Properties

Label 8003.2.a.b.1.10
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 1.10
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.53517 q^{2} +1.42230 q^{3} +4.42707 q^{4} -0.780530 q^{5} -3.60576 q^{6} +3.78955 q^{7} -6.15303 q^{8} -0.977076 q^{9} +O(q^{10})\) \(q-2.53517 q^{2} +1.42230 q^{3} +4.42707 q^{4} -0.780530 q^{5} -3.60576 q^{6} +3.78955 q^{7} -6.15303 q^{8} -0.977076 q^{9} +1.97877 q^{10} +2.96223 q^{11} +6.29660 q^{12} +1.57830 q^{13} -9.60715 q^{14} -1.11014 q^{15} +6.74482 q^{16} +2.53935 q^{17} +2.47705 q^{18} -7.71279 q^{19} -3.45546 q^{20} +5.38986 q^{21} -7.50974 q^{22} -4.09240 q^{23} -8.75143 q^{24} -4.39077 q^{25} -4.00126 q^{26} -5.65658 q^{27} +16.7766 q^{28} -0.435120 q^{29} +2.81440 q^{30} -1.49375 q^{31} -4.79318 q^{32} +4.21316 q^{33} -6.43767 q^{34} -2.95786 q^{35} -4.32558 q^{36} -0.989655 q^{37} +19.5532 q^{38} +2.24481 q^{39} +4.80263 q^{40} +12.0832 q^{41} -13.6642 q^{42} -0.490917 q^{43} +13.1140 q^{44} +0.762637 q^{45} +10.3749 q^{46} -4.41763 q^{47} +9.59313 q^{48} +7.36070 q^{49} +11.1313 q^{50} +3.61170 q^{51} +6.98725 q^{52} -1.00000 q^{53} +14.3404 q^{54} -2.31211 q^{55} -23.3172 q^{56} -10.9699 q^{57} +1.10310 q^{58} +8.60279 q^{59} -4.91469 q^{60} -9.88072 q^{61} +3.78691 q^{62} -3.70268 q^{63} -1.33813 q^{64} -1.23191 q^{65} -10.6811 q^{66} +3.59744 q^{67} +11.2419 q^{68} -5.82060 q^{69} +7.49866 q^{70} -10.9407 q^{71} +6.01198 q^{72} -14.3983 q^{73} +2.50894 q^{74} -6.24498 q^{75} -34.1451 q^{76} +11.2255 q^{77} -5.69097 q^{78} -14.4925 q^{79} -5.26453 q^{80} -5.11410 q^{81} -30.6329 q^{82} +4.85792 q^{83} +23.8613 q^{84} -1.98204 q^{85} +1.24456 q^{86} -0.618869 q^{87} -18.2267 q^{88} -2.41218 q^{89} -1.93341 q^{90} +5.98105 q^{91} -18.1173 q^{92} -2.12456 q^{93} +11.1994 q^{94} +6.02006 q^{95} -6.81732 q^{96} +4.04116 q^{97} -18.6606 q^{98} -2.89432 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53517 −1.79263 −0.896317 0.443414i \(-0.853767\pi\)
−0.896317 + 0.443414i \(0.853767\pi\)
\(3\) 1.42230 0.821163 0.410581 0.911824i \(-0.365326\pi\)
0.410581 + 0.911824i \(0.365326\pi\)
\(4\) 4.42707 2.21354
\(5\) −0.780530 −0.349064 −0.174532 0.984652i \(-0.555841\pi\)
−0.174532 + 0.984652i \(0.555841\pi\)
\(6\) −3.60576 −1.47204
\(7\) 3.78955 1.43232 0.716158 0.697938i \(-0.245899\pi\)
0.716158 + 0.697938i \(0.245899\pi\)
\(8\) −6.15303 −2.17543
\(9\) −0.977076 −0.325692
\(10\) 1.97877 0.625743
\(11\) 2.96223 0.893145 0.446572 0.894748i \(-0.352645\pi\)
0.446572 + 0.894748i \(0.352645\pi\)
\(12\) 6.29660 1.81767
\(13\) 1.57830 0.437742 0.218871 0.975754i \(-0.429763\pi\)
0.218871 + 0.975754i \(0.429763\pi\)
\(14\) −9.60715 −2.56762
\(15\) −1.11014 −0.286638
\(16\) 6.74482 1.68620
\(17\) 2.53935 0.615882 0.307941 0.951405i \(-0.400360\pi\)
0.307941 + 0.951405i \(0.400360\pi\)
\(18\) 2.47705 0.583846
\(19\) −7.71279 −1.76944 −0.884718 0.466127i \(-0.845649\pi\)
−0.884718 + 0.466127i \(0.845649\pi\)
\(20\) −3.45546 −0.772665
\(21\) 5.38986 1.17616
\(22\) −7.50974 −1.60108
\(23\) −4.09240 −0.853324 −0.426662 0.904411i \(-0.640311\pi\)
−0.426662 + 0.904411i \(0.640311\pi\)
\(24\) −8.75143 −1.78638
\(25\) −4.39077 −0.878155
\(26\) −4.00126 −0.784711
\(27\) −5.65658 −1.08861
\(28\) 16.7766 3.17048
\(29\) −0.435120 −0.0807997 −0.0403999 0.999184i \(-0.512863\pi\)
−0.0403999 + 0.999184i \(0.512863\pi\)
\(30\) 2.81440 0.513837
\(31\) −1.49375 −0.268286 −0.134143 0.990962i \(-0.542828\pi\)
−0.134143 + 0.990962i \(0.542828\pi\)
\(32\) −4.79318 −0.847323
\(33\) 4.21316 0.733417
\(34\) −6.43767 −1.10405
\(35\) −2.95786 −0.499969
\(36\) −4.32558 −0.720931
\(37\) −0.989655 −0.162698 −0.0813491 0.996686i \(-0.525923\pi\)
−0.0813491 + 0.996686i \(0.525923\pi\)
\(38\) 19.5532 3.17195
\(39\) 2.24481 0.359457
\(40\) 4.80263 0.759362
\(41\) 12.0832 1.88708 0.943540 0.331259i \(-0.107473\pi\)
0.943540 + 0.331259i \(0.107473\pi\)
\(42\) −13.6642 −2.10843
\(43\) −0.490917 −0.0748642 −0.0374321 0.999299i \(-0.511918\pi\)
−0.0374321 + 0.999299i \(0.511918\pi\)
\(44\) 13.1140 1.97701
\(45\) 0.762637 0.113687
\(46\) 10.3749 1.52970
\(47\) −4.41763 −0.644378 −0.322189 0.946675i \(-0.604419\pi\)
−0.322189 + 0.946675i \(0.604419\pi\)
\(48\) 9.59313 1.38465
\(49\) 7.36070 1.05153
\(50\) 11.1313 1.57421
\(51\) 3.61170 0.505739
\(52\) 6.98725 0.968957
\(53\) −1.00000 −0.137361
\(54\) 14.3404 1.95148
\(55\) −2.31211 −0.311764
\(56\) −23.3172 −3.11590
\(57\) −10.9699 −1.45299
\(58\) 1.10310 0.144844
\(59\) 8.60279 1.11999 0.559994 0.828497i \(-0.310803\pi\)
0.559994 + 0.828497i \(0.310803\pi\)
\(60\) −4.91469 −0.634483
\(61\) −9.88072 −1.26510 −0.632548 0.774521i \(-0.717991\pi\)
−0.632548 + 0.774521i \(0.717991\pi\)
\(62\) 3.78691 0.480939
\(63\) −3.70268 −0.466494
\(64\) −1.33813 −0.167266
\(65\) −1.23191 −0.152800
\(66\) −10.6811 −1.31475
\(67\) 3.59744 0.439497 0.219748 0.975557i \(-0.429476\pi\)
0.219748 + 0.975557i \(0.429476\pi\)
\(68\) 11.2419 1.36328
\(69\) −5.82060 −0.700718
\(70\) 7.49866 0.896262
\(71\) −10.9407 −1.29843 −0.649213 0.760607i \(-0.724902\pi\)
−0.649213 + 0.760607i \(0.724902\pi\)
\(72\) 6.01198 0.708518
\(73\) −14.3983 −1.68519 −0.842595 0.538548i \(-0.818973\pi\)
−0.842595 + 0.538548i \(0.818973\pi\)
\(74\) 2.50894 0.291658
\(75\) −6.24498 −0.721108
\(76\) −34.1451 −3.91671
\(77\) 11.2255 1.27927
\(78\) −5.69097 −0.644375
\(79\) −14.4925 −1.63053 −0.815267 0.579085i \(-0.803410\pi\)
−0.815267 + 0.579085i \(0.803410\pi\)
\(80\) −5.26453 −0.588593
\(81\) −5.11410 −0.568233
\(82\) −30.6329 −3.38284
\(83\) 4.85792 0.533226 0.266613 0.963804i \(-0.414095\pi\)
0.266613 + 0.963804i \(0.414095\pi\)
\(84\) 23.8613 2.60348
\(85\) −1.98204 −0.214982
\(86\) 1.24456 0.134204
\(87\) −0.618869 −0.0663497
\(88\) −18.2267 −1.94297
\(89\) −2.41218 −0.255690 −0.127845 0.991794i \(-0.540806\pi\)
−0.127845 + 0.991794i \(0.540806\pi\)
\(90\) −1.93341 −0.203800
\(91\) 5.98105 0.626985
\(92\) −18.1173 −1.88886
\(93\) −2.12456 −0.220306
\(94\) 11.1994 1.15513
\(95\) 6.02006 0.617645
\(96\) −6.81732 −0.695790
\(97\) 4.04116 0.410318 0.205159 0.978729i \(-0.434229\pi\)
0.205159 + 0.978729i \(0.434229\pi\)
\(98\) −18.6606 −1.88501
\(99\) −2.89432 −0.290890
\(100\) −19.4383 −1.94383
\(101\) −15.3894 −1.53130 −0.765650 0.643257i \(-0.777583\pi\)
−0.765650 + 0.643257i \(0.777583\pi\)
\(102\) −9.15627 −0.906606
\(103\) 2.16277 0.213104 0.106552 0.994307i \(-0.466019\pi\)
0.106552 + 0.994307i \(0.466019\pi\)
\(104\) −9.71134 −0.952275
\(105\) −4.20695 −0.410556
\(106\) 2.53517 0.246237
\(107\) 12.7260 1.23026 0.615132 0.788424i \(-0.289103\pi\)
0.615132 + 0.788424i \(0.289103\pi\)
\(108\) −25.0421 −2.40967
\(109\) −2.19302 −0.210053 −0.105027 0.994469i \(-0.533493\pi\)
−0.105027 + 0.994469i \(0.533493\pi\)
\(110\) 5.86157 0.558879
\(111\) −1.40758 −0.133602
\(112\) 25.5598 2.41518
\(113\) 6.09623 0.573485 0.286742 0.958008i \(-0.407428\pi\)
0.286742 + 0.958008i \(0.407428\pi\)
\(114\) 27.8104 2.60469
\(115\) 3.19424 0.297864
\(116\) −1.92631 −0.178853
\(117\) −1.54212 −0.142569
\(118\) −21.8095 −2.00773
\(119\) 9.62299 0.882138
\(120\) 6.83075 0.623559
\(121\) −2.22522 −0.202293
\(122\) 25.0493 2.26785
\(123\) 17.1859 1.54960
\(124\) −6.61295 −0.593861
\(125\) 7.32978 0.655595
\(126\) 9.38691 0.836252
\(127\) −20.5673 −1.82506 −0.912528 0.409014i \(-0.865873\pi\)
−0.912528 + 0.409014i \(0.865873\pi\)
\(128\) 12.9787 1.14717
\(129\) −0.698229 −0.0614756
\(130\) 3.12310 0.273914
\(131\) −16.6749 −1.45689 −0.728446 0.685104i \(-0.759757\pi\)
−0.728446 + 0.685104i \(0.759757\pi\)
\(132\) 18.6520 1.62344
\(133\) −29.2280 −2.53439
\(134\) −9.12011 −0.787857
\(135\) 4.41513 0.379994
\(136\) −15.6247 −1.33981
\(137\) 0.202869 0.0173323 0.00866613 0.999962i \(-0.497241\pi\)
0.00866613 + 0.999962i \(0.497241\pi\)
\(138\) 14.7562 1.25613
\(139\) 14.4046 1.22178 0.610891 0.791715i \(-0.290811\pi\)
0.610891 + 0.791715i \(0.290811\pi\)
\(140\) −13.0947 −1.10670
\(141\) −6.28318 −0.529139
\(142\) 27.7366 2.32760
\(143\) 4.67528 0.390967
\(144\) −6.59020 −0.549183
\(145\) 0.339624 0.0282043
\(146\) 36.5020 3.02093
\(147\) 10.4691 0.863476
\(148\) −4.38127 −0.360138
\(149\) −3.90790 −0.320148 −0.160074 0.987105i \(-0.551173\pi\)
−0.160074 + 0.987105i \(0.551173\pi\)
\(150\) 15.8321 1.29268
\(151\) −1.00000 −0.0813788
\(152\) 47.4570 3.84927
\(153\) −2.48114 −0.200588
\(154\) −28.4585 −2.29325
\(155\) 1.16592 0.0936489
\(156\) 9.93793 0.795672
\(157\) 16.1979 1.29274 0.646368 0.763026i \(-0.276287\pi\)
0.646368 + 0.763026i \(0.276287\pi\)
\(158\) 36.7409 2.92295
\(159\) −1.42230 −0.112795
\(160\) 3.74122 0.295769
\(161\) −15.5084 −1.22223
\(162\) 12.9651 1.01863
\(163\) −13.8251 −1.08287 −0.541433 0.840744i \(-0.682118\pi\)
−0.541433 + 0.840744i \(0.682118\pi\)
\(164\) 53.4932 4.17712
\(165\) −3.28850 −0.256009
\(166\) −12.3156 −0.955879
\(167\) −7.81948 −0.605089 −0.302545 0.953135i \(-0.597836\pi\)
−0.302545 + 0.953135i \(0.597836\pi\)
\(168\) −33.1640 −2.55866
\(169\) −10.5090 −0.808382
\(170\) 5.02479 0.385384
\(171\) 7.53598 0.576291
\(172\) −2.17333 −0.165714
\(173\) −22.6389 −1.72120 −0.860602 0.509277i \(-0.829913\pi\)
−0.860602 + 0.509277i \(0.829913\pi\)
\(174\) 1.56894 0.118941
\(175\) −16.6391 −1.25779
\(176\) 19.9797 1.50602
\(177\) 12.2357 0.919693
\(178\) 6.11527 0.458359
\(179\) −17.3408 −1.29611 −0.648056 0.761592i \(-0.724418\pi\)
−0.648056 + 0.761592i \(0.724418\pi\)
\(180\) 3.37625 0.251651
\(181\) −10.8386 −0.805624 −0.402812 0.915283i \(-0.631967\pi\)
−0.402812 + 0.915283i \(0.631967\pi\)
\(182\) −15.1630 −1.12395
\(183\) −14.0533 −1.03885
\(184\) 25.1807 1.85634
\(185\) 0.772455 0.0567920
\(186\) 5.38611 0.394929
\(187\) 7.52212 0.550072
\(188\) −19.5572 −1.42635
\(189\) −21.4359 −1.55923
\(190\) −15.2619 −1.10721
\(191\) 17.6961 1.28045 0.640224 0.768188i \(-0.278842\pi\)
0.640224 + 0.768188i \(0.278842\pi\)
\(192\) −1.90321 −0.137352
\(193\) 17.8255 1.28310 0.641552 0.767079i \(-0.278291\pi\)
0.641552 + 0.767079i \(0.278291\pi\)
\(194\) −10.2450 −0.735550
\(195\) −1.75214 −0.125473
\(196\) 32.5863 2.32760
\(197\) −0.546629 −0.0389457 −0.0194728 0.999810i \(-0.506199\pi\)
−0.0194728 + 0.999810i \(0.506199\pi\)
\(198\) 7.33758 0.521459
\(199\) 3.54426 0.251246 0.125623 0.992078i \(-0.459907\pi\)
0.125623 + 0.992078i \(0.459907\pi\)
\(200\) 27.0166 1.91036
\(201\) 5.11662 0.360898
\(202\) 39.0146 2.74506
\(203\) −1.64891 −0.115731
\(204\) 15.9893 1.11947
\(205\) −9.43130 −0.658711
\(206\) −5.48298 −0.382018
\(207\) 3.99858 0.277921
\(208\) 10.6454 0.738123
\(209\) −22.8470 −1.58036
\(210\) 10.6653 0.735977
\(211\) −3.04660 −0.209737 −0.104868 0.994486i \(-0.533442\pi\)
−0.104868 + 0.994486i \(0.533442\pi\)
\(212\) −4.42707 −0.304053
\(213\) −15.5610 −1.06622
\(214\) −32.2624 −2.20541
\(215\) 0.383176 0.0261324
\(216\) 34.8051 2.36819
\(217\) −5.66066 −0.384270
\(218\) 5.55967 0.376549
\(219\) −20.4786 −1.38381
\(220\) −10.2359 −0.690101
\(221\) 4.00785 0.269597
\(222\) 3.56845 0.239499
\(223\) −5.88157 −0.393859 −0.196929 0.980418i \(-0.563097\pi\)
−0.196929 + 0.980418i \(0.563097\pi\)
\(224\) −18.1640 −1.21363
\(225\) 4.29012 0.286008
\(226\) −15.4549 −1.02805
\(227\) 10.2859 0.682696 0.341348 0.939937i \(-0.389116\pi\)
0.341348 + 0.939937i \(0.389116\pi\)
\(228\) −48.5644 −3.21625
\(229\) −0.407756 −0.0269453 −0.0134726 0.999909i \(-0.504289\pi\)
−0.0134726 + 0.999909i \(0.504289\pi\)
\(230\) −8.09793 −0.533962
\(231\) 15.9660 1.05048
\(232\) 2.67731 0.175774
\(233\) −18.0135 −1.18010 −0.590052 0.807365i \(-0.700893\pi\)
−0.590052 + 0.807365i \(0.700893\pi\)
\(234\) 3.90953 0.255574
\(235\) 3.44809 0.224929
\(236\) 38.0852 2.47913
\(237\) −20.6126 −1.33893
\(238\) −24.3959 −1.58135
\(239\) 26.3806 1.70642 0.853211 0.521567i \(-0.174652\pi\)
0.853211 + 0.521567i \(0.174652\pi\)
\(240\) −7.48772 −0.483330
\(241\) −29.4002 −1.89383 −0.946916 0.321482i \(-0.895819\pi\)
−0.946916 + 0.321482i \(0.895819\pi\)
\(242\) 5.64131 0.362637
\(243\) 9.69598 0.621997
\(244\) −43.7427 −2.80034
\(245\) −5.74525 −0.367050
\(246\) −43.5691 −2.77786
\(247\) −12.1731 −0.774556
\(248\) 9.19111 0.583636
\(249\) 6.90939 0.437865
\(250\) −18.5822 −1.17524
\(251\) 13.3300 0.841381 0.420690 0.907204i \(-0.361788\pi\)
0.420690 + 0.907204i \(0.361788\pi\)
\(252\) −16.3920 −1.03260
\(253\) −12.1226 −0.762142
\(254\) 52.1416 3.27166
\(255\) −2.81904 −0.176535
\(256\) −30.2270 −1.88919
\(257\) 16.5338 1.03135 0.515676 0.856784i \(-0.327541\pi\)
0.515676 + 0.856784i \(0.327541\pi\)
\(258\) 1.77013 0.110203
\(259\) −3.75035 −0.233035
\(260\) −5.45376 −0.338228
\(261\) 0.425145 0.0263158
\(262\) 42.2736 2.61167
\(263\) −23.6621 −1.45907 −0.729534 0.683945i \(-0.760263\pi\)
−0.729534 + 0.683945i \(0.760263\pi\)
\(264\) −25.9237 −1.59549
\(265\) 0.780530 0.0479476
\(266\) 74.0979 4.54323
\(267\) −3.43083 −0.209963
\(268\) 15.9261 0.972842
\(269\) 17.9531 1.09462 0.547311 0.836930i \(-0.315652\pi\)
0.547311 + 0.836930i \(0.315652\pi\)
\(270\) −11.1931 −0.681189
\(271\) 18.4020 1.11784 0.558922 0.829220i \(-0.311215\pi\)
0.558922 + 0.829220i \(0.311215\pi\)
\(272\) 17.1274 1.03850
\(273\) 8.50682 0.514856
\(274\) −0.514307 −0.0310704
\(275\) −13.0065 −0.784319
\(276\) −25.7682 −1.55106
\(277\) 1.14262 0.0686532 0.0343266 0.999411i \(-0.489071\pi\)
0.0343266 + 0.999411i \(0.489071\pi\)
\(278\) −36.5180 −2.19021
\(279\) 1.45951 0.0873786
\(280\) 18.1998 1.08765
\(281\) 6.49174 0.387265 0.193632 0.981074i \(-0.437973\pi\)
0.193632 + 0.981074i \(0.437973\pi\)
\(282\) 15.9289 0.948552
\(283\) −13.5329 −0.804446 −0.402223 0.915542i \(-0.631762\pi\)
−0.402223 + 0.915542i \(0.631762\pi\)
\(284\) −48.4354 −2.87411
\(285\) 8.56231 0.507187
\(286\) −11.8526 −0.700860
\(287\) 45.7899 2.70289
\(288\) 4.68330 0.275966
\(289\) −10.5517 −0.620689
\(290\) −0.861004 −0.0505599
\(291\) 5.74773 0.336938
\(292\) −63.7422 −3.73023
\(293\) −0.789509 −0.0461236 −0.0230618 0.999734i \(-0.507341\pi\)
−0.0230618 + 0.999734i \(0.507341\pi\)
\(294\) −26.5409 −1.54790
\(295\) −6.71474 −0.390947
\(296\) 6.08938 0.353938
\(297\) −16.7561 −0.972285
\(298\) 9.90717 0.573907
\(299\) −6.45904 −0.373536
\(300\) −27.6470 −1.59620
\(301\) −1.86036 −0.107229
\(302\) 2.53517 0.145882
\(303\) −21.8882 −1.25745
\(304\) −52.0214 −2.98363
\(305\) 7.71220 0.441599
\(306\) 6.29009 0.359581
\(307\) 7.19759 0.410788 0.205394 0.978679i \(-0.434152\pi\)
0.205394 + 0.978679i \(0.434152\pi\)
\(308\) 49.6961 2.83170
\(309\) 3.07610 0.174993
\(310\) −2.95580 −0.167878
\(311\) −17.1788 −0.974122 −0.487061 0.873368i \(-0.661931\pi\)
−0.487061 + 0.873368i \(0.661931\pi\)
\(312\) −13.8124 −0.781972
\(313\) 0.710526 0.0401613 0.0200806 0.999798i \(-0.493608\pi\)
0.0200806 + 0.999798i \(0.493608\pi\)
\(314\) −41.0645 −2.31740
\(315\) 2.89005 0.162836
\(316\) −64.1593 −3.60924
\(317\) 7.16933 0.402670 0.201335 0.979522i \(-0.435472\pi\)
0.201335 + 0.979522i \(0.435472\pi\)
\(318\) 3.60576 0.202201
\(319\) −1.28892 −0.0721659
\(320\) 1.04445 0.0583864
\(321\) 18.1001 1.01025
\(322\) 39.3163 2.19101
\(323\) −19.5855 −1.08976
\(324\) −22.6405 −1.25780
\(325\) −6.92996 −0.384405
\(326\) 35.0490 1.94118
\(327\) −3.11912 −0.172488
\(328\) −74.3483 −4.10520
\(329\) −16.7408 −0.922952
\(330\) 8.33689 0.458931
\(331\) 18.1768 0.999088 0.499544 0.866288i \(-0.333501\pi\)
0.499544 + 0.866288i \(0.333501\pi\)
\(332\) 21.5064 1.18031
\(333\) 0.966968 0.0529895
\(334\) 19.8237 1.08470
\(335\) −2.80791 −0.153412
\(336\) 36.3536 1.98325
\(337\) 7.47309 0.407085 0.203543 0.979066i \(-0.434754\pi\)
0.203543 + 0.979066i \(0.434754\pi\)
\(338\) 26.6420 1.44913
\(339\) 8.67063 0.470924
\(340\) −8.77462 −0.475871
\(341\) −4.42483 −0.239618
\(342\) −19.1050 −1.03308
\(343\) 1.36689 0.0738053
\(344\) 3.02063 0.162861
\(345\) 4.54315 0.244595
\(346\) 57.3934 3.08549
\(347\) 10.6215 0.570191 0.285096 0.958499i \(-0.407975\pi\)
0.285096 + 0.958499i \(0.407975\pi\)
\(348\) −2.73978 −0.146868
\(349\) −23.1081 −1.23695 −0.618475 0.785804i \(-0.712249\pi\)
−0.618475 + 0.785804i \(0.712249\pi\)
\(350\) 42.1828 2.25477
\(351\) −8.92778 −0.476530
\(352\) −14.1985 −0.756781
\(353\) −0.312466 −0.0166309 −0.00831545 0.999965i \(-0.502647\pi\)
−0.00831545 + 0.999965i \(0.502647\pi\)
\(354\) −31.0196 −1.64867
\(355\) 8.53957 0.453233
\(356\) −10.6789 −0.565980
\(357\) 13.6867 0.724379
\(358\) 43.9618 2.32346
\(359\) −18.1619 −0.958547 −0.479274 0.877665i \(-0.659100\pi\)
−0.479274 + 0.877665i \(0.659100\pi\)
\(360\) −4.69253 −0.247318
\(361\) 40.4871 2.13090
\(362\) 27.4776 1.44419
\(363\) −3.16492 −0.166115
\(364\) 26.4785 1.38785
\(365\) 11.2383 0.588238
\(366\) 35.6275 1.86228
\(367\) −4.23375 −0.221000 −0.110500 0.993876i \(-0.535245\pi\)
−0.110500 + 0.993876i \(0.535245\pi\)
\(368\) −27.6025 −1.43888
\(369\) −11.8062 −0.614607
\(370\) −1.95830 −0.101807
\(371\) −3.78955 −0.196744
\(372\) −9.40557 −0.487656
\(373\) −1.42926 −0.0740044 −0.0370022 0.999315i \(-0.511781\pi\)
−0.0370022 + 0.999315i \(0.511781\pi\)
\(374\) −19.0698 −0.986077
\(375\) 10.4251 0.538350
\(376\) 27.1818 1.40180
\(377\) −0.686750 −0.0353694
\(378\) 54.3436 2.79513
\(379\) 8.98996 0.461783 0.230892 0.972979i \(-0.425836\pi\)
0.230892 + 0.972979i \(0.425836\pi\)
\(380\) 26.6513 1.36718
\(381\) −29.2528 −1.49867
\(382\) −44.8627 −2.29537
\(383\) 20.8480 1.06528 0.532642 0.846341i \(-0.321199\pi\)
0.532642 + 0.846341i \(0.321199\pi\)
\(384\) 18.4596 0.942012
\(385\) −8.76184 −0.446545
\(386\) −45.1905 −2.30014
\(387\) 0.479663 0.0243827
\(388\) 17.8905 0.908253
\(389\) 27.1287 1.37548 0.687740 0.725957i \(-0.258603\pi\)
0.687740 + 0.725957i \(0.258603\pi\)
\(390\) 4.44197 0.224928
\(391\) −10.3920 −0.525547
\(392\) −45.2906 −2.28752
\(393\) −23.7166 −1.19634
\(394\) 1.38580 0.0698153
\(395\) 11.3118 0.569160
\(396\) −12.8134 −0.643895
\(397\) −33.3046 −1.67151 −0.835755 0.549102i \(-0.814970\pi\)
−0.835755 + 0.549102i \(0.814970\pi\)
\(398\) −8.98529 −0.450392
\(399\) −41.5709 −2.08115
\(400\) −29.6150 −1.48075
\(401\) −20.8965 −1.04352 −0.521759 0.853093i \(-0.674724\pi\)
−0.521759 + 0.853093i \(0.674724\pi\)
\(402\) −12.9715 −0.646959
\(403\) −2.35759 −0.117440
\(404\) −68.1299 −3.38959
\(405\) 3.99170 0.198349
\(406\) 4.18026 0.207463
\(407\) −2.93158 −0.145313
\(408\) −22.2229 −1.10020
\(409\) 33.2954 1.64635 0.823175 0.567788i \(-0.192201\pi\)
0.823175 + 0.567788i \(0.192201\pi\)
\(410\) 23.9099 1.18083
\(411\) 0.288540 0.0142326
\(412\) 9.57474 0.471714
\(413\) 32.6007 1.60418
\(414\) −10.1371 −0.498210
\(415\) −3.79175 −0.186130
\(416\) −7.56508 −0.370909
\(417\) 20.4876 1.00328
\(418\) 57.9210 2.83301
\(419\) 9.14241 0.446636 0.223318 0.974746i \(-0.428311\pi\)
0.223318 + 0.974746i \(0.428311\pi\)
\(420\) −18.6245 −0.908781
\(421\) −7.30262 −0.355908 −0.177954 0.984039i \(-0.556948\pi\)
−0.177954 + 0.984039i \(0.556948\pi\)
\(422\) 7.72364 0.375981
\(423\) 4.31636 0.209869
\(424\) 6.15303 0.298818
\(425\) −11.1497 −0.540840
\(426\) 39.4496 1.91134
\(427\) −37.4435 −1.81202
\(428\) 56.3387 2.72323
\(429\) 6.64963 0.321047
\(430\) −0.971414 −0.0468457
\(431\) −12.7117 −0.612299 −0.306150 0.951983i \(-0.599041\pi\)
−0.306150 + 0.951983i \(0.599041\pi\)
\(432\) −38.1526 −1.83562
\(433\) 20.0799 0.964977 0.482489 0.875902i \(-0.339733\pi\)
0.482489 + 0.875902i \(0.339733\pi\)
\(434\) 14.3507 0.688856
\(435\) 0.483046 0.0231603
\(436\) −9.70866 −0.464961
\(437\) 31.5638 1.50990
\(438\) 51.9166 2.48067
\(439\) 3.28138 0.156612 0.0783058 0.996929i \(-0.475049\pi\)
0.0783058 + 0.996929i \(0.475049\pi\)
\(440\) 14.2265 0.678220
\(441\) −7.19196 −0.342474
\(442\) −10.1606 −0.483290
\(443\) −27.5654 −1.30967 −0.654837 0.755771i \(-0.727263\pi\)
−0.654837 + 0.755771i \(0.727263\pi\)
\(444\) −6.23146 −0.295732
\(445\) 1.88278 0.0892522
\(446\) 14.9108 0.706045
\(447\) −5.55819 −0.262893
\(448\) −5.07090 −0.239578
\(449\) −40.6193 −1.91694 −0.958471 0.285191i \(-0.907943\pi\)
−0.958471 + 0.285191i \(0.907943\pi\)
\(450\) −10.8762 −0.512707
\(451\) 35.7932 1.68543
\(452\) 26.9884 1.26943
\(453\) −1.42230 −0.0668253
\(454\) −26.0764 −1.22382
\(455\) −4.66839 −0.218858
\(456\) 67.4979 3.16088
\(457\) 24.3174 1.13752 0.568761 0.822503i \(-0.307423\pi\)
0.568761 + 0.822503i \(0.307423\pi\)
\(458\) 1.03373 0.0483030
\(459\) −14.3640 −0.670455
\(460\) 14.1411 0.659334
\(461\) −12.8419 −0.598107 −0.299053 0.954236i \(-0.596671\pi\)
−0.299053 + 0.954236i \(0.596671\pi\)
\(462\) −40.4764 −1.88313
\(463\) 21.3933 0.994230 0.497115 0.867685i \(-0.334393\pi\)
0.497115 + 0.867685i \(0.334393\pi\)
\(464\) −2.93481 −0.136245
\(465\) 1.65828 0.0769010
\(466\) 45.6672 2.11549
\(467\) 7.86624 0.364006 0.182003 0.983298i \(-0.441742\pi\)
0.182003 + 0.983298i \(0.441742\pi\)
\(468\) −6.82707 −0.315582
\(469\) 13.6327 0.629498
\(470\) −8.74149 −0.403215
\(471\) 23.0382 1.06155
\(472\) −52.9333 −2.43645
\(473\) −1.45421 −0.0668645
\(474\) 52.2564 2.40022
\(475\) 33.8651 1.55384
\(476\) 42.6017 1.95264
\(477\) 0.977076 0.0447372
\(478\) −66.8793 −3.05899
\(479\) 12.3114 0.562521 0.281261 0.959631i \(-0.409247\pi\)
0.281261 + 0.959631i \(0.409247\pi\)
\(480\) 5.32112 0.242875
\(481\) −1.56197 −0.0712198
\(482\) 74.5343 3.39495
\(483\) −22.0575 −1.00365
\(484\) −9.85121 −0.447782
\(485\) −3.15425 −0.143227
\(486\) −24.5809 −1.11501
\(487\) −2.12100 −0.0961115 −0.0480558 0.998845i \(-0.515303\pi\)
−0.0480558 + 0.998845i \(0.515303\pi\)
\(488\) 60.7964 2.75212
\(489\) −19.6634 −0.889210
\(490\) 14.5652 0.657987
\(491\) 5.02536 0.226791 0.113396 0.993550i \(-0.463827\pi\)
0.113396 + 0.993550i \(0.463827\pi\)
\(492\) 76.0832 3.43009
\(493\) −1.10492 −0.0497631
\(494\) 30.8608 1.38850
\(495\) 2.25910 0.101539
\(496\) −10.0751 −0.452385
\(497\) −41.4605 −1.85976
\(498\) −17.5165 −0.784932
\(499\) −22.1075 −0.989669 −0.494834 0.868987i \(-0.664771\pi\)
−0.494834 + 0.868987i \(0.664771\pi\)
\(500\) 32.4495 1.45118
\(501\) −11.1216 −0.496877
\(502\) −33.7937 −1.50829
\(503\) 14.5539 0.648929 0.324464 0.945898i \(-0.394816\pi\)
0.324464 + 0.945898i \(0.394816\pi\)
\(504\) 22.7827 1.01482
\(505\) 12.0119 0.534521
\(506\) 30.7328 1.36624
\(507\) −14.9469 −0.663813
\(508\) −91.0531 −4.03983
\(509\) 1.43602 0.0636503 0.0318252 0.999493i \(-0.489868\pi\)
0.0318252 + 0.999493i \(0.489868\pi\)
\(510\) 7.14674 0.316463
\(511\) −54.5630 −2.41372
\(512\) 50.6730 2.23945
\(513\) 43.6280 1.92622
\(514\) −41.9160 −1.84884
\(515\) −1.68811 −0.0743869
\(516\) −3.09111 −0.136079
\(517\) −13.0860 −0.575522
\(518\) 9.50776 0.417747
\(519\) −32.1992 −1.41339
\(520\) 7.57999 0.332404
\(521\) −38.2031 −1.67371 −0.836854 0.547426i \(-0.815608\pi\)
−0.836854 + 0.547426i \(0.815608\pi\)
\(522\) −1.07781 −0.0471746
\(523\) 2.65160 0.115946 0.0579731 0.998318i \(-0.481536\pi\)
0.0579731 + 0.998318i \(0.481536\pi\)
\(524\) −73.8209 −3.22488
\(525\) −23.6657 −1.03285
\(526\) 59.9874 2.61557
\(527\) −3.79316 −0.165233
\(528\) 28.4170 1.23669
\(529\) −6.25227 −0.271838
\(530\) −1.97877 −0.0859524
\(531\) −8.40558 −0.364771
\(532\) −129.395 −5.60996
\(533\) 19.0709 0.826054
\(534\) 8.69773 0.376387
\(535\) −9.93299 −0.429440
\(536\) −22.1351 −0.956093
\(537\) −24.6638 −1.06432
\(538\) −45.5142 −1.96225
\(539\) 21.8041 0.939167
\(540\) 19.5461 0.841130
\(541\) 21.7655 0.935774 0.467887 0.883788i \(-0.345016\pi\)
0.467887 + 0.883788i \(0.345016\pi\)
\(542\) −46.6522 −2.00388
\(543\) −15.4156 −0.661548
\(544\) −12.1716 −0.521851
\(545\) 1.71172 0.0733220
\(546\) −21.5662 −0.922949
\(547\) 14.0132 0.599161 0.299580 0.954071i \(-0.403153\pi\)
0.299580 + 0.954071i \(0.403153\pi\)
\(548\) 0.898115 0.0383656
\(549\) 9.65421 0.412032
\(550\) 32.9735 1.40600
\(551\) 3.35599 0.142970
\(552\) 35.8143 1.52436
\(553\) −54.9201 −2.33544
\(554\) −2.89673 −0.123070
\(555\) 1.09866 0.0466355
\(556\) 63.7702 2.70446
\(557\) 43.0859 1.82561 0.912804 0.408399i \(-0.133913\pi\)
0.912804 + 0.408399i \(0.133913\pi\)
\(558\) −3.70010 −0.156638
\(559\) −0.774815 −0.0327712
\(560\) −19.9502 −0.843051
\(561\) 10.6987 0.451698
\(562\) −16.4577 −0.694224
\(563\) 28.6212 1.20624 0.603120 0.797650i \(-0.293924\pi\)
0.603120 + 0.797650i \(0.293924\pi\)
\(564\) −27.8161 −1.17127
\(565\) −4.75829 −0.200183
\(566\) 34.3081 1.44208
\(567\) −19.3801 −0.813889
\(568\) 67.3187 2.82463
\(569\) −4.18452 −0.175424 −0.0877120 0.996146i \(-0.527956\pi\)
−0.0877120 + 0.996146i \(0.527956\pi\)
\(570\) −21.7069 −0.909201
\(571\) 25.5669 1.06994 0.534972 0.844870i \(-0.320322\pi\)
0.534972 + 0.844870i \(0.320322\pi\)
\(572\) 20.6978 0.865419
\(573\) 25.1691 1.05146
\(574\) −116.085 −4.84530
\(575\) 17.9688 0.749351
\(576\) 1.30745 0.0544772
\(577\) 2.49787 0.103988 0.0519939 0.998647i \(-0.483442\pi\)
0.0519939 + 0.998647i \(0.483442\pi\)
\(578\) 26.7504 1.11267
\(579\) 25.3531 1.05364
\(580\) 1.50354 0.0624311
\(581\) 18.4093 0.763748
\(582\) −14.5714 −0.604006
\(583\) −2.96223 −0.122683
\(584\) 88.5930 3.66600
\(585\) 1.20367 0.0497657
\(586\) 2.00154 0.0826827
\(587\) −1.86412 −0.0769407 −0.0384703 0.999260i \(-0.512249\pi\)
−0.0384703 + 0.999260i \(0.512249\pi\)
\(588\) 46.3474 1.91134
\(589\) 11.5210 0.474715
\(590\) 17.0230 0.700825
\(591\) −0.777467 −0.0319807
\(592\) −6.67504 −0.274343
\(593\) −22.8207 −0.937135 −0.468567 0.883428i \(-0.655230\pi\)
−0.468567 + 0.883428i \(0.655230\pi\)
\(594\) 42.4794 1.74295
\(595\) −7.51103 −0.307922
\(596\) −17.3005 −0.708658
\(597\) 5.04098 0.206314
\(598\) 16.3747 0.669613
\(599\) −26.2578 −1.07286 −0.536432 0.843943i \(-0.680228\pi\)
−0.536432 + 0.843943i \(0.680228\pi\)
\(600\) 38.4255 1.56872
\(601\) 10.7505 0.438521 0.219260 0.975666i \(-0.429636\pi\)
0.219260 + 0.975666i \(0.429636\pi\)
\(602\) 4.71631 0.192223
\(603\) −3.51497 −0.143141
\(604\) −4.42707 −0.180135
\(605\) 1.73685 0.0706131
\(606\) 55.4903 2.25414
\(607\) 13.4646 0.546510 0.273255 0.961942i \(-0.411900\pi\)
0.273255 + 0.961942i \(0.411900\pi\)
\(608\) 36.9688 1.49928
\(609\) −2.34524 −0.0950338
\(610\) −19.5517 −0.791626
\(611\) −6.97235 −0.282071
\(612\) −10.9842 −0.444008
\(613\) −5.15806 −0.208332 −0.104166 0.994560i \(-0.533217\pi\)
−0.104166 + 0.994560i \(0.533217\pi\)
\(614\) −18.2471 −0.736393
\(615\) −13.4141 −0.540909
\(616\) −69.0709 −2.78295
\(617\) −33.7739 −1.35968 −0.679842 0.733359i \(-0.737952\pi\)
−0.679842 + 0.733359i \(0.737952\pi\)
\(618\) −7.79842 −0.313699
\(619\) 3.65876 0.147058 0.0735290 0.997293i \(-0.476574\pi\)
0.0735290 + 0.997293i \(0.476574\pi\)
\(620\) 5.16161 0.207295
\(621\) 23.1490 0.928936
\(622\) 43.5512 1.74624
\(623\) −9.14107 −0.366229
\(624\) 15.1408 0.606119
\(625\) 16.2328 0.649310
\(626\) −1.80130 −0.0719945
\(627\) −32.4952 −1.29773
\(628\) 71.7094 2.86152
\(629\) −2.51308 −0.100203
\(630\) −7.32676 −0.291905
\(631\) 6.80376 0.270853 0.135427 0.990787i \(-0.456759\pi\)
0.135427 + 0.990787i \(0.456759\pi\)
\(632\) 89.1728 3.54710
\(633\) −4.33317 −0.172228
\(634\) −18.1755 −0.721840
\(635\) 16.0534 0.637061
\(636\) −6.29660 −0.249677
\(637\) 11.6174 0.460298
\(638\) 3.26764 0.129367
\(639\) 10.6899 0.422887
\(640\) −10.1303 −0.400435
\(641\) 17.7786 0.702211 0.351106 0.936336i \(-0.385806\pi\)
0.351106 + 0.936336i \(0.385806\pi\)
\(642\) −45.8867 −1.81100
\(643\) −14.1207 −0.556866 −0.278433 0.960456i \(-0.589815\pi\)
−0.278433 + 0.960456i \(0.589815\pi\)
\(644\) −68.6566 −2.70545
\(645\) 0.544989 0.0214589
\(646\) 49.6524 1.95355
\(647\) 4.75522 0.186947 0.0934734 0.995622i \(-0.470203\pi\)
0.0934734 + 0.995622i \(0.470203\pi\)
\(648\) 31.4672 1.23615
\(649\) 25.4834 1.00031
\(650\) 17.5686 0.689098
\(651\) −8.05112 −0.315548
\(652\) −61.2048 −2.39696
\(653\) 43.0314 1.68395 0.841974 0.539519i \(-0.181394\pi\)
0.841974 + 0.539519i \(0.181394\pi\)
\(654\) 7.90750 0.309208
\(655\) 13.0152 0.508548
\(656\) 81.4990 3.18200
\(657\) 14.0682 0.548853
\(658\) 42.4408 1.65452
\(659\) −9.02180 −0.351440 −0.175720 0.984440i \(-0.556225\pi\)
−0.175720 + 0.984440i \(0.556225\pi\)
\(660\) −14.5584 −0.566685
\(661\) −18.3879 −0.715206 −0.357603 0.933874i \(-0.616406\pi\)
−0.357603 + 0.933874i \(0.616406\pi\)
\(662\) −46.0813 −1.79100
\(663\) 5.70035 0.221383
\(664\) −29.8909 −1.15999
\(665\) 22.8133 0.884663
\(666\) −2.45142 −0.0949908
\(667\) 1.78068 0.0689484
\(668\) −34.6174 −1.33939
\(669\) −8.36533 −0.323422
\(670\) 7.11851 0.275012
\(671\) −29.2689 −1.12991
\(672\) −25.8346 −0.996590
\(673\) −23.6751 −0.912607 −0.456304 0.889824i \(-0.650827\pi\)
−0.456304 + 0.889824i \(0.650827\pi\)
\(674\) −18.9455 −0.729754
\(675\) 24.8367 0.955967
\(676\) −46.5239 −1.78938
\(677\) −27.5152 −1.05749 −0.528747 0.848779i \(-0.677338\pi\)
−0.528747 + 0.848779i \(0.677338\pi\)
\(678\) −21.9815 −0.844195
\(679\) 15.3142 0.587705
\(680\) 12.1955 0.467677
\(681\) 14.6295 0.560605
\(682\) 11.2177 0.429548
\(683\) 39.1901 1.49957 0.749783 0.661684i \(-0.230158\pi\)
0.749783 + 0.661684i \(0.230158\pi\)
\(684\) 33.3623 1.27564
\(685\) −0.158345 −0.00605006
\(686\) −3.46530 −0.132306
\(687\) −0.579949 −0.0221264
\(688\) −3.31115 −0.126236
\(689\) −1.57830 −0.0601285
\(690\) −11.5177 −0.438469
\(691\) 16.3346 0.621397 0.310699 0.950508i \(-0.399437\pi\)
0.310699 + 0.950508i \(0.399437\pi\)
\(692\) −100.224 −3.80995
\(693\) −10.9682 −0.416646
\(694\) −26.9272 −1.02214
\(695\) −11.2432 −0.426479
\(696\) 3.80792 0.144339
\(697\) 30.6835 1.16222
\(698\) 58.5830 2.21740
\(699\) −25.6205 −0.969057
\(700\) −73.6623 −2.78417
\(701\) −13.5453 −0.511598 −0.255799 0.966730i \(-0.582339\pi\)
−0.255799 + 0.966730i \(0.582339\pi\)
\(702\) 22.6334 0.854243
\(703\) 7.63300 0.287884
\(704\) −3.96383 −0.149393
\(705\) 4.90421 0.184703
\(706\) 0.792154 0.0298131
\(707\) −58.3188 −2.19331
\(708\) 54.1684 2.03577
\(709\) 42.6654 1.60233 0.801166 0.598443i \(-0.204214\pi\)
0.801166 + 0.598443i \(0.204214\pi\)
\(710\) −21.6492 −0.812481
\(711\) 14.1603 0.531052
\(712\) 14.8422 0.556235
\(713\) 6.11303 0.228935
\(714\) −34.6982 −1.29855
\(715\) −3.64920 −0.136472
\(716\) −76.7690 −2.86899
\(717\) 37.5210 1.40125
\(718\) 46.0434 1.71832
\(719\) 19.2476 0.717815 0.358907 0.933373i \(-0.383149\pi\)
0.358907 + 0.933373i \(0.383149\pi\)
\(720\) 5.14385 0.191700
\(721\) 8.19593 0.305232
\(722\) −102.642 −3.81993
\(723\) −41.8157 −1.55514
\(724\) −47.9831 −1.78328
\(725\) 1.91051 0.0709547
\(726\) 8.02360 0.297784
\(727\) −29.0737 −1.07829 −0.539143 0.842214i \(-0.681252\pi\)
−0.539143 + 0.842214i \(0.681252\pi\)
\(728\) −36.8016 −1.36396
\(729\) 29.1328 1.07899
\(730\) −28.4909 −1.05450
\(731\) −1.24661 −0.0461075
\(732\) −62.2150 −2.29953
\(733\) −1.79727 −0.0663838 −0.0331919 0.999449i \(-0.510567\pi\)
−0.0331919 + 0.999449i \(0.510567\pi\)
\(734\) 10.7333 0.396172
\(735\) −8.17144 −0.301408
\(736\) 19.6156 0.723041
\(737\) 10.6564 0.392534
\(738\) 29.9307 1.10176
\(739\) −48.7938 −1.79491 −0.897455 0.441107i \(-0.854586\pi\)
−0.897455 + 0.441107i \(0.854586\pi\)
\(740\) 3.41971 0.125711
\(741\) −17.3137 −0.636036
\(742\) 9.60715 0.352689
\(743\) −50.9387 −1.86876 −0.934380 0.356278i \(-0.884046\pi\)
−0.934380 + 0.356278i \(0.884046\pi\)
\(744\) 13.0725 0.479260
\(745\) 3.05023 0.111752
\(746\) 3.62342 0.132663
\(747\) −4.74655 −0.173667
\(748\) 33.3010 1.21760
\(749\) 48.2256 1.76213
\(750\) −26.4294 −0.965065
\(751\) −35.0681 −1.27965 −0.639827 0.768519i \(-0.720994\pi\)
−0.639827 + 0.768519i \(0.720994\pi\)
\(752\) −29.7961 −1.08655
\(753\) 18.9592 0.690910
\(754\) 1.74103 0.0634044
\(755\) 0.780530 0.0284064
\(756\) −94.8982 −3.45141
\(757\) 16.5499 0.601516 0.300758 0.953700i \(-0.402760\pi\)
0.300758 + 0.953700i \(0.402760\pi\)
\(758\) −22.7910 −0.827808
\(759\) −17.2419 −0.625842
\(760\) −37.0416 −1.34364
\(761\) 29.6846 1.07607 0.538034 0.842923i \(-0.319167\pi\)
0.538034 + 0.842923i \(0.319167\pi\)
\(762\) 74.1608 2.68656
\(763\) −8.31057 −0.300863
\(764\) 78.3421 2.83432
\(765\) 1.93660 0.0700179
\(766\) −52.8532 −1.90966
\(767\) 13.5778 0.490266
\(768\) −42.9917 −1.55133
\(769\) 20.0497 0.723010 0.361505 0.932370i \(-0.382263\pi\)
0.361505 + 0.932370i \(0.382263\pi\)
\(770\) 22.2127 0.800491
\(771\) 23.5160 0.846908
\(772\) 78.9146 2.84020
\(773\) 0.372095 0.0133833 0.00669167 0.999978i \(-0.497870\pi\)
0.00669167 + 0.999978i \(0.497870\pi\)
\(774\) −1.21603 −0.0437092
\(775\) 6.55873 0.235597
\(776\) −24.8654 −0.892616
\(777\) −5.33410 −0.191360
\(778\) −68.7758 −2.46573
\(779\) −93.1952 −3.33907
\(780\) −7.75686 −0.277740
\(781\) −32.4089 −1.15968
\(782\) 26.3455 0.942114
\(783\) 2.46129 0.0879593
\(784\) 49.6466 1.77309
\(785\) −12.6430 −0.451247
\(786\) 60.1256 2.14461
\(787\) −3.80482 −0.135627 −0.0678136 0.997698i \(-0.521602\pi\)
−0.0678136 + 0.997698i \(0.521602\pi\)
\(788\) −2.41996 −0.0862077
\(789\) −33.6545 −1.19813
\(790\) −28.6774 −1.02030
\(791\) 23.1020 0.821411
\(792\) 17.8088 0.632809
\(793\) −15.5947 −0.553786
\(794\) 84.4327 2.99641
\(795\) 1.11014 0.0393728
\(796\) 15.6907 0.556142
\(797\) −33.6789 −1.19297 −0.596484 0.802625i \(-0.703436\pi\)
−0.596484 + 0.802625i \(0.703436\pi\)
\(798\) 105.389 3.73073
\(799\) −11.2179 −0.396861
\(800\) 21.0458 0.744080
\(801\) 2.35688 0.0832763
\(802\) 52.9760 1.87065
\(803\) −42.6509 −1.50512
\(804\) 22.6516 0.798862
\(805\) 12.1047 0.426636
\(806\) 5.97689 0.210527
\(807\) 25.5346 0.898862
\(808\) 94.6913 3.33123
\(809\) 34.7214 1.22074 0.610370 0.792116i \(-0.291021\pi\)
0.610370 + 0.792116i \(0.291021\pi\)
\(810\) −10.1196 −0.355568
\(811\) −36.1909 −1.27083 −0.635417 0.772169i \(-0.719172\pi\)
−0.635417 + 0.772169i \(0.719172\pi\)
\(812\) −7.29984 −0.256174
\(813\) 26.1731 0.917931
\(814\) 7.43205 0.260493
\(815\) 10.7909 0.377989
\(816\) 24.3603 0.852780
\(817\) 3.78634 0.132467
\(818\) −84.4093 −2.95130
\(819\) −5.84394 −0.204204
\(820\) −41.7531 −1.45808
\(821\) −46.1025 −1.60899 −0.804494 0.593961i \(-0.797563\pi\)
−0.804494 + 0.593961i \(0.797563\pi\)
\(822\) −0.731496 −0.0255138
\(823\) 7.50333 0.261550 0.130775 0.991412i \(-0.458254\pi\)
0.130775 + 0.991412i \(0.458254\pi\)
\(824\) −13.3076 −0.463592
\(825\) −18.4990 −0.644053
\(826\) −82.6483 −2.87570
\(827\) 12.0627 0.419461 0.209731 0.977759i \(-0.432741\pi\)
0.209731 + 0.977759i \(0.432741\pi\)
\(828\) 17.7020 0.615188
\(829\) −24.4058 −0.847647 −0.423824 0.905745i \(-0.639312\pi\)
−0.423824 + 0.905745i \(0.639312\pi\)
\(830\) 9.61272 0.333662
\(831\) 1.62514 0.0563755
\(832\) −2.11197 −0.0732193
\(833\) 18.6914 0.647618
\(834\) −51.9394 −1.79852
\(835\) 6.10334 0.211215
\(836\) −101.145 −3.49819
\(837\) 8.44953 0.292059
\(838\) −23.1775 −0.800655
\(839\) −2.92428 −0.100957 −0.0504787 0.998725i \(-0.516075\pi\)
−0.0504787 + 0.998725i \(0.516075\pi\)
\(840\) 25.8855 0.893134
\(841\) −28.8107 −0.993471
\(842\) 18.5134 0.638012
\(843\) 9.23318 0.318007
\(844\) −13.4875 −0.464260
\(845\) 8.20256 0.282177
\(846\) −10.9427 −0.376218
\(847\) −8.43259 −0.289747
\(848\) −6.74482 −0.231618
\(849\) −19.2477 −0.660581
\(850\) 28.2663 0.969528
\(851\) 4.05006 0.138834
\(852\) −68.8895 −2.36011
\(853\) −39.4593 −1.35106 −0.675531 0.737332i \(-0.736085\pi\)
−0.675531 + 0.737332i \(0.736085\pi\)
\(854\) 94.9255 3.24828
\(855\) −5.88206 −0.201162
\(856\) −78.3032 −2.67635
\(857\) −20.9968 −0.717236 −0.358618 0.933484i \(-0.616752\pi\)
−0.358618 + 0.933484i \(0.616752\pi\)
\(858\) −16.8579 −0.575520
\(859\) −21.5884 −0.736587 −0.368293 0.929710i \(-0.620058\pi\)
−0.368293 + 0.929710i \(0.620058\pi\)
\(860\) 1.69635 0.0578449
\(861\) 65.1268 2.21952
\(862\) 32.2262 1.09763
\(863\) 23.1424 0.787777 0.393888 0.919158i \(-0.371130\pi\)
0.393888 + 0.919158i \(0.371130\pi\)
\(864\) 27.1130 0.922403
\(865\) 17.6704 0.600810
\(866\) −50.9058 −1.72985
\(867\) −15.0077 −0.509687
\(868\) −25.0601 −0.850596
\(869\) −42.9301 −1.45630
\(870\) −1.22460 −0.0415179
\(871\) 5.67784 0.192386
\(872\) 13.4937 0.456955
\(873\) −3.94852 −0.133637
\(874\) −80.0195 −2.70670
\(875\) 27.7766 0.939020
\(876\) −90.6602 −3.06312
\(877\) −34.9614 −1.18056 −0.590281 0.807198i \(-0.700983\pi\)
−0.590281 + 0.807198i \(0.700983\pi\)
\(878\) −8.31884 −0.280747
\(879\) −1.12291 −0.0378750
\(880\) −15.5947 −0.525698
\(881\) 34.3059 1.15580 0.577898 0.816109i \(-0.303873\pi\)
0.577898 + 0.816109i \(0.303873\pi\)
\(882\) 18.2328 0.613931
\(883\) −55.0181 −1.85151 −0.925754 0.378127i \(-0.876568\pi\)
−0.925754 + 0.378127i \(0.876568\pi\)
\(884\) 17.7431 0.596764
\(885\) −9.55034 −0.321031
\(886\) 69.8830 2.34776
\(887\) 10.6841 0.358737 0.179369 0.983782i \(-0.442595\pi\)
0.179369 + 0.983782i \(0.442595\pi\)
\(888\) 8.66089 0.290641
\(889\) −77.9410 −2.61406
\(890\) −4.77316 −0.159997
\(891\) −15.1491 −0.507514
\(892\) −26.0381 −0.871821
\(893\) 34.0723 1.14018
\(894\) 14.0909 0.471271
\(895\) 13.5350 0.452426
\(896\) 49.1836 1.64311
\(897\) −9.18666 −0.306734
\(898\) 102.977 3.43637
\(899\) 0.649962 0.0216774
\(900\) 18.9927 0.633089
\(901\) −2.53935 −0.0845979
\(902\) −90.7417 −3.02137
\(903\) −2.64598 −0.0880525
\(904\) −37.5103 −1.24757
\(905\) 8.45982 0.281214
\(906\) 3.60576 0.119793
\(907\) −0.370896 −0.0123154 −0.00615769 0.999981i \(-0.501960\pi\)
−0.00615769 + 0.999981i \(0.501960\pi\)
\(908\) 45.5362 1.51117
\(909\) 15.0366 0.498732
\(910\) 11.8351 0.392331
\(911\) 6.15809 0.204027 0.102013 0.994783i \(-0.467472\pi\)
0.102013 + 0.994783i \(0.467472\pi\)
\(912\) −73.9898 −2.45005
\(913\) 14.3902 0.476248
\(914\) −61.6487 −2.03916
\(915\) 10.9690 0.362625
\(916\) −1.80516 −0.0596443
\(917\) −63.1903 −2.08673
\(918\) 36.4152 1.20188
\(919\) −27.7930 −0.916805 −0.458403 0.888745i \(-0.651578\pi\)
−0.458403 + 0.888745i \(0.651578\pi\)
\(920\) −19.6543 −0.647982
\(921\) 10.2371 0.337324
\(922\) 32.5564 1.07219
\(923\) −17.2678 −0.568376
\(924\) 70.6826 2.32529
\(925\) 4.34535 0.142874
\(926\) −54.2355 −1.78229
\(927\) −2.11319 −0.0694063
\(928\) 2.08561 0.0684634
\(929\) 45.6786 1.49867 0.749334 0.662192i \(-0.230374\pi\)
0.749334 + 0.662192i \(0.230374\pi\)
\(930\) −4.20402 −0.137855
\(931\) −56.7715 −1.86061
\(932\) −79.7471 −2.61220
\(933\) −24.4334 −0.799913
\(934\) −19.9422 −0.652530
\(935\) −5.87124 −0.192010
\(936\) 9.48871 0.310148
\(937\) 11.3620 0.371180 0.185590 0.982627i \(-0.440580\pi\)
0.185590 + 0.982627i \(0.440580\pi\)
\(938\) −34.5611 −1.12846
\(939\) 1.01058 0.0329789
\(940\) 15.2650 0.497888
\(941\) −3.92984 −0.128109 −0.0640545 0.997946i \(-0.520403\pi\)
−0.0640545 + 0.997946i \(0.520403\pi\)
\(942\) −58.4058 −1.90296
\(943\) −49.4493 −1.61029
\(944\) 58.0243 1.88853
\(945\) 16.7314 0.544271
\(946\) 3.68666 0.119864
\(947\) −22.3293 −0.725605 −0.362803 0.931866i \(-0.618180\pi\)
−0.362803 + 0.931866i \(0.618180\pi\)
\(948\) −91.2535 −2.96378
\(949\) −22.7248 −0.737678
\(950\) −85.8537 −2.78546
\(951\) 10.1969 0.330657
\(952\) −59.2106 −1.91903
\(953\) 23.7675 0.769905 0.384952 0.922936i \(-0.374218\pi\)
0.384952 + 0.922936i \(0.374218\pi\)
\(954\) −2.47705 −0.0801975
\(955\) −13.8124 −0.446958
\(956\) 116.789 3.77722
\(957\) −1.83323 −0.0592599
\(958\) −31.2114 −1.00839
\(959\) 0.768782 0.0248253
\(960\) 1.48551 0.0479448
\(961\) −28.7687 −0.928023
\(962\) 3.95986 0.127671
\(963\) −12.4342 −0.400687
\(964\) −130.157 −4.19206
\(965\) −13.9133 −0.447885
\(966\) 55.9194 1.79918
\(967\) 10.0873 0.324387 0.162193 0.986759i \(-0.448143\pi\)
0.162193 + 0.986759i \(0.448143\pi\)
\(968\) 13.6919 0.440073
\(969\) −27.8563 −0.894873
\(970\) 7.99655 0.256754
\(971\) −1.27634 −0.0409598 −0.0204799 0.999790i \(-0.506519\pi\)
−0.0204799 + 0.999790i \(0.506519\pi\)
\(972\) 42.9248 1.37681
\(973\) 54.5869 1.74998
\(974\) 5.37708 0.172293
\(975\) −9.85645 −0.315659
\(976\) −66.6437 −2.13321
\(977\) −56.1942 −1.79781 −0.898906 0.438141i \(-0.855637\pi\)
−0.898906 + 0.438141i \(0.855637\pi\)
\(978\) 49.8500 1.59403
\(979\) −7.14542 −0.228368
\(980\) −25.4346 −0.812479
\(981\) 2.14275 0.0684127
\(982\) −12.7401 −0.406554
\(983\) −11.7197 −0.373802 −0.186901 0.982379i \(-0.559844\pi\)
−0.186901 + 0.982379i \(0.559844\pi\)
\(984\) −105.745 −3.37104
\(985\) 0.426660 0.0135945
\(986\) 2.80116 0.0892071
\(987\) −23.8104 −0.757894
\(988\) −53.8912 −1.71451
\(989\) 2.00903 0.0638834
\(990\) −5.72720 −0.182022
\(991\) 1.12898 0.0358634 0.0179317 0.999839i \(-0.494292\pi\)
0.0179317 + 0.999839i \(0.494292\pi\)
\(992\) 7.15983 0.227325
\(993\) 25.8528 0.820414
\(994\) 105.109 3.33386
\(995\) −2.76640 −0.0877008
\(996\) 30.5884 0.969230
\(997\) 40.7124 1.28937 0.644687 0.764447i \(-0.276988\pi\)
0.644687 + 0.764447i \(0.276988\pi\)
\(998\) 56.0463 1.77411
\(999\) 5.59806 0.177115
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.1.10 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.10 153 1.1 even 1 trivial