 −0.866443 −0.433221 0.901288i \(-0.642623\pi\)
−0.433221 + 0.901288i \(0.642623\pi\)
\(338\) 29.3987 1.59908
\(339\) −10.0430 −0.545458
\(340\) 18.7016 1.01424
\(341\) 32.1109 1.73890
\(342\) 15.1770 0.820676
\(343\) −7.42377 −0.400846
\(344\) 49.6124 2.67492
\(345\) 9.25733 0.498398
\(346\) 9.68837 0.520850
\(347\) −12.2218 −0.656098 −0.328049 0.944661i \(-0.606391\pi\)
−0.328049 + 0.944661i \(0.606391\pi\)
\(348\) 13.7834 0.738866
\(349\) 19.0876 1.02174 0.510868 0.859659i \(-0.329324\pi\)
0.510868 + 0.859659i \(0.329324\pi\)
\(350\) −22.4014 −1.19740
\(351\) −5.17342 −0.276137
\(352\) 5.51237 0.293810
\(353\) −7.52709 −0.400627 −0.200313 0.979732i \(-0.564196\pi\)
−0.200313 + 0.979732i \(0.564196\pi\)
\(354\) −30.2151 −1.60592
\(355\) 5.95155 0.315875
\(356\) 23.7815 1.26042
\(357\) 16.4086 0.868435
\(358\) 7.78943 0.411684
\(359\) 18.9712 1.00126 0.500631 0.865661i \(-0.333101\pi\)
0.500631 + 0.865661i \(0.333101\pi\)
\(360\) 7.89806 0.416265
\(361\) 14.5155 0.763975
\(362\) 14.1142 0.741828
\(363\) −4.46719 −0.234466
\(364\) 14.0067 0.734150
\(365\) −9.21378 −0.482271
\(366\) 4.51192 0.235842
\(367\) −9.85226 −0.514284 −0.257142 0.966374i \(-0.582781\pi\)
−0.257142 + 0.966374i \(0.582781\pi\)
\(368\) −12.6035 −0.657005
\(369\) −2.53934 −0.132193
\(370\) 5.80111 0.301585
\(371\) 3.98295 0.206784
\(372\) −45.2741 −2.34735
\(373\) 9.68880 0.501667 0.250833 0.968030i \(-0.419295\pi\)
0.250833 + 0.968030i \(0.419295\pi\)
\(374\) −27.1398 −1.40337
\(375\) 16.5792 0.856145
\(376\) 57.3519 2.95770
\(377\) 2.37185 0.122157
\(378\) 54.4239 2.79926
\(379\) 15.7389 0.808454 0.404227 0.914659i \(-0.367541\pi\)
0.404227 + 0.914659i \(0.367541\pi\)
\(380\) 36.3721 1.86585
\(381\) 18.4161 0.943485
\(382\) −23.4816 −1.20143
\(383\) 11.3510 0.580011 0.290006 0.957025i \(-0.406343\pi\)
0.290006 + 0.957025i \(0.406343\pi\)
\(384\) −28.3842 −1.44847
\(385\) −24.5633 −1.25186
\(386\) −25.7906 −1.31271
\(387\) 12.0808 0.614101
\(388\) 30.2067 1.53351
\(389\) −14.6443 −0.742497 −0.371248 0.928534i \(-0.621070\pi\)
−0.371248 + 0.928534i \(0.621070\pi\)
\(390\) −5.00554 −0.253465
\(391\) −12.1779 −0.615863
\(392\) −39.4798 −1.99403
\(393\) 4.22473 0.213110
\(394\) 39.5981 1.99492
\(395\) 25.5587 1.28600
\(396\) −15.7201 −0.789967
\(397\) 14.9090 0.748259 0.374130 0.927376i \(-0.377942\pi\)
0.374130 + 0.927376i \(0.377942\pi\)
\(398\) −5.31878 −0.266607
\(399\) 31.9125 1.59763
\(400\) −7.16833 −0.358416
\(401\) 1.59608 0.0797046 0.0398523 0.999206i \(-0.487311\pi\)
0.0398523 + 0.999206i \(0.487311\pi\)
\(402\) 15.2953 0.762861
\(403\) −7.79080 −0.388087
\(404\) −1.41519 −0.0704081
\(405\) −7.47190 −0.371282
\(406\) −24.9517 −1.23833
\(407\) −5.53682 −0.274450
\(408\) 18.3492 0.908423
\(409\) −24.0325 −1.18833 −0.594165 0.804343i \(-0.702517\pi\)
−0.594165 + 0.804343i \(0.702517\pi\)
\(410\) −9.25301 −0.456974
\(411\) −5.57521 −0.275005
\(412\) 23.9009 1.17751
\(413\) 35.9741 1.77017
\(414\) −10.7251 −0.527109
\(415\) −7.31896 −0.359274
\(416\) −1.33742 −0.0655725
\(417\) 12.1560 0.595282
\(418\) −52.7833 −2.58172
\(419\) −3.90937 −0.190985 −0.0954926 0.995430i \(-0.530443\pi\)
−0.0954926 + 0.995430i \(0.530443\pi\)
\(420\) 34.6325 1.68989
\(421\) −26.7436 −1.30340 −0.651702 0.758475i \(-0.725945\pi\)
−0.651702 + 0.758475i \(0.725945\pi\)
\(422\) 42.2409 2.05625
\(423\) 13.9654 0.679020
\(424\) 4.45401 0.216306
\(425\) −6.92624 −0.335972
\(426\) 12.1774 0.589998
\(427\) −5.37190 −0.259964
\(428\) 2.69070 0.130060
\(429\) 4.77749 0.230660
\(430\) 44.0208 2.12287
\(431\) 19.9942 0.963085 0.481542 0.876423i \(-0.340077\pi\)
0.481542 + 0.876423i \(0.340077\pi\)
\(432\) 17.4154 0.837898
\(433\) −21.6850 −1.04212 −0.521058 0.853521i \(-0.674462\pi\)
−0.521058 + 0.853521i \(0.674462\pi\)
\(434\) 81.9585 3.93413
\(435\) 5.86457 0.281185
\(436\) 9.32792 0.446727
\(437\) −23.6844 −1.13298
\(438\) −18.8522 −0.900795
\(439\) 8.46045 0.403795 0.201898 0.979407i \(-0.435289\pi\)
0.201898 + 0.979407i \(0.435289\pi\)
\(440\) −27.4684 −1.30950
\(441\) −9.61347 −0.457784
\(442\) 6.58471 0.313203
\(443\) 8.06860 0.383351 0.191675 0.981458i \(-0.438608\pi\)
0.191675 + 0.981458i \(0.438608\pi\)
\(444\) 7.80653 0.370482
\(445\) 10.1186 0.479668
\(446\) −20.8300 −0.986329
\(447\) 14.9422 0.706741
\(448\) 38.6103 1.82417
\(449\) 25.3021 1.19408 0.597040 0.802212i \(-0.296344\pi\)
0.597040 + 0.802212i \(0.296344\pi\)
\(450\) −6.09994 −0.287554
\(451\) 8.83146 0.415857
\(452\) 27.8843 1.31157
\(453\) 1.38399 0.0650256
\(454\) −53.2482 −2.49906
\(455\) 5.95959 0.279390
\(456\) 35.6868 1.67119
\(457\) 8.51913 0.398508 0.199254 0.979948i \(-0.436148\pi\)
0.199254 + 0.979948i \(0.436148\pi\)
\(458\) −18.9343 −0.884740
\(459\) 16.8272 0.785428
\(460\) −25.7030 −1.19841
\(461\) 8.48556 0.395212 0.197606 0.980282i \(-0.436683\pi\)
0.197606 + 0.980282i \(0.436683\pi\)
\(462\) −50.2588 −2.33825
\(463\) 5.16705 0.240133 0.120067 0.992766i \(-0.461689\pi\)
0.120067 + 0.992766i \(0.461689\pi\)
\(464\) −7.98441 −0.370667
\(465\) −19.2633 −0.893314
\(466\) 23.2719 1.07805
\(467\) 31.6688 1.46546 0.732728 0.680522i \(-0.238247\pi\)
0.732728 + 0.680522i \(0.238247\pi\)
\(468\) 3.81405 0.176305
\(469\) −18.2106 −0.840887
\(470\) 50.8880 2.34729
\(471\) −31.0889 −1.43250
\(472\) 40.2287 1.85168
\(473\) −42.0153 −1.93186
\(474\) 52.2954 2.40201
\(475\) −13.4706 −0.618074
\(476\) −45.5586 −2.08817
\(477\) 1.08457 0.0496589
\(478\) 22.0415 1.00816
\(479\) 8.84548 0.404160 0.202080 0.979369i \(-0.435230\pi\)
0.202080 + 0.979369i \(0.435230\pi\)
\(480\) −3.30687 −0.150937
\(481\) 1.34335 0.0612517
\(482\) −15.7911 −0.719264
\(483\) −22.5516 −1.02613
\(484\) 12.4032 0.563780
\(485\) 12.8524 0.583598
\(486\) 25.7045 1.16598
\(487\) −13.7042 −0.620995 −0.310497 0.950574i \(-0.600496\pi\)
−0.310497 + 0.950574i \(0.600496\pi\)
\(488\) −6.00722 −0.271934
\(489\) 8.38689 0.379268
\(490\) −35.0302 −1.58250
\(491\) −38.3817 −1.73214 −0.866071 0.499920i \(-0.833363\pi\)
−0.866071 + 0.499920i \(0.833363\pi\)
\(492\) −12.4517 −0.561368
\(493\) −7.71477 −0.347456
\(494\) 12.8064 0.576187
\(495\) −6.68864 −0.300632
\(496\) 26.2263 1.17760
\(497\) −14.4984 −0.650344
\(498\) −14.9753 −0.671058
\(499\) −36.7846 −1.64671 −0.823353 0.567529i \(-0.807899\pi\)
−0.823353 + 0.567529i \(0.807899\pi\)
\(500\) −46.0322 −2.05862
\(501\) −35.6694 −1.59359
\(502\) −41.9269 −1.87129
\(503\) −5.91854 −0.263895 −0.131947 0.991257i \(-0.542123\pi\)
−0.131947 + 0.991257i \(0.542123\pi\)
\(504\) −19.2403 −0.857031
\(505\) −0.602136 −0.0267947
\(506\) 37.3003 1.65820
\(507\) 16.8328 0.747570
\(508\) −51.1324 −2.26863
\(509\) 0.239785 0.0106283 0.00531414 0.999986i \(-0.498308\pi\)
0.00531414 + 0.999986i \(0.498308\pi\)
\(510\) 16.2812 0.720942
\(511\) 22.4455 0.992930
\(512\) 31.9454 1.41180
\(513\) 32.7267 1.44492
\(514\) 12.1297 0.535019
\(515\) 10.1694 0.448117
\(516\) 59.2386 2.60783
\(517\) −48.5696 −2.13609
\(518\) −14.1320 −0.620923
\(519\) 5.54727 0.243498
\(520\) 6.66443 0.292254
\(521\) 3.17983 0.139311 0.0696555 0.997571i \(-0.477810\pi\)
0.0696555 + 0.997571i \(0.477810\pi\)
\(522\) −6.79440 −0.297383
\(523\) −31.4780 −1.37643 −0.688217 0.725505i \(-0.741606\pi\)
−0.688217 + 0.725505i \(0.741606\pi\)
\(524\) −11.7300 −0.512427
\(525\) −12.8263 −0.559787
\(526\) −61.0921 −2.66374
\(527\) 25.3406 1.10385
\(528\) −16.0826 −0.699904
\(529\) −6.26299 −0.272304
\(530\) 3.95202 0.171665
\(531\) 9.79583 0.425103
\(532\) −88.6054 −3.84153
\(533\) −2.14271 −0.0928109
\(534\) 20.7036 0.895933
\(535\) 1.14484 0.0494959
\(536\) −20.3643 −0.879606
\(537\) 4.45999 0.192463
\(538\) 30.3583 1.30884
\(539\) 33.4343 1.44012
\(540\) 35.5161 1.52837
\(541\) 2.14069 0.0920354 0.0460177 0.998941i \(-0.485347\pi\)
0.0460177 + 0.998941i \(0.485347\pi\)
\(542\) 7.27397 0.312444
\(543\) 8.08138 0.346805
\(544\) 4.35014 0.186511
\(545\) 3.96886 0.170007
\(546\) 12.1939 0.521850
\(547\) −28.0229 −1.19817 −0.599086 0.800685i \(-0.704469\pi\)
−0.599086 + 0.800685i \(0.704469\pi\)
\(548\) 15.4796 0.661257
\(549\) −1.46278 −0.0624299
\(550\) 21.2148 0.904600
\(551\) −15.0042 −0.639200
\(552\) −25.2188 −1.07338
\(553\) −62.2629 −2.64769
\(554\) 60.5234 2.57139
\(555\) 3.32154 0.140991
\(556\) −33.7512 −1.43137
\(557\) −29.5015 −1.25002 −0.625010 0.780617i \(-0.714905\pi\)
−0.625010 + 0.780617i \(0.714905\pi\)
\(558\) 22.3175 0.944774
\(559\) 10.1938 0.431153
\(560\) −20.0619 −0.847769
\(561\) −15.5394 −0.656075
\(562\) −11.1169 −0.468940
\(563\) 7.90008 0.332949 0.166474 0.986046i \(-0.446762\pi\)
0.166474 + 0.986046i \(0.446762\pi\)
\(564\) 68.4798 2.88352
\(565\) 11.8643 0.499134
\(566\) −69.1591 −2.90697
\(567\) 18.2021 0.764418
\(568\) −16.2132 −0.680289
\(569\) −20.1934 −0.846553 −0.423276 0.906001i \(-0.639120\pi\)
−0.423276 + 0.906001i \(0.639120\pi\)
\(570\) 31.6647 1.32629
\(571\) −5.92942 −0.248139 −0.124069 0.992274i \(-0.539595\pi\)
−0.124069 + 0.992274i \(0.539595\pi\)
\(572\) −13.2647 −0.554627
\(573\) −13.4449 −0.561668
\(574\) 22.5411 0.940846
\(575\) 9.51926 0.396981
\(576\) 10.5137 0.438070
\(577\) −27.0196 −1.12484 −0.562421 0.826851i \(-0.690130\pi\)
−0.562421 + 0.826851i \(0.690130\pi\)
\(578\) 19.6741 0.818333
\(579\) −14.7669 −0.613692
\(580\) −16.2830 −0.676116
\(581\) 17.8296 0.739695
\(582\) 26.2972 1.09006
\(583\) −3.77197 −0.156219
\(584\) 25.1001 1.03865
\(585\) 1.62281 0.0670950
\(586\) 8.81506 0.364147
\(587\) 43.3296 1.78840 0.894201 0.447665i \(-0.147744\pi\)
0.894201 + 0.447665i \(0.147744\pi\)
\(588\) −47.1400 −1.94402
\(589\) 49.2841 2.03072
\(590\) 35.6947 1.46953
\(591\) 22.6727 0.932628
\(592\) −4.52216 −0.185860
\(593\) −3.21606 −0.132068 −0.0660338 0.997817i \(-0.521035\pi\)
−0.0660338 + 0.997817i \(0.521035\pi\)
\(594\) −51.5410 −2.11475
\(595\) −19.3844 −0.794681
\(596\) −41.4871 −1.69938
\(597\) −3.04537 −0.124639
\(598\) −9.04988 −0.370077
\(599\) 18.8454 0.770000 0.385000 0.922916i \(-0.374201\pi\)
0.385000 + 0.922916i \(0.374201\pi\)
\(600\) −14.3433 −0.585563
\(601\) −13.3998 −0.546590 −0.273295 0.961930i \(-0.588114\pi\)
−0.273295 + 0.961930i \(0.588114\pi\)
\(602\) −107.238 −4.37070
\(603\) −4.95879 −0.201937
\(604\) −3.84266 −0.156356
\(605\) 5.27732 0.214554
\(606\) −1.23203 −0.0500476
\(607\) 45.9041 1.86319 0.931594 0.363500i \(-0.118418\pi\)
0.931594 + 0.363500i \(0.118418\pi\)
\(608\) 8.46045 0.343117
\(609\) −14.2866 −0.578921
\(610\) −5.33018 −0.215813
\(611\) 11.7841 0.476732
\(612\) −12.4057 −0.501471
\(613\) 31.4026 1.26834 0.634169 0.773195i \(-0.281342\pi\)
0.634169 + 0.773195i \(0.281342\pi\)
\(614\) 7.79218 0.314467
\(615\) −5.29799 −0.213636
\(616\) 66.9151 2.69609
\(617\) 14.5913 0.587423 0.293711 0.955894i \(-0.405110\pi\)
0.293711 + 0.955894i \(0.405110\pi\)
\(618\) 20.8075 0.837002
\(619\) 2.31345 0.0929854 0.0464927 0.998919i \(-0.485196\pi\)
0.0464927 + 0.998919i \(0.485196\pi\)
\(620\) 53.4847 2.14800
\(621\) −23.1270 −0.928053
\(622\) 32.8067 1.31543
\(623\) −24.6497 −0.987570
\(624\) 3.90198 0.156204
\(625\) −7.95173 −0.318069
\(626\) 32.1502 1.28498
\(627\) −30.2221 −1.20695
\(628\) 86.3185 3.44448
\(629\) −4.36944 −0.174221
\(630\) −17.0718 −0.680157
\(631\) −28.4395 −1.13216 −0.566080 0.824350i \(-0.691541\pi\)
−0.566080 + 0.824350i \(0.691541\pi\)
\(632\) −69.6267 −2.76960
\(633\) 24.1858 0.961301
\(634\) −38.5816 −1.53227
\(635\) −21.7559 −0.863357
\(636\) 5.31821 0.210881
\(637\) −8.11190 −0.321405
\(638\) 23.6300 0.935519
\(639\) −3.94796 −0.156179
\(640\) 33.5317 1.32546
\(641\) −46.8720 −1.85133 −0.925667 0.378340i \(-0.876495\pi\)
−0.925667 + 0.378340i \(0.876495\pi\)
\(642\) 2.34246 0.0924494
\(643\) −23.4527 −0.924886 −0.462443 0.886649i \(-0.653027\pi\)
−0.462443 + 0.886649i \(0.653027\pi\)
\(644\) 62.6147 2.46736
\(645\) 25.2050 0.992445
\(646\) −41.6545 −1.63887
\(647\) 29.5807 1.16294 0.581468 0.813569i \(-0.302479\pi\)
0.581468 + 0.813569i \(0.302479\pi\)
\(648\) 20.3549 0.799616
\(649\) −34.0685 −1.33731
\(650\) −5.14716 −0.201888
\(651\) 46.9269 1.83921
\(652\) −23.2862 −0.911960
\(653\) −8.87991 −0.347498 −0.173749 0.984790i \(-0.555588\pi\)
−0.173749 + 0.984790i \(0.555588\pi\)
\(654\) 8.12067 0.317543
\(655\) −4.99090 −0.195011
\(656\) 7.21303 0.281621
\(657\) 6.11196 0.238450
\(658\) −123.967 −4.83274
\(659\) 20.5142 0.799118 0.399559 0.916707i \(-0.369163\pi\)
0.399559 + 0.916707i \(0.369163\pi\)
\(660\) −32.7980 −1.27666
\(661\) 26.8031 1.04252 0.521260 0.853398i \(-0.325462\pi\)
0.521260 + 0.853398i \(0.325462\pi\)
\(662\) 23.6599 0.919567
\(663\) 3.77021 0.146423
\(664\) 19.9382 0.773754
\(665\) −37.7000 −1.46194
\(666\) −3.84817 −0.149113
\(667\) 10.6030 0.410549
\(668\) 99.0364 3.83183
\(669\) −11.9266 −0.461110
\(670\) −18.0692 −0.698073
\(671\) 5.08734 0.196395
\(672\) 8.05580 0.310759
\(673\) −15.8695 −0.611724 −0.305862 0.952076i \(-0.598945\pi\)
−0.305862 + 0.952076i \(0.598945\pi\)
\(674\) 38.4468 1.48092
\(675\) −13.1536 −0.506281
\(676\) −46.7363 −1.79755
\(677\) −35.0648 −1.34765 −0.673826 0.738890i \(-0.735350\pi\)
−0.673826 + 0.738890i \(0.735350\pi\)
\(678\) 24.2754 0.932292
\(679\) −31.3095 −1.20155
\(680\) −21.6769 −0.831272
\(681\) −30.4883 −1.16831
\(682\) −77.6171 −2.97211
\(683\) −4.38314 −0.167716 −0.0838581 0.996478i \(-0.526724\pi\)
−0.0838581 + 0.996478i \(0.526724\pi\)
\(684\) −24.1274 −0.922536
\(685\) 6.58630 0.251650
\(686\) 17.9444 0.685122
\(687\) −10.8412 −0.413617
\(688\) −34.3157 −1.30827
\(689\) 0.915163 0.0348649
\(690\) −22.3765 −0.851857
\(691\) 36.4667 1.38726 0.693630 0.720332i \(-0.256010\pi\)
0.693630 + 0.720332i \(0.256010\pi\)
\(692\) −15.4020 −0.585497
\(693\) 16.2941 0.618960
\(694\) 29.5419 1.12140
\(695\) −14.3605 −0.544726
\(696\) −15.9762 −0.605577
\(697\) 6.96943 0.263986
\(698\) −46.1378 −1.74634
\(699\) 13.3248 0.503990
\(700\) 35.6124 1.34602
\(701\) −21.7976 −0.823284 −0.411642 0.911346i \(-0.635045\pi\)
−0.411642 + 0.911346i \(0.635045\pi\)
\(702\) 12.5050 0.471970
\(703\) −8.49798 −0.320507
\(704\) −36.5651 −1.37810
\(705\) 29.1369 1.09736
\(706\) 18.1942 0.684747
\(707\) 1.46685 0.0551666
\(708\) 48.0343 1.80524
\(709\) −16.7299 −0.628303 −0.314151 0.949373i \(-0.601720\pi\)
−0.314151 + 0.949373i \(0.601720\pi\)
\(710\) −14.3858 −0.539891
\(711\) −16.9543 −0.635837
\(712\) −27.5650 −1.03304
\(713\) −34.8275 −1.30430
\(714\) −39.6622 −1.48432
\(715\) −5.64391 −0.211070
\(716\) −12.3832 −0.462781
\(717\) 12.6203 0.471313
\(718\) −45.8564 −1.71135
\(719\) −42.8163 −1.59678 −0.798389 0.602142i \(-0.794314\pi\)
−0.798389 + 0.602142i \(0.794314\pi\)
\(720\) −5.46290 −0.203590
\(721\) −24.7734 −0.922611
\(722\) −35.0864 −1.30578
\(723\) −9.04149 −0.336257
\(724\) −22.4380 −0.833902
\(725\) 6.03051 0.223967
\(726\) 10.7979 0.400748
\(727\) −40.7249 −1.51040 −0.755201 0.655493i \(-0.772461\pi\)
−0.755201 + 0.655493i \(0.772461\pi\)
\(728\) −16.2351 −0.601712
\(729\) 28.4276 1.05288
\(730\) 22.2712 0.824293
\(731\) −33.1568 −1.22635
\(732\) −7.17280 −0.265114
\(733\) 24.4080 0.901529 0.450764 0.892643i \(-0.351151\pi\)
0.450764 + 0.892643i \(0.351151\pi\)
\(734\) 23.8145 0.879009
\(735\) −20.0572 −0.739822
\(736\) −5.97874 −0.220379
\(737\) 17.2460 0.635263
\(738\) 6.13798 0.225942
\(739\) −45.2432 −1.66430 −0.832149 0.554551i \(-0.812890\pi\)
−0.832149 + 0.554551i \(0.812890\pi\)
\(740\) −9.22227 −0.339018
\(741\) 7.33255 0.269368
\(742\) −9.62743 −0.353434
\(743\) −30.4294 −1.11635 −0.558173 0.829725i \(-0.688497\pi\)
−0.558173 + 0.829725i \(0.688497\pi\)
\(744\) 52.4769 1.92390
\(745\) −17.6520 −0.646719
\(746\) −23.4194 −0.857444
\(747\) 4.85503 0.177636
\(748\) 43.1453 1.57755
\(749\) −2.78893 −0.101905
\(750\) −40.0745 −1.46331
\(751\) −49.4718 −1.80525 −0.902627 0.430424i \(-0.858364\pi\)
−0.902627 + 0.430424i \(0.858364\pi\)
\(752\) −39.6689 −1.44658
\(753\) −24.0061 −0.874829
\(754\) −5.73315 −0.208789
\(755\) −1.63498 −0.0595031
\(756\) −86.5200 −3.14670
\(757\) −16.4969 −0.599589 −0.299794 0.954004i \(-0.596918\pi\)
−0.299794 + 0.954004i \(0.596918\pi\)
\(758\) −38.0435 −1.38180
\(759\) 21.3570 0.775211
\(760\) −42.1587 −1.52926
\(761\) 36.5717 1.32572 0.662861 0.748743i \(-0.269342\pi\)
0.662861 + 0.748743i \(0.269342\pi\)
\(762\) −44.5146 −1.61260
\(763\) −9.66847 −0.350022
\(764\) 37.3298 1.35054
\(765\) −5.27841 −0.190841
\(766\) −27.4373 −0.991350
\(767\) 8.26578 0.298460
\(768\) 41.7765 1.50748
\(769\) 6.05562 0.218371 0.109186 0.994021i \(-0.465176\pi\)
0.109186 + 0.994021i \(0.465176\pi\)
\(770\) 59.3734 2.13967
\(771\) 6.94510 0.250122
\(772\) 41.0004 1.47564
\(773\) −42.7471 −1.53751 −0.768753 0.639546i \(-0.779122\pi\)
−0.768753 + 0.639546i \(0.779122\pi\)
\(774\) −29.2012 −1.04962
\(775\) −19.8083 −0.711537
\(776\) −35.0124 −1.25687
\(777\) −8.09153 −0.290282
\(778\) 35.3977 1.26907
\(779\) 13.5546 0.485645
\(780\) 7.95752 0.284925
\(781\) 13.7304 0.491314
\(782\) 29.4359 1.05263
\(783\) −14.6511 −0.523586
\(784\) 27.3072 0.975258
\(785\) 36.7270 1.31084
\(786\) −10.2119 −0.364245
\(787\) 20.9093 0.745335 0.372667 0.927965i \(-0.378443\pi\)
0.372667 + 0.927965i \(0.378443\pi\)
\(788\) −62.9508 −2.24253
\(789\) −34.9795 −1.24530
\(790\) −61.7793 −2.19801
\(791\) −28.9023 −1.02765
\(792\) 18.2211 0.647460
\(793\) −1.23430 −0.0438313
\(794\) −36.0373 −1.27892
\(795\) 2.26280 0.0802534
\(796\) 8.45550 0.299697
\(797\) 5.55691 0.196836 0.0984179 0.995145i \(-0.468622\pi\)
0.0984179 + 0.995145i \(0.468622\pi\)
\(798\) −77.1377 −2.73065
\(799\) −38.3292 −1.35599
\(800\) −3.40044 −0.120224
\(801\) −6.71218 −0.237163
\(802\) −3.85799 −0.136230
\(803\) −21.2565 −0.750127
\(804\) −24.3156 −0.857545
\(805\) 26.6414 0.938986
\(806\) 18.8316 0.663315
\(807\) 17.3822 0.611883
\(808\) 1.64033 0.0577067
\(809\) 2.42037 0.0850957 0.0425478 0.999094i \(-0.486453\pi\)
0.0425478 + 0.999094i \(0.486453\pi\)
\(810\) 18.0608 0.634591
\(811\) 15.3009 0.537288 0.268644 0.963240i \(-0.413425\pi\)
0.268644 + 0.963240i \(0.413425\pi\)
\(812\) 39.6667 1.39203
\(813\) 4.16485 0.146068
\(814\) 13.3834 0.469087
\(815\) −9.90788 −0.347058
\(816\) −12.6917 −0.444299
\(817\) −64.4855 −2.25606
\(818\) 58.0903 2.03108
\(819\) −3.95329 −0.138139
\(820\) 14.7099 0.513692
\(821\) 4.32367 0.150897 0.0754486 0.997150i \(-0.475961\pi\)
0.0754486 + 0.997150i \(0.475961\pi\)
\(822\) 13.4762 0.470036
\(823\) −24.2140 −0.844045 −0.422023 0.906585i \(-0.638680\pi\)
−0.422023 + 0.906585i \(0.638680\pi\)
\(824\) −27.7034 −0.965093
\(825\) 12.1469 0.422901
\(826\) −86.9552 −3.02556
\(827\) 4.11769 0.143186 0.0715931 0.997434i \(-0.477192\pi\)
0.0715931 + 0.997434i \(0.477192\pi\)
\(828\) 17.0501 0.592532
\(829\) −45.8257 −1.59159 −0.795796 0.605564i \(-0.792948\pi\)
−0.795796 + 0.605564i \(0.792948\pi\)
\(830\) 17.6911 0.614067
\(831\) 34.6538 1.20213
\(832\) 8.87150 0.307564
\(833\) 26.3850 0.914187
\(834\) −29.3830 −1.01745
\(835\) 42.1382 1.45825
\(836\) 83.9119 2.90215
\(837\) 48.1242 1.66341
\(838\) 9.44957 0.326430
\(839\) −49.6182 −1.71301 −0.856506 0.516137i \(-0.827369\pi\)
−0.856506 + 0.516137i \(0.827369\pi\)
\(840\) −40.1424 −1.38504
\(841\) −22.2829 −0.768377
\(842\) 64.6436 2.22777
\(843\) −6.36522 −0.219230
\(844\) −67.1521 −2.31147
\(845\) −19.8855 −0.684080
\(846\) −33.7565 −1.16057
\(847\) −12.8560 −0.441737
\(848\) −3.08073 −0.105793
\(849\) −39.5984 −1.35901
\(850\) 16.7418 0.574240
\(851\) 6.00525 0.205857
\(852\) −19.3590 −0.663227
\(853\) −44.5214 −1.52438 −0.762192 0.647351i \(-0.775877\pi\)
−0.762192 + 0.647351i \(0.775877\pi\)
\(854\) 12.9847 0.444328
\(855\) −10.2658 −0.351083
\(856\) −3.11877 −0.106598
\(857\) −26.1115 −0.891953 −0.445977 0.895045i \(-0.647144\pi\)
−0.445977 + 0.895045i \(0.647144\pi\)
\(858\) −11.5480 −0.394241
\(859\) −18.3390 −0.625719 −0.312860 0.949799i \(-0.601287\pi\)
−0.312860 + 0.949799i \(0.601287\pi\)
\(860\) −69.9817 −2.38636
\(861\) 12.9063 0.439846
\(862\) −48.3291 −1.64609
\(863\) −37.4770 −1.27573 −0.637867 0.770147i \(-0.720183\pi\)
−0.637867 + 0.770147i \(0.720183\pi\)
\(864\) 8.26133 0.281056
\(865\) −6.55328 −0.222818
\(866\) 52.4162 1.78117
\(867\) 11.2648 0.382572
\(868\) −130.293 −4.42243
\(869\) 58.9648 2.00024
\(870\) −14.1756 −0.480598
\(871\) −4.18425 −0.141778
\(872\) −10.8119 −0.366139
\(873\) −8.52564 −0.288549
\(874\) 57.2489 1.93647
\(875\) 47.7127 1.61298
\(876\) 29.9702 1.01260
\(877\) −4.38994 −0.148238 −0.0741188 0.997249i \(-0.523614\pi\)
−0.0741188 + 0.997249i \(0.523614\pi\)
\(878\) −20.4503 −0.690163
\(879\) 5.04723 0.170239
\(880\) 18.9992 0.640463
\(881\) 1.04419 0.0351796 0.0175898 0.999845i \(-0.494401\pi\)
0.0175898 + 0.999845i \(0.494401\pi\)
\(882\) 23.2373 0.782441
\(883\) −7.75537 −0.260989 −0.130495 0.991449i \(-0.541656\pi\)
−0.130495 + 0.991449i \(0.541656\pi\)
\(884\) −10.4680 −0.352077
\(885\) 20.4377 0.687006
\(886\) −19.5031 −0.655220
\(887\) 10.7999 0.362624 0.181312 0.983426i \(-0.441966\pi\)
0.181312 + 0.983426i \(0.441966\pi\)
\(888\) −9.04851 −0.303648
\(889\) 52.9991 1.77753
\(890\) −24.4583 −0.819844
\(891\) −17.2380 −0.577494
\(892\) 33.1144 1.10875
\(893\) −74.5452 −2.49456
\(894\) −36.1176 −1.20795
\(895\) −5.26882 −0.176117
\(896\) −81.6860 −2.72894
\(897\) −5.18168 −0.173011
\(898\) −61.1592 −2.04091
\(899\) −22.0634 −0.735857
\(900\) 9.69734 0.323245
\(901\) −2.97669 −0.0991678
\(902\) −21.3470 −0.710779
\(903\) −61.4013 −2.04331
\(904\) −32.3206 −1.07497
\(905\) −9.54697 −0.317352
\(906\) −3.34533 −0.111141
\(907\) 31.1281 1.03359 0.516796 0.856108i \(-0.327124\pi\)
0.516796 + 0.856108i \(0.327124\pi\)
\(908\) 84.6509 2.80924
\(909\) 0.399427 0.0132481
\(910\) −14.4053 −0.477531
\(911\) 18.5023 0.613008 0.306504 0.951869i \(-0.400841\pi\)
0.306504 + 0.951869i \(0.400841\pi\)
\(912\) −24.6837 −0.817359
\(913\) −16.8851 −0.558816
\(914\) −20.5921 −0.681126
\(915\) −3.05190 −0.100893
\(916\) 30.1006 0.994552
\(917\) 12.1582 0.401500
\(918\) −40.6741 −1.34245
\(919\) −45.5882 −1.50382 −0.751908 0.659268i \(-0.770866\pi\)
−0.751908 + 0.659268i \(0.770866\pi\)
\(920\) 29.7923 0.982222
\(921\) 4.46157 0.147014
\(922\) −20.5110 −0.675492
\(923\) −3.33131 −0.109651
\(924\) 79.8985 2.62847
\(925\) 3.41552 0.112302
\(926\) −12.4896 −0.410433
\(927\) −6.74587 −0.221563
\(928\) −3.78756 −0.124333
\(929\) 13.4186 0.440251 0.220125 0.975472i \(-0.429353\pi\)
0.220125 + 0.975472i \(0.429353\pi\)
\(930\) 46.5625 1.52684
\(931\) 51.3153 1.68179
\(932\) −36.9964 −1.21186
\(933\) 18.7841 0.614964
\(934\) −76.5485 −2.50474
\(935\) 18.3576 0.600356
\(936\) −4.42085 −0.144500
\(937\) −34.9653 −1.14227 −0.571134 0.820857i \(-0.693496\pi\)
−0.571134 + 0.820857i \(0.693496\pi\)
\(938\) 44.0179 1.43724
\(939\) 18.4082 0.600730
\(940\) −80.8988 −2.63863
\(941\) −29.3230 −0.955902 −0.477951 0.878386i \(-0.658620\pi\)
−0.477951 + 0.878386i \(0.658620\pi\)
\(942\) 75.1468 2.44841
\(943\) −9.57863 −0.311923
\(944\) −27.8252 −0.905634
\(945\) −36.8127 −1.19752
\(946\) 101.558 3.30192
\(947\) −0.132313 −0.00429959 −0.00214980 0.999998i \(-0.500684\pi\)
−0.00214980 + 0.999998i \(0.500684\pi\)
\(948\) −83.1362 −2.70014
\(949\) 5.15730 0.167413
\(950\) 32.5606 1.05641
\(951\) −22.0906 −0.716337
\(952\) 52.8067 1.71148
\(953\) −59.8694 −1.93936 −0.969680 0.244379i \(-0.921416\pi\)
−0.969680 + 0.244379i \(0.921416\pi\)
\(954\) −2.62157 −0.0848765
\(955\) 15.8831 0.513967
\(956\) −35.0403 −1.13329
\(957\) 13.5298 0.437356
\(958\) −21.3809 −0.690787
\(959\) −16.0447 −0.518112
\(960\) 21.9354 0.707962
\(961\) 41.4715 1.33779
\(962\) −3.24710 −0.104691
\(963\) −0.759432 −0.0244724
\(964\) 25.1038 0.808538
\(965\) 17.4449 0.561572
\(966\) 54.5108 1.75386
\(967\) −34.2593 −1.10170 −0.550852 0.834603i \(-0.685697\pi\)
−0.550852 + 0.834603i \(0.685697\pi\)
\(968\) −14.3764 −0.462076
\(969\) −23.8501 −0.766175
\(970\) −31.0663 −0.997480
\(971\) 27.2510 0.874525 0.437263 0.899334i \(-0.355948\pi\)
0.437263 + 0.899334i \(0.355948\pi\)
\(972\) −40.8635 −1.31070
\(973\) 34.9834 1.12152
\(974\) 33.1252 1.06140
\(975\) −2.94711 −0.0943830
\(976\) 4.15505 0.133000
\(977\) −19.1638 −0.613104 −0.306552 0.951854i \(-0.599175\pi\)
−0.306552 + 0.951854i \(0.599175\pi\)
\(978\) −20.2725 −0.648241
\(979\) 23.3440 0.746078
\(980\) 55.6891 1.77892
\(981\) −2.63275 −0.0840571
\(982\) 92.7748 2.96056
\(983\) −33.6066 −1.07188 −0.535942 0.844255i \(-0.680043\pi\)
−0.535942 + 0.844255i \(0.680043\pi\)
\(984\) 14.4327 0.460099
\(985\) −26.7844 −0.853423
\(986\) 18.6478 0.593868
\(987\) −70.9798 −2.25931
\(988\) −20.3589 −0.647702
\(989\) 45.5699 1.44904
\(990\) 16.1675 0.513837
\(991\) −17.5259 −0.556727 −0.278364 0.960476i \(-0.589792\pi\)
−0.278364 + 0.960476i \(0.589792\pi\)
\(992\) 12.4410 0.395001
\(993\) 13.5469 0.429898
\(994\) 35.0450 1.11156
\(995\) 3.59766 0.114054
\(996\) 23.8068 0.754348
\(997\) −8.00286 −0.253453 −0.126727 0.991938i \(-0.540447\pi\)
−0.126727 + 0.991938i \(0.540447\pi\)
\(998\) 88.9143 2.81453
\(999\) −8.29797 −0.262536
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 8003.2.a.b.1.14 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.14 153 1.1 even 1 trivial