Properties

Label 8003.2.a.b.1.9
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 1.9
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.54449 q^{2} -2.75216 q^{3} +4.47442 q^{4} -0.0821866 q^{5} +7.00285 q^{6} -2.51361 q^{7} -6.29612 q^{8} +4.57441 q^{9} +O(q^{10})\) \(q-2.54449 q^{2} -2.75216 q^{3} +4.47442 q^{4} -0.0821866 q^{5} +7.00285 q^{6} -2.51361 q^{7} -6.29612 q^{8} +4.57441 q^{9} +0.209123 q^{10} -4.33563 q^{11} -12.3143 q^{12} -6.03114 q^{13} +6.39585 q^{14} +0.226191 q^{15} +7.07156 q^{16} -4.63559 q^{17} -11.6395 q^{18} +1.23205 q^{19} -0.367737 q^{20} +6.91787 q^{21} +11.0320 q^{22} -8.79311 q^{23} +17.3280 q^{24} -4.99325 q^{25} +15.3462 q^{26} -4.33303 q^{27} -11.2469 q^{28} -3.61276 q^{29} -0.575540 q^{30} -6.33205 q^{31} -5.40126 q^{32} +11.9324 q^{33} +11.7952 q^{34} +0.206585 q^{35} +20.4678 q^{36} +2.98659 q^{37} -3.13494 q^{38} +16.5987 q^{39} +0.517457 q^{40} +11.0158 q^{41} -17.6024 q^{42} -0.747991 q^{43} -19.3994 q^{44} -0.375955 q^{45} +22.3740 q^{46} +4.74881 q^{47} -19.4621 q^{48} -0.681756 q^{49} +12.7052 q^{50} +12.7579 q^{51} -26.9858 q^{52} -1.00000 q^{53} +11.0254 q^{54} +0.356331 q^{55} +15.8260 q^{56} -3.39081 q^{57} +9.19262 q^{58} +15.0256 q^{59} +1.01207 q^{60} -8.06472 q^{61} +16.1118 q^{62} -11.4983 q^{63} -0.399679 q^{64} +0.495679 q^{65} -30.3618 q^{66} +1.53748 q^{67} -20.7415 q^{68} +24.2001 q^{69} -0.525653 q^{70} +10.6166 q^{71} -28.8010 q^{72} +0.140557 q^{73} -7.59933 q^{74} +13.7422 q^{75} +5.51272 q^{76} +10.8981 q^{77} -42.2352 q^{78} +9.74079 q^{79} -0.581188 q^{80} -1.79800 q^{81} -28.0295 q^{82} +7.93714 q^{83} +30.9534 q^{84} +0.380983 q^{85} +1.90325 q^{86} +9.94291 q^{87} +27.2977 q^{88} -1.05875 q^{89} +0.956613 q^{90} +15.1600 q^{91} -39.3440 q^{92} +17.4268 q^{93} -12.0833 q^{94} -0.101258 q^{95} +14.8652 q^{96} +8.11423 q^{97} +1.73472 q^{98} -19.8330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54449 −1.79922 −0.899612 0.436690i \(-0.856151\pi\)
−0.899612 + 0.436690i \(0.856151\pi\)
\(3\) −2.75216 −1.58896 −0.794481 0.607288i \(-0.792257\pi\)
−0.794481 + 0.607288i \(0.792257\pi\)
\(4\) 4.47442 2.23721
\(5\) −0.0821866 −0.0367550 −0.0183775 0.999831i \(-0.505850\pi\)
−0.0183775 + 0.999831i \(0.505850\pi\)
\(6\) 7.00285 2.85890
\(7\) −2.51361 −0.950056 −0.475028 0.879971i \(-0.657562\pi\)
−0.475028 + 0.879971i \(0.657562\pi\)
\(8\) −6.29612 −2.22601
\(9\) 4.57441 1.52480
\(10\) 0.209123 0.0661304
\(11\) −4.33563 −1.30724 −0.653621 0.756822i \(-0.726751\pi\)
−0.653621 + 0.756822i \(0.726751\pi\)
\(12\) −12.3143 −3.55484
\(13\) −6.03114 −1.67274 −0.836369 0.548166i \(-0.815326\pi\)
−0.836369 + 0.548166i \(0.815326\pi\)
\(14\) 6.39585 1.70936
\(15\) 0.226191 0.0584023
\(16\) 7.07156 1.76789
\(17\) −4.63559 −1.12429 −0.562147 0.827037i \(-0.690025\pi\)
−0.562147 + 0.827037i \(0.690025\pi\)
\(18\) −11.6395 −2.74346
\(19\) 1.23205 0.282652 0.141326 0.989963i \(-0.454863\pi\)
0.141326 + 0.989963i \(0.454863\pi\)
\(20\) −0.367737 −0.0822285
\(21\) 6.91787 1.50960
\(22\) 11.0320 2.35202
\(23\) −8.79311 −1.83349 −0.916745 0.399473i \(-0.869193\pi\)
−0.916745 + 0.399473i \(0.869193\pi\)
\(24\) 17.3280 3.53705
\(25\) −4.99325 −0.998649
\(26\) 15.3462 3.00963
\(27\) −4.33303 −0.833893
\(28\) −11.2469 −2.12547
\(29\) −3.61276 −0.670873 −0.335436 0.942063i \(-0.608884\pi\)
−0.335436 + 0.942063i \(0.608884\pi\)
\(30\) −0.575540 −0.105079
\(31\) −6.33205 −1.13727 −0.568635 0.822590i \(-0.692528\pi\)
−0.568635 + 0.822590i \(0.692528\pi\)
\(32\) −5.40126 −0.954817
\(33\) 11.9324 2.07716
\(34\) 11.7952 2.02286
\(35\) 0.206585 0.0349193
\(36\) 20.4678 3.41130
\(37\) 2.98659 0.490992 0.245496 0.969398i \(-0.421049\pi\)
0.245496 + 0.969398i \(0.421049\pi\)
\(38\) −3.13494 −0.508555
\(39\) 16.5987 2.65792
\(40\) 0.517457 0.0818171
\(41\) 11.0158 1.72038 0.860189 0.509976i \(-0.170346\pi\)
0.860189 + 0.509976i \(0.170346\pi\)
\(42\) −17.6024 −2.71612
\(43\) −0.747991 −0.114068 −0.0570338 0.998372i \(-0.518164\pi\)
−0.0570338 + 0.998372i \(0.518164\pi\)
\(44\) −19.3994 −2.92457
\(45\) −0.375955 −0.0560441
\(46\) 22.3740 3.29886
\(47\) 4.74881 0.692685 0.346343 0.938108i \(-0.387424\pi\)
0.346343 + 0.938108i \(0.387424\pi\)
\(48\) −19.4621 −2.80911
\(49\) −0.681756 −0.0973937
\(50\) 12.7052 1.79679
\(51\) 12.7579 1.78646
\(52\) −26.9858 −3.74226
\(53\) −1.00000 −0.137361
\(54\) 11.0254 1.50036
\(55\) 0.356331 0.0480476
\(56\) 15.8260 2.11484
\(57\) −3.39081 −0.449124
\(58\) 9.19262 1.20705
\(59\) 15.0256 1.95617 0.978086 0.208203i \(-0.0667616\pi\)
0.978086 + 0.208203i \(0.0667616\pi\)
\(60\) 1.01207 0.130658
\(61\) −8.06472 −1.03258 −0.516291 0.856413i \(-0.672688\pi\)
−0.516291 + 0.856413i \(0.672688\pi\)
\(62\) 16.1118 2.04620
\(63\) −11.4983 −1.44865
\(64\) −0.399679 −0.0499599
\(65\) 0.495679 0.0614814
\(66\) −30.3618 −3.73728
\(67\) 1.53748 0.187833 0.0939166 0.995580i \(-0.470061\pi\)
0.0939166 + 0.995580i \(0.470061\pi\)
\(68\) −20.7415 −2.51528
\(69\) 24.2001 2.91335
\(70\) −0.525653 −0.0628276
\(71\) 10.6166 1.25996 0.629978 0.776613i \(-0.283064\pi\)
0.629978 + 0.776613i \(0.283064\pi\)
\(72\) −28.8010 −3.39423
\(73\) 0.140557 0.0164510 0.00822550 0.999966i \(-0.497382\pi\)
0.00822550 + 0.999966i \(0.497382\pi\)
\(74\) −7.59933 −0.883404
\(75\) 13.7422 1.58682
\(76\) 5.51272 0.632352
\(77\) 10.8981 1.24195
\(78\) −42.2352 −4.78219
\(79\) 9.74079 1.09592 0.547962 0.836503i \(-0.315404\pi\)
0.547962 + 0.836503i \(0.315404\pi\)
\(80\) −0.581188 −0.0649788
\(81\) −1.79800 −0.199778
\(82\) −28.0295 −3.09535
\(83\) 7.93714 0.871214 0.435607 0.900137i \(-0.356534\pi\)
0.435607 + 0.900137i \(0.356534\pi\)
\(84\) 30.9534 3.37730
\(85\) 0.380983 0.0413234
\(86\) 1.90325 0.205233
\(87\) 9.94291 1.06599
\(88\) 27.2977 2.90994
\(89\) −1.05875 −0.112228 −0.0561138 0.998424i \(-0.517871\pi\)
−0.0561138 + 0.998424i \(0.517871\pi\)
\(90\) 0.956613 0.100836
\(91\) 15.1600 1.58920
\(92\) −39.3440 −4.10190
\(93\) 17.4268 1.80708
\(94\) −12.0833 −1.24630
\(95\) −0.101258 −0.0103889
\(96\) 14.8652 1.51717
\(97\) 8.11423 0.823875 0.411938 0.911212i \(-0.364852\pi\)
0.411938 + 0.911212i \(0.364852\pi\)
\(98\) 1.73472 0.175233
\(99\) −19.8330 −1.99329
\(100\) −22.3419 −2.23419
\(101\) −2.76688 −0.275315 −0.137658 0.990480i \(-0.543957\pi\)
−0.137658 + 0.990480i \(0.543957\pi\)
\(102\) −32.4623 −3.21425
\(103\) 12.4584 1.22756 0.613782 0.789475i \(-0.289647\pi\)
0.613782 + 0.789475i \(0.289647\pi\)
\(104\) 37.9728 3.72354
\(105\) −0.568556 −0.0554854
\(106\) 2.54449 0.247142
\(107\) −9.01422 −0.871437 −0.435719 0.900083i \(-0.643506\pi\)
−0.435719 + 0.900083i \(0.643506\pi\)
\(108\) −19.3878 −1.86559
\(109\) 0.0571811 0.00547696 0.00273848 0.999996i \(-0.499128\pi\)
0.00273848 + 0.999996i \(0.499128\pi\)
\(110\) −0.906679 −0.0864485
\(111\) −8.21958 −0.780168
\(112\) −17.7752 −1.67959
\(113\) −3.77611 −0.355226 −0.177613 0.984100i \(-0.556838\pi\)
−0.177613 + 0.984100i \(0.556838\pi\)
\(114\) 8.62788 0.808075
\(115\) 0.722676 0.0673899
\(116\) −16.1650 −1.50088
\(117\) −27.5889 −2.55060
\(118\) −38.2325 −3.51959
\(119\) 11.6521 1.06814
\(120\) −1.42413 −0.130004
\(121\) 7.79771 0.708882
\(122\) 20.5206 1.85785
\(123\) −30.3173 −2.73362
\(124\) −28.3322 −2.54431
\(125\) 0.821311 0.0734603
\(126\) 29.2573 2.60644
\(127\) −18.1415 −1.60979 −0.804897 0.593414i \(-0.797780\pi\)
−0.804897 + 0.593414i \(0.797780\pi\)
\(128\) 11.8195 1.04471
\(129\) 2.05859 0.181249
\(130\) −1.26125 −0.110619
\(131\) 10.4895 0.916469 0.458234 0.888831i \(-0.348482\pi\)
0.458234 + 0.888831i \(0.348482\pi\)
\(132\) 53.3904 4.64704
\(133\) −3.09690 −0.268535
\(134\) −3.91210 −0.337954
\(135\) 0.356117 0.0306497
\(136\) 29.1862 2.50270
\(137\) 10.0206 0.856116 0.428058 0.903751i \(-0.359198\pi\)
0.428058 + 0.903751i \(0.359198\pi\)
\(138\) −61.5768 −5.24177
\(139\) −1.80560 −0.153149 −0.0765745 0.997064i \(-0.524398\pi\)
−0.0765745 + 0.997064i \(0.524398\pi\)
\(140\) 0.924348 0.0781217
\(141\) −13.0695 −1.10065
\(142\) −27.0138 −2.26694
\(143\) 26.1488 2.18667
\(144\) 32.3482 2.69569
\(145\) 0.296921 0.0246579
\(146\) −0.357647 −0.0295990
\(147\) 1.87631 0.154755
\(148\) 13.3632 1.09845
\(149\) −11.5656 −0.947494 −0.473747 0.880661i \(-0.657099\pi\)
−0.473747 + 0.880661i \(0.657099\pi\)
\(150\) −34.9669 −2.85504
\(151\) −1.00000 −0.0813788
\(152\) −7.75715 −0.629188
\(153\) −21.2051 −1.71433
\(154\) −27.7301 −2.23455
\(155\) 0.520410 0.0418003
\(156\) 74.2695 5.94632
\(157\) −21.3893 −1.70705 −0.853525 0.521052i \(-0.825540\pi\)
−0.853525 + 0.521052i \(0.825540\pi\)
\(158\) −24.7853 −1.97181
\(159\) 2.75216 0.218261
\(160\) 0.443911 0.0350943
\(161\) 22.1025 1.74192
\(162\) 4.57500 0.359446
\(163\) −6.07776 −0.476047 −0.238023 0.971259i \(-0.576499\pi\)
−0.238023 + 0.971259i \(0.576499\pi\)
\(164\) 49.2892 3.84884
\(165\) −0.980681 −0.0763459
\(166\) −20.1960 −1.56751
\(167\) 5.43525 0.420592 0.210296 0.977638i \(-0.432557\pi\)
0.210296 + 0.977638i \(0.432557\pi\)
\(168\) −43.5557 −3.36040
\(169\) 23.3747 1.79805
\(170\) −0.969406 −0.0743501
\(171\) 5.63591 0.430989
\(172\) −3.34682 −0.255193
\(173\) −12.0989 −0.919864 −0.459932 0.887954i \(-0.652126\pi\)
−0.459932 + 0.887954i \(0.652126\pi\)
\(174\) −25.2996 −1.91796
\(175\) 12.5511 0.948772
\(176\) −30.6597 −2.31106
\(177\) −41.3530 −3.10828
\(178\) 2.69398 0.201922
\(179\) −12.9739 −0.969713 −0.484856 0.874594i \(-0.661128\pi\)
−0.484856 + 0.874594i \(0.661128\pi\)
\(180\) −1.68218 −0.125382
\(181\) 1.53497 0.114093 0.0570466 0.998372i \(-0.481832\pi\)
0.0570466 + 0.998372i \(0.481832\pi\)
\(182\) −38.5743 −2.85932
\(183\) 22.1955 1.64073
\(184\) 55.3625 4.08137
\(185\) −0.245457 −0.0180464
\(186\) −44.3424 −3.25134
\(187\) 20.0982 1.46973
\(188\) 21.2481 1.54968
\(189\) 10.8916 0.792245
\(190\) 0.257650 0.0186919
\(191\) −10.0634 −0.728159 −0.364079 0.931368i \(-0.618616\pi\)
−0.364079 + 0.931368i \(0.618616\pi\)
\(192\) 1.09998 0.0793844
\(193\) 1.53965 0.110827 0.0554133 0.998464i \(-0.482352\pi\)
0.0554133 + 0.998464i \(0.482352\pi\)
\(194\) −20.6466 −1.48234
\(195\) −1.36419 −0.0976917
\(196\) −3.05046 −0.217890
\(197\) 21.5930 1.53843 0.769217 0.638987i \(-0.220646\pi\)
0.769217 + 0.638987i \(0.220646\pi\)
\(198\) 50.4647 3.58637
\(199\) 9.94310 0.704847 0.352424 0.935841i \(-0.385358\pi\)
0.352424 + 0.935841i \(0.385358\pi\)
\(200\) 31.4381 2.22301
\(201\) −4.23140 −0.298460
\(202\) 7.04030 0.495354
\(203\) 9.08108 0.637367
\(204\) 57.0841 3.99669
\(205\) −0.905350 −0.0632324
\(206\) −31.7003 −2.20866
\(207\) −40.2233 −2.79571
\(208\) −42.6496 −2.95722
\(209\) −5.34173 −0.369495
\(210\) 1.44668 0.0998307
\(211\) 12.5417 0.863404 0.431702 0.902016i \(-0.357913\pi\)
0.431702 + 0.902016i \(0.357913\pi\)
\(212\) −4.47442 −0.307304
\(213\) −29.2186 −2.00202
\(214\) 22.9366 1.56791
\(215\) 0.0614748 0.00419255
\(216\) 27.2813 1.85626
\(217\) 15.9163 1.08047
\(218\) −0.145497 −0.00985428
\(219\) −0.386837 −0.0261400
\(220\) 1.59437 0.107493
\(221\) 27.9579 1.88065
\(222\) 20.9146 1.40370
\(223\) −0.124446 −0.00833353 −0.00416677 0.999991i \(-0.501326\pi\)
−0.00416677 + 0.999991i \(0.501326\pi\)
\(224\) 13.5767 0.907130
\(225\) −22.8412 −1.52274
\(226\) 9.60825 0.639131
\(227\) 12.9103 0.856888 0.428444 0.903568i \(-0.359062\pi\)
0.428444 + 0.903568i \(0.359062\pi\)
\(228\) −15.1719 −1.00478
\(229\) −25.7767 −1.70338 −0.851688 0.524050i \(-0.824421\pi\)
−0.851688 + 0.524050i \(0.824421\pi\)
\(230\) −1.83884 −0.121249
\(231\) −29.9934 −1.97342
\(232\) 22.7464 1.49337
\(233\) −3.43074 −0.224755 −0.112378 0.993666i \(-0.535847\pi\)
−0.112378 + 0.993666i \(0.535847\pi\)
\(234\) 70.1997 4.58910
\(235\) −0.390288 −0.0254596
\(236\) 67.2309 4.37636
\(237\) −26.8083 −1.74138
\(238\) −29.6485 −1.92183
\(239\) 27.0614 1.75046 0.875228 0.483711i \(-0.160711\pi\)
0.875228 + 0.483711i \(0.160711\pi\)
\(240\) 1.59952 0.103249
\(241\) −11.8479 −0.763188 −0.381594 0.924330i \(-0.624625\pi\)
−0.381594 + 0.924330i \(0.624625\pi\)
\(242\) −19.8412 −1.27544
\(243\) 17.9475 1.15133
\(244\) −36.0849 −2.31010
\(245\) 0.0560312 0.00357970
\(246\) 77.1419 4.91839
\(247\) −7.43069 −0.472803
\(248\) 39.8673 2.53158
\(249\) −21.8443 −1.38433
\(250\) −2.08981 −0.132171
\(251\) −15.4632 −0.976027 −0.488014 0.872836i \(-0.662278\pi\)
−0.488014 + 0.872836i \(0.662278\pi\)
\(252\) −51.4481 −3.24093
\(253\) 38.1237 2.39682
\(254\) 46.1607 2.89638
\(255\) −1.04853 −0.0656614
\(256\) −29.2752 −1.82970
\(257\) −19.7042 −1.22912 −0.614558 0.788872i \(-0.710666\pi\)
−0.614558 + 0.788872i \(0.710666\pi\)
\(258\) −5.23807 −0.326108
\(259\) −7.50712 −0.466470
\(260\) 2.21787 0.137547
\(261\) −16.5262 −1.02295
\(262\) −26.6903 −1.64893
\(263\) −1.81497 −0.111916 −0.0559578 0.998433i \(-0.517821\pi\)
−0.0559578 + 0.998433i \(0.517821\pi\)
\(264\) −75.1276 −4.62379
\(265\) 0.0821866 0.00504868
\(266\) 7.88003 0.483155
\(267\) 2.91386 0.178325
\(268\) 6.87933 0.420222
\(269\) −10.4110 −0.634767 −0.317384 0.948297i \(-0.602804\pi\)
−0.317384 + 0.948297i \(0.602804\pi\)
\(270\) −0.906136 −0.0551457
\(271\) −0.454510 −0.0276095 −0.0138048 0.999905i \(-0.504394\pi\)
−0.0138048 + 0.999905i \(0.504394\pi\)
\(272\) −32.7808 −1.98763
\(273\) −41.7227 −2.52517
\(274\) −25.4972 −1.54034
\(275\) 21.6489 1.30548
\(276\) 108.281 6.51776
\(277\) 9.13852 0.549080 0.274540 0.961576i \(-0.411474\pi\)
0.274540 + 0.961576i \(0.411474\pi\)
\(278\) 4.59432 0.275549
\(279\) −28.9654 −1.73411
\(280\) −1.30068 −0.0777308
\(281\) 22.9703 1.37030 0.685148 0.728404i \(-0.259738\pi\)
0.685148 + 0.728404i \(0.259738\pi\)
\(282\) 33.2552 1.98032
\(283\) 7.83880 0.465968 0.232984 0.972481i \(-0.425151\pi\)
0.232984 + 0.972481i \(0.425151\pi\)
\(284\) 47.5030 2.81879
\(285\) 0.278679 0.0165075
\(286\) −66.5354 −3.93432
\(287\) −27.6894 −1.63446
\(288\) −24.7076 −1.45591
\(289\) 4.48866 0.264039
\(290\) −0.755511 −0.0443651
\(291\) −22.3317 −1.30911
\(292\) 0.628912 0.0368043
\(293\) 5.44982 0.318382 0.159191 0.987248i \(-0.449111\pi\)
0.159191 + 0.987248i \(0.449111\pi\)
\(294\) −4.77423 −0.278439
\(295\) −1.23491 −0.0718990
\(296\) −18.8039 −1.09295
\(297\) 18.7864 1.09010
\(298\) 29.4286 1.70475
\(299\) 53.0325 3.06695
\(300\) 61.4885 3.55004
\(301\) 1.88016 0.108371
\(302\) 2.54449 0.146419
\(303\) 7.61492 0.437465
\(304\) 8.71254 0.499698
\(305\) 0.662812 0.0379525
\(306\) 53.9560 3.08446
\(307\) −10.1468 −0.579109 −0.289554 0.957162i \(-0.593507\pi\)
−0.289554 + 0.957162i \(0.593507\pi\)
\(308\) 48.7626 2.77851
\(309\) −34.2876 −1.95055
\(310\) −1.32418 −0.0752081
\(311\) 16.3459 0.926894 0.463447 0.886125i \(-0.346613\pi\)
0.463447 + 0.886125i \(0.346613\pi\)
\(312\) −104.507 −5.91657
\(313\) −25.5288 −1.44297 −0.721487 0.692428i \(-0.756541\pi\)
−0.721487 + 0.692428i \(0.756541\pi\)
\(314\) 54.4247 3.07137
\(315\) 0.945005 0.0532450
\(316\) 43.5843 2.45181
\(317\) 0.404252 0.0227050 0.0113525 0.999936i \(-0.496386\pi\)
0.0113525 + 0.999936i \(0.496386\pi\)
\(318\) −7.00285 −0.392700
\(319\) 15.6636 0.876993
\(320\) 0.0328483 0.00183627
\(321\) 24.8086 1.38468
\(322\) −56.2394 −3.13410
\(323\) −5.71129 −0.317784
\(324\) −8.04502 −0.446946
\(325\) 30.1150 1.67048
\(326\) 15.4648 0.856514
\(327\) −0.157372 −0.00870269
\(328\) −69.3567 −3.82958
\(329\) −11.9367 −0.658089
\(330\) 2.49533 0.137363
\(331\) 23.6570 1.30031 0.650153 0.759803i \(-0.274705\pi\)
0.650153 + 0.759803i \(0.274705\pi\)
\(332\) 35.5141 1.94909
\(333\) 13.6619 0.748666
\(334\) −13.8299 −0.756740
\(335\) −0.126360 −0.00690380
\(336\) 48.9202 2.66881
\(337\) 1.17881 0.0642137 0.0321069 0.999484i \(-0.489778\pi\)
0.0321069 + 0.999484i \(0.489778\pi\)
\(338\) −59.4766 −3.23510
\(339\) 10.3925 0.564441
\(340\) 1.70468 0.0924490
\(341\) 27.4534 1.48669
\(342\) −14.3405 −0.775446
\(343\) 19.3090 1.04259
\(344\) 4.70944 0.253916
\(345\) −1.98892 −0.107080
\(346\) 30.7856 1.65504
\(347\) 5.11097 0.274371 0.137186 0.990545i \(-0.456194\pi\)
0.137186 + 0.990545i \(0.456194\pi\)
\(348\) 44.4887 2.38485
\(349\) 22.5638 1.20781 0.603906 0.797055i \(-0.293610\pi\)
0.603906 + 0.797055i \(0.293610\pi\)
\(350\) −31.9361 −1.70705
\(351\) 26.1332 1.39488
\(352\) 23.4179 1.24818
\(353\) 31.8014 1.69262 0.846309 0.532692i \(-0.178819\pi\)
0.846309 + 0.532692i \(0.178819\pi\)
\(354\) 105.222 5.59250
\(355\) −0.872541 −0.0463097
\(356\) −4.73730 −0.251076
\(357\) −32.0684 −1.69724
\(358\) 33.0119 1.74473
\(359\) −32.3931 −1.70964 −0.854820 0.518925i \(-0.826332\pi\)
−0.854820 + 0.518925i \(0.826332\pi\)
\(360\) 2.36706 0.124755
\(361\) −17.4820 −0.920108
\(362\) −3.90570 −0.205279
\(363\) −21.4606 −1.12639
\(364\) 67.8319 3.55536
\(365\) −0.0115519 −0.000604656 0
\(366\) −56.4760 −2.95205
\(367\) 2.80775 0.146563 0.0732817 0.997311i \(-0.476653\pi\)
0.0732817 + 0.997311i \(0.476653\pi\)
\(368\) −62.1810 −3.24141
\(369\) 50.3907 2.62324
\(370\) 0.624563 0.0324695
\(371\) 2.51361 0.130500
\(372\) 77.9750 4.04281
\(373\) 27.7629 1.43751 0.718754 0.695264i \(-0.244713\pi\)
0.718754 + 0.695264i \(0.244713\pi\)
\(374\) −51.1396 −2.64437
\(375\) −2.26038 −0.116726
\(376\) −29.8991 −1.54193
\(377\) 21.7891 1.12220
\(378\) −27.7135 −1.42543
\(379\) 15.3066 0.786246 0.393123 0.919486i \(-0.371395\pi\)
0.393123 + 0.919486i \(0.371395\pi\)
\(380\) −0.453071 −0.0232421
\(381\) 49.9283 2.55790
\(382\) 25.6061 1.31012
\(383\) 7.84978 0.401105 0.200552 0.979683i \(-0.435726\pi\)
0.200552 + 0.979683i \(0.435726\pi\)
\(384\) −32.5292 −1.66000
\(385\) −0.895677 −0.0456479
\(386\) −3.91762 −0.199402
\(387\) −3.42162 −0.173931
\(388\) 36.3064 1.84318
\(389\) −2.75006 −0.139433 −0.0697167 0.997567i \(-0.522210\pi\)
−0.0697167 + 0.997567i \(0.522210\pi\)
\(390\) 3.47117 0.175769
\(391\) 40.7612 2.06138
\(392\) 4.29242 0.216800
\(393\) −28.8687 −1.45624
\(394\) −54.9430 −2.76799
\(395\) −0.800562 −0.0402807
\(396\) −88.7409 −4.45940
\(397\) −20.2299 −1.01531 −0.507655 0.861561i \(-0.669487\pi\)
−0.507655 + 0.861561i \(0.669487\pi\)
\(398\) −25.3001 −1.26818
\(399\) 8.52318 0.426693
\(400\) −35.3100 −1.76550
\(401\) −16.4144 −0.819696 −0.409848 0.912154i \(-0.634418\pi\)
−0.409848 + 0.912154i \(0.634418\pi\)
\(402\) 10.7667 0.536996
\(403\) 38.1895 1.90236
\(404\) −12.3802 −0.615937
\(405\) 0.147772 0.00734284
\(406\) −23.1067 −1.14677
\(407\) −12.9487 −0.641845
\(408\) −80.3252 −3.97669
\(409\) −21.3334 −1.05487 −0.527434 0.849596i \(-0.676846\pi\)
−0.527434 + 0.849596i \(0.676846\pi\)
\(410\) 2.30365 0.113769
\(411\) −27.5783 −1.36034
\(412\) 55.7441 2.74632
\(413\) −37.7686 −1.85847
\(414\) 102.348 5.03011
\(415\) −0.652327 −0.0320214
\(416\) 32.5758 1.59716
\(417\) 4.96931 0.243348
\(418\) 13.5920 0.664804
\(419\) 20.4484 0.998970 0.499485 0.866323i \(-0.333523\pi\)
0.499485 + 0.866323i \(0.333523\pi\)
\(420\) −2.54396 −0.124132
\(421\) −16.7493 −0.816311 −0.408156 0.912912i \(-0.633828\pi\)
−0.408156 + 0.912912i \(0.633828\pi\)
\(422\) −31.9121 −1.55346
\(423\) 21.7230 1.05621
\(424\) 6.29612 0.305767
\(425\) 23.1466 1.12278
\(426\) 74.3463 3.60209
\(427\) 20.2716 0.981011
\(428\) −40.3334 −1.94959
\(429\) −71.9659 −3.47454
\(430\) −0.156422 −0.00754334
\(431\) 22.6048 1.08884 0.544418 0.838814i \(-0.316751\pi\)
0.544418 + 0.838814i \(0.316751\pi\)
\(432\) −30.6413 −1.47423
\(433\) 17.3449 0.833541 0.416770 0.909012i \(-0.363162\pi\)
0.416770 + 0.909012i \(0.363162\pi\)
\(434\) −40.4989 −1.94401
\(435\) −0.817174 −0.0391805
\(436\) 0.255852 0.0122531
\(437\) −10.8336 −0.518240
\(438\) 0.984302 0.0470318
\(439\) 14.7166 0.702383 0.351191 0.936304i \(-0.385777\pi\)
0.351191 + 0.936304i \(0.385777\pi\)
\(440\) −2.24350 −0.106955
\(441\) −3.11863 −0.148506
\(442\) −71.1385 −3.38371
\(443\) 20.6598 0.981576 0.490788 0.871279i \(-0.336709\pi\)
0.490788 + 0.871279i \(0.336709\pi\)
\(444\) −36.7778 −1.74540
\(445\) 0.0870152 0.00412492
\(446\) 0.316652 0.0149939
\(447\) 31.8305 1.50553
\(448\) 1.00464 0.0474647
\(449\) 2.46837 0.116489 0.0582447 0.998302i \(-0.481450\pi\)
0.0582447 + 0.998302i \(0.481450\pi\)
\(450\) 58.1190 2.73976
\(451\) −47.7604 −2.24895
\(452\) −16.8959 −0.794715
\(453\) 2.75216 0.129308
\(454\) −32.8502 −1.54173
\(455\) −1.24595 −0.0584108
\(456\) 21.3490 0.999756
\(457\) 3.60533 0.168650 0.0843251 0.996438i \(-0.473127\pi\)
0.0843251 + 0.996438i \(0.473127\pi\)
\(458\) 65.5886 3.06475
\(459\) 20.0862 0.937541
\(460\) 3.23355 0.150765
\(461\) 25.7420 1.19893 0.599463 0.800403i \(-0.295381\pi\)
0.599463 + 0.800403i \(0.295381\pi\)
\(462\) 76.3177 3.55062
\(463\) −19.7761 −0.919072 −0.459536 0.888159i \(-0.651984\pi\)
−0.459536 + 0.888159i \(0.651984\pi\)
\(464\) −25.5479 −1.18603
\(465\) −1.43225 −0.0664192
\(466\) 8.72948 0.404385
\(467\) −6.27833 −0.290526 −0.145263 0.989393i \(-0.546403\pi\)
−0.145263 + 0.989393i \(0.546403\pi\)
\(468\) −123.444 −5.70622
\(469\) −3.86463 −0.178452
\(470\) 0.993084 0.0458075
\(471\) 58.8668 2.71244
\(472\) −94.6032 −4.35446
\(473\) 3.24301 0.149114
\(474\) 68.2133 3.13314
\(475\) −6.15194 −0.282270
\(476\) 52.1362 2.38966
\(477\) −4.57441 −0.209448
\(478\) −68.8574 −3.14946
\(479\) −36.6003 −1.67231 −0.836155 0.548494i \(-0.815202\pi\)
−0.836155 + 0.548494i \(0.815202\pi\)
\(480\) −1.22172 −0.0557635
\(481\) −18.0125 −0.821301
\(482\) 30.1468 1.37315
\(483\) −60.8296 −2.76784
\(484\) 34.8902 1.58592
\(485\) −0.666881 −0.0302815
\(486\) −45.6672 −2.07151
\(487\) −20.9091 −0.947481 −0.473741 0.880664i \(-0.657097\pi\)
−0.473741 + 0.880664i \(0.657097\pi\)
\(488\) 50.7765 2.29854
\(489\) 16.7270 0.756420
\(490\) −0.142571 −0.00644069
\(491\) 30.6214 1.38192 0.690962 0.722891i \(-0.257187\pi\)
0.690962 + 0.722891i \(0.257187\pi\)
\(492\) −135.652 −6.11567
\(493\) 16.7473 0.754259
\(494\) 18.9073 0.850679
\(495\) 1.63000 0.0732632
\(496\) −44.7775 −2.01057
\(497\) −26.6860 −1.19703
\(498\) 55.5826 2.49072
\(499\) −30.7377 −1.37601 −0.688003 0.725707i \(-0.741513\pi\)
−0.688003 + 0.725707i \(0.741513\pi\)
\(500\) 3.67489 0.164346
\(501\) −14.9587 −0.668305
\(502\) 39.3459 1.75609
\(503\) 39.7702 1.77327 0.886634 0.462473i \(-0.153038\pi\)
0.886634 + 0.462473i \(0.153038\pi\)
\(504\) 72.3946 3.22471
\(505\) 0.227401 0.0101192
\(506\) −97.0052 −4.31241
\(507\) −64.3310 −2.85704
\(508\) −81.1724 −3.60144
\(509\) −15.1723 −0.672502 −0.336251 0.941772i \(-0.609159\pi\)
−0.336251 + 0.941772i \(0.609159\pi\)
\(510\) 2.66797 0.118140
\(511\) −0.353307 −0.0156294
\(512\) 50.8514 2.24734
\(513\) −5.33853 −0.235702
\(514\) 50.1371 2.21145
\(515\) −1.02391 −0.0451191
\(516\) 9.21101 0.405492
\(517\) −20.5891 −0.905507
\(518\) 19.1018 0.839283
\(519\) 33.2982 1.46163
\(520\) −3.12086 −0.136859
\(521\) 39.8510 1.74590 0.872952 0.487807i \(-0.162203\pi\)
0.872952 + 0.487807i \(0.162203\pi\)
\(522\) 42.0508 1.84051
\(523\) −33.0569 −1.44548 −0.722738 0.691122i \(-0.757117\pi\)
−0.722738 + 0.691122i \(0.757117\pi\)
\(524\) 46.9342 2.05033
\(525\) −34.5426 −1.50756
\(526\) 4.61816 0.201361
\(527\) 29.3528 1.27863
\(528\) 84.3805 3.67219
\(529\) 54.3188 2.36169
\(530\) −0.209123 −0.00908371
\(531\) 68.7334 2.98278
\(532\) −13.8568 −0.600770
\(533\) −66.4378 −2.87774
\(534\) −7.41428 −0.320847
\(535\) 0.740848 0.0320296
\(536\) −9.68016 −0.418119
\(537\) 35.7062 1.54084
\(538\) 26.4905 1.14209
\(539\) 2.95584 0.127317
\(540\) 1.59342 0.0685698
\(541\) −7.65697 −0.329199 −0.164600 0.986360i \(-0.552633\pi\)
−0.164600 + 0.986360i \(0.552633\pi\)
\(542\) 1.15650 0.0496757
\(543\) −4.22448 −0.181290
\(544\) 25.0380 1.07350
\(545\) −0.00469952 −0.000201305 0
\(546\) 106.163 4.54335
\(547\) 6.11122 0.261297 0.130648 0.991429i \(-0.458294\pi\)
0.130648 + 0.991429i \(0.458294\pi\)
\(548\) 44.8362 1.91531
\(549\) −36.8914 −1.57448
\(550\) −55.0853 −2.34884
\(551\) −4.45111 −0.189624
\(552\) −152.367 −6.48515
\(553\) −24.4846 −1.04119
\(554\) −23.2528 −0.987919
\(555\) 0.675539 0.0286750
\(556\) −8.07900 −0.342626
\(557\) −19.9654 −0.845960 −0.422980 0.906139i \(-0.639016\pi\)
−0.422980 + 0.906139i \(0.639016\pi\)
\(558\) 73.7021 3.12006
\(559\) 4.51124 0.190805
\(560\) 1.46088 0.0617334
\(561\) −55.3135 −2.33534
\(562\) −58.4478 −2.46547
\(563\) 13.7152 0.578028 0.289014 0.957325i \(-0.406673\pi\)
0.289014 + 0.957325i \(0.406673\pi\)
\(564\) −58.4784 −2.46238
\(565\) 0.310345 0.0130563
\(566\) −19.9457 −0.838382
\(567\) 4.51949 0.189801
\(568\) −66.8433 −2.80468
\(569\) 17.1926 0.720751 0.360376 0.932807i \(-0.382649\pi\)
0.360376 + 0.932807i \(0.382649\pi\)
\(570\) −0.709096 −0.0297008
\(571\) −39.7594 −1.66388 −0.831939 0.554867i \(-0.812769\pi\)
−0.831939 + 0.554867i \(0.812769\pi\)
\(572\) 117.001 4.89205
\(573\) 27.6960 1.15702
\(574\) 70.4554 2.94075
\(575\) 43.9062 1.83101
\(576\) −1.82830 −0.0761790
\(577\) 6.22280 0.259059 0.129529 0.991576i \(-0.458653\pi\)
0.129529 + 0.991576i \(0.458653\pi\)
\(578\) −11.4213 −0.475065
\(579\) −4.23737 −0.176099
\(580\) 1.32855 0.0551649
\(581\) −19.9509 −0.827702
\(582\) 56.8227 2.35538
\(583\) 4.33563 0.179564
\(584\) −0.884966 −0.0366202
\(585\) 2.26744 0.0937471
\(586\) −13.8670 −0.572840
\(587\) −4.57601 −0.188872 −0.0944361 0.995531i \(-0.530105\pi\)
−0.0944361 + 0.995531i \(0.530105\pi\)
\(588\) 8.39537 0.346219
\(589\) −7.80142 −0.321452
\(590\) 3.14220 0.129362
\(591\) −59.4274 −2.44452
\(592\) 21.1198 0.868020
\(593\) −27.8178 −1.14234 −0.571171 0.820831i \(-0.693511\pi\)
−0.571171 + 0.820831i \(0.693511\pi\)
\(594\) −47.8019 −1.96133
\(595\) −0.957643 −0.0392595
\(596\) −51.7495 −2.11974
\(597\) −27.3650 −1.11998
\(598\) −134.941 −5.51813
\(599\) −35.2287 −1.43940 −0.719702 0.694283i \(-0.755722\pi\)
−0.719702 + 0.694283i \(0.755722\pi\)
\(600\) −86.5227 −3.53228
\(601\) −29.1471 −1.18894 −0.594468 0.804119i \(-0.702637\pi\)
−0.594468 + 0.804119i \(0.702637\pi\)
\(602\) −4.78404 −0.194983
\(603\) 7.03307 0.286409
\(604\) −4.47442 −0.182061
\(605\) −0.640867 −0.0260549
\(606\) −19.3761 −0.787099
\(607\) 20.3246 0.824948 0.412474 0.910969i \(-0.364665\pi\)
0.412474 + 0.910969i \(0.364665\pi\)
\(608\) −6.65464 −0.269881
\(609\) −24.9926 −1.01275
\(610\) −1.68652 −0.0682851
\(611\) −28.6408 −1.15868
\(612\) −94.8803 −3.83531
\(613\) −18.1015 −0.731112 −0.365556 0.930789i \(-0.619121\pi\)
−0.365556 + 0.930789i \(0.619121\pi\)
\(614\) 25.8184 1.04195
\(615\) 2.49167 0.100474
\(616\) −68.6157 −2.76461
\(617\) −43.0603 −1.73354 −0.866771 0.498707i \(-0.833808\pi\)
−0.866771 + 0.498707i \(0.833808\pi\)
\(618\) 87.2444 3.50948
\(619\) −37.2095 −1.49557 −0.747787 0.663938i \(-0.768884\pi\)
−0.747787 + 0.663938i \(0.768884\pi\)
\(620\) 2.32853 0.0935160
\(621\) 38.1008 1.52893
\(622\) −41.5920 −1.66769
\(623\) 2.66129 0.106622
\(624\) 117.379 4.69891
\(625\) 24.8987 0.995949
\(626\) 64.9578 2.59624
\(627\) 14.7013 0.587114
\(628\) −95.7045 −3.81903
\(629\) −13.8446 −0.552019
\(630\) −2.40455 −0.0957997
\(631\) −27.0966 −1.07870 −0.539349 0.842082i \(-0.681330\pi\)
−0.539349 + 0.842082i \(0.681330\pi\)
\(632\) −61.3292 −2.43954
\(633\) −34.5168 −1.37192
\(634\) −1.02861 −0.0408514
\(635\) 1.49099 0.0591679
\(636\) 12.3143 0.488295
\(637\) 4.11177 0.162914
\(638\) −39.8558 −1.57791
\(639\) 48.5646 1.92119
\(640\) −0.971405 −0.0383981
\(641\) −25.8139 −1.01959 −0.509795 0.860296i \(-0.670279\pi\)
−0.509795 + 0.860296i \(0.670279\pi\)
\(642\) −63.1252 −2.49135
\(643\) 36.8107 1.45167 0.725836 0.687868i \(-0.241453\pi\)
0.725836 + 0.687868i \(0.241453\pi\)
\(644\) 98.8956 3.89703
\(645\) −0.169189 −0.00666180
\(646\) 14.5323 0.571765
\(647\) −21.3255 −0.838393 −0.419196 0.907896i \(-0.637688\pi\)
−0.419196 + 0.907896i \(0.637688\pi\)
\(648\) 11.3205 0.444709
\(649\) −65.1456 −2.55719
\(650\) −76.6272 −3.00557
\(651\) −43.8043 −1.71683
\(652\) −27.1944 −1.06502
\(653\) 27.6488 1.08198 0.540991 0.841028i \(-0.318049\pi\)
0.540991 + 0.841028i \(0.318049\pi\)
\(654\) 0.400431 0.0156581
\(655\) −0.862094 −0.0336848
\(656\) 77.8989 3.04144
\(657\) 0.642967 0.0250845
\(658\) 30.3727 1.18405
\(659\) −1.84756 −0.0719707 −0.0359853 0.999352i \(-0.511457\pi\)
−0.0359853 + 0.999352i \(0.511457\pi\)
\(660\) −4.38797 −0.170802
\(661\) 3.21923 0.125213 0.0626067 0.998038i \(-0.480059\pi\)
0.0626067 + 0.998038i \(0.480059\pi\)
\(662\) −60.1949 −2.33954
\(663\) −76.9447 −2.98829
\(664\) −49.9732 −1.93934
\(665\) 0.254524 0.00987001
\(666\) −34.7625 −1.34702
\(667\) 31.7674 1.23004
\(668\) 24.3196 0.940952
\(669\) 0.342496 0.0132417
\(670\) 0.321522 0.0124215
\(671\) 34.9657 1.34984
\(672\) −37.3653 −1.44140
\(673\) 21.8528 0.842362 0.421181 0.906977i \(-0.361616\pi\)
0.421181 + 0.906977i \(0.361616\pi\)
\(674\) −2.99946 −0.115535
\(675\) 21.6359 0.832766
\(676\) 104.588 4.02262
\(677\) −35.8799 −1.37898 −0.689488 0.724297i \(-0.742165\pi\)
−0.689488 + 0.724297i \(0.742165\pi\)
\(678\) −26.4435 −1.01556
\(679\) −20.3960 −0.782727
\(680\) −2.39871 −0.0919865
\(681\) −35.5313 −1.36156
\(682\) −69.8549 −2.67488
\(683\) −24.3429 −0.931457 −0.465728 0.884928i \(-0.654208\pi\)
−0.465728 + 0.884928i \(0.654208\pi\)
\(684\) 25.2174 0.964212
\(685\) −0.823557 −0.0314665
\(686\) −49.1314 −1.87584
\(687\) 70.9418 2.70660
\(688\) −5.28946 −0.201659
\(689\) 6.03114 0.229768
\(690\) 5.06079 0.192661
\(691\) −0.695643 −0.0264635 −0.0132318 0.999912i \(-0.504212\pi\)
−0.0132318 + 0.999912i \(0.504212\pi\)
\(692\) −54.1356 −2.05793
\(693\) 49.8524 1.89373
\(694\) −13.0048 −0.493655
\(695\) 0.148396 0.00562898
\(696\) −62.6018 −2.37291
\(697\) −51.0646 −1.93421
\(698\) −57.4133 −2.17313
\(699\) 9.44197 0.357128
\(700\) 56.1587 2.12260
\(701\) −18.4070 −0.695224 −0.347612 0.937638i \(-0.613007\pi\)
−0.347612 + 0.937638i \(0.613007\pi\)
\(702\) −66.4955 −2.50971
\(703\) 3.67963 0.138780
\(704\) 1.73286 0.0653097
\(705\) 1.07414 0.0404544
\(706\) −80.9183 −3.04540
\(707\) 6.95487 0.261565
\(708\) −185.031 −6.95388
\(709\) 33.5958 1.26172 0.630859 0.775897i \(-0.282703\pi\)
0.630859 + 0.775897i \(0.282703\pi\)
\(710\) 2.22017 0.0833215
\(711\) 44.5584 1.67107
\(712\) 6.66603 0.249820
\(713\) 55.6784 2.08517
\(714\) 81.5976 3.05371
\(715\) −2.14908 −0.0803711
\(716\) −58.0505 −2.16945
\(717\) −74.4774 −2.78141
\(718\) 82.4237 3.07603
\(719\) −19.6546 −0.732992 −0.366496 0.930420i \(-0.619443\pi\)
−0.366496 + 0.930420i \(0.619443\pi\)
\(720\) −2.65859 −0.0990798
\(721\) −31.3156 −1.16625
\(722\) 44.4828 1.65548
\(723\) 32.6073 1.21268
\(724\) 6.86808 0.255250
\(725\) 18.0394 0.669967
\(726\) 54.6061 2.02662
\(727\) −2.90746 −0.107832 −0.0539158 0.998545i \(-0.517170\pi\)
−0.0539158 + 0.998545i \(0.517170\pi\)
\(728\) −95.4489 −3.53757
\(729\) −44.0005 −1.62965
\(730\) 0.0293937 0.00108791
\(731\) 3.46738 0.128246
\(732\) 99.3117 3.67066
\(733\) 15.5628 0.574823 0.287412 0.957807i \(-0.407205\pi\)
0.287412 + 0.957807i \(0.407205\pi\)
\(734\) −7.14429 −0.263700
\(735\) −0.154207 −0.00568802
\(736\) 47.4939 1.75065
\(737\) −6.66595 −0.245543
\(738\) −128.219 −4.71979
\(739\) 37.7847 1.38993 0.694966 0.719043i \(-0.255419\pi\)
0.694966 + 0.719043i \(0.255419\pi\)
\(740\) −1.09828 −0.0403735
\(741\) 20.4505 0.751267
\(742\) −6.39585 −0.234799
\(743\) 3.52976 0.129494 0.0647472 0.997902i \(-0.479376\pi\)
0.0647472 + 0.997902i \(0.479376\pi\)
\(744\) −109.721 −4.02259
\(745\) 0.950540 0.0348251
\(746\) −70.6424 −2.58640
\(747\) 36.3077 1.32843
\(748\) 89.9277 3.28808
\(749\) 22.6582 0.827914
\(750\) 5.75151 0.210016
\(751\) −37.5878 −1.37160 −0.685800 0.727790i \(-0.740548\pi\)
−0.685800 + 0.727790i \(0.740548\pi\)
\(752\) 33.5815 1.22459
\(753\) 42.5572 1.55087
\(754\) −55.4421 −2.01908
\(755\) 0.0821866 0.00299108
\(756\) 48.7334 1.77242
\(757\) −40.2226 −1.46191 −0.730957 0.682423i \(-0.760926\pi\)
−0.730957 + 0.682423i \(0.760926\pi\)
\(758\) −38.9474 −1.41463
\(759\) −104.923 −3.80845
\(760\) 0.637534 0.0231258
\(761\) 35.9693 1.30389 0.651943 0.758268i \(-0.273954\pi\)
0.651943 + 0.758268i \(0.273954\pi\)
\(762\) −127.042 −4.60224
\(763\) −0.143731 −0.00520342
\(764\) −45.0276 −1.62904
\(765\) 1.74277 0.0630101
\(766\) −19.9737 −0.721678
\(767\) −90.6218 −3.27216
\(768\) 80.5702 2.90733
\(769\) 42.6516 1.53806 0.769028 0.639215i \(-0.220741\pi\)
0.769028 + 0.639215i \(0.220741\pi\)
\(770\) 2.27904 0.0821309
\(771\) 54.2293 1.95302
\(772\) 6.88904 0.247942
\(773\) −11.2535 −0.404761 −0.202381 0.979307i \(-0.564868\pi\)
−0.202381 + 0.979307i \(0.564868\pi\)
\(774\) 8.70626 0.312940
\(775\) 31.6175 1.13573
\(776\) −51.0881 −1.83396
\(777\) 20.6608 0.741203
\(778\) 6.99748 0.250872
\(779\) 13.5720 0.486269
\(780\) −6.10396 −0.218557
\(781\) −46.0296 −1.64707
\(782\) −103.716 −3.70889
\(783\) 15.6542 0.559436
\(784\) −4.82108 −0.172181
\(785\) 1.75791 0.0627426
\(786\) 73.4561 2.62009
\(787\) 11.1517 0.397515 0.198757 0.980049i \(-0.436309\pi\)
0.198757 + 0.980049i \(0.436309\pi\)
\(788\) 96.6158 3.44180
\(789\) 4.99509 0.177830
\(790\) 2.03702 0.0724740
\(791\) 9.49166 0.337485
\(792\) 124.871 4.43709
\(793\) 48.6395 1.72724
\(794\) 51.4747 1.82677
\(795\) −0.226191 −0.00802217
\(796\) 44.4895 1.57689
\(797\) 23.0908 0.817920 0.408960 0.912552i \(-0.365892\pi\)
0.408960 + 0.912552i \(0.365892\pi\)
\(798\) −21.6871 −0.767716
\(799\) −22.0135 −0.778782
\(800\) 26.9698 0.953528
\(801\) −4.84317 −0.171125
\(802\) 41.7662 1.47482
\(803\) −0.609405 −0.0215054
\(804\) −18.9330 −0.667717
\(805\) −1.81653 −0.0640241
\(806\) −97.1727 −3.42276
\(807\) 28.6527 1.00862
\(808\) 17.4206 0.612855
\(809\) 41.9200 1.47383 0.736914 0.675986i \(-0.236282\pi\)
0.736914 + 0.675986i \(0.236282\pi\)
\(810\) −0.376004 −0.0132114
\(811\) 31.9734 1.12274 0.561369 0.827566i \(-0.310275\pi\)
0.561369 + 0.827566i \(0.310275\pi\)
\(812\) 40.6325 1.42592
\(813\) 1.25089 0.0438705
\(814\) 32.9479 1.15482
\(815\) 0.499510 0.0174971
\(816\) 90.2182 3.15827
\(817\) −0.921564 −0.0322415
\(818\) 54.2826 1.89795
\(819\) 69.3479 2.42321
\(820\) −4.05091 −0.141464
\(821\) 9.34786 0.326243 0.163121 0.986606i \(-0.447844\pi\)
0.163121 + 0.986606i \(0.447844\pi\)
\(822\) 70.1726 2.44755
\(823\) 25.9014 0.902865 0.451433 0.892305i \(-0.350913\pi\)
0.451433 + 0.892305i \(0.350913\pi\)
\(824\) −78.4397 −2.73258
\(825\) −59.5813 −2.07435
\(826\) 96.1018 3.34381
\(827\) −28.0019 −0.973722 −0.486861 0.873479i \(-0.661858\pi\)
−0.486861 + 0.873479i \(0.661858\pi\)
\(828\) −179.976 −6.25459
\(829\) 38.4111 1.33407 0.667036 0.745025i \(-0.267563\pi\)
0.667036 + 0.745025i \(0.267563\pi\)
\(830\) 1.65984 0.0576138
\(831\) −25.1507 −0.872468
\(832\) 2.41052 0.0835698
\(833\) 3.16034 0.109499
\(834\) −12.6443 −0.437838
\(835\) −0.446705 −0.0154588
\(836\) −23.9011 −0.826637
\(837\) 27.4370 0.948361
\(838\) −52.0307 −1.79737
\(839\) 29.9158 1.03281 0.516405 0.856345i \(-0.327270\pi\)
0.516405 + 0.856345i \(0.327270\pi\)
\(840\) 3.57970 0.123511
\(841\) −15.9480 −0.549930
\(842\) 42.6184 1.46873
\(843\) −63.2182 −2.17735
\(844\) 56.1167 1.93162
\(845\) −1.92109 −0.0660874
\(846\) −55.2739 −1.90036
\(847\) −19.6004 −0.673478
\(848\) −7.07156 −0.242838
\(849\) −21.5737 −0.740407
\(850\) −58.8963 −2.02013
\(851\) −26.2614 −0.900228
\(852\) −130.736 −4.47895
\(853\) −51.3535 −1.75831 −0.879155 0.476537i \(-0.841892\pi\)
−0.879155 + 0.476537i \(0.841892\pi\)
\(854\) −51.5808 −1.76506
\(855\) −0.463197 −0.0158410
\(856\) 56.7546 1.93983
\(857\) 12.4954 0.426833 0.213417 0.976961i \(-0.431541\pi\)
0.213417 + 0.976961i \(0.431541\pi\)
\(858\) 183.116 6.25149
\(859\) 0.742927 0.0253483 0.0126742 0.999920i \(-0.495966\pi\)
0.0126742 + 0.999920i \(0.495966\pi\)
\(860\) 0.275064 0.00937960
\(861\) 76.2059 2.59709
\(862\) −57.5176 −1.95906
\(863\) 12.4872 0.425069 0.212534 0.977154i \(-0.431828\pi\)
0.212534 + 0.977154i \(0.431828\pi\)
\(864\) 23.4039 0.796216
\(865\) 0.994370 0.0338096
\(866\) −44.1338 −1.49973
\(867\) −12.3535 −0.419547
\(868\) 71.2162 2.41724
\(869\) −42.2325 −1.43264
\(870\) 2.07929 0.0704945
\(871\) −9.27277 −0.314196
\(872\) −0.360019 −0.0121918
\(873\) 37.1178 1.25625
\(874\) 27.5659 0.932430
\(875\) −2.06446 −0.0697914
\(876\) −1.73087 −0.0584807
\(877\) 13.8040 0.466127 0.233064 0.972461i \(-0.425125\pi\)
0.233064 + 0.972461i \(0.425125\pi\)
\(878\) −37.4461 −1.26374
\(879\) −14.9988 −0.505897
\(880\) 2.51982 0.0849430
\(881\) −6.26251 −0.210989 −0.105495 0.994420i \(-0.533643\pi\)
−0.105495 + 0.994420i \(0.533643\pi\)
\(882\) 7.93532 0.267196
\(883\) 37.9742 1.27793 0.638966 0.769235i \(-0.279362\pi\)
0.638966 + 0.769235i \(0.279362\pi\)
\(884\) 125.095 4.20741
\(885\) 3.39866 0.114245
\(886\) −52.5686 −1.76608
\(887\) −6.05758 −0.203394 −0.101697 0.994815i \(-0.532427\pi\)
−0.101697 + 0.994815i \(0.532427\pi\)
\(888\) 51.7514 1.73666
\(889\) 45.6006 1.52939
\(890\) −0.221409 −0.00742165
\(891\) 7.79549 0.261159
\(892\) −0.556824 −0.0186438
\(893\) 5.85078 0.195789
\(894\) −80.9924 −2.70879
\(895\) 1.06628 0.0356418
\(896\) −29.7096 −0.992530
\(897\) −145.954 −4.87327
\(898\) −6.28073 −0.209591
\(899\) 22.8762 0.762964
\(900\) −102.201 −3.40669
\(901\) 4.63559 0.154434
\(902\) 121.526 4.04637
\(903\) −5.17451 −0.172197
\(904\) 23.7748 0.790738
\(905\) −0.126154 −0.00419349
\(906\) −7.00285 −0.232654
\(907\) 16.4302 0.545557 0.272778 0.962077i \(-0.412057\pi\)
0.272778 + 0.962077i \(0.412057\pi\)
\(908\) 57.7662 1.91704
\(909\) −12.6569 −0.419801
\(910\) 3.17029 0.105094
\(911\) 6.22670 0.206300 0.103150 0.994666i \(-0.467108\pi\)
0.103150 + 0.994666i \(0.467108\pi\)
\(912\) −23.9783 −0.794002
\(913\) −34.4125 −1.13889
\(914\) −9.17371 −0.303439
\(915\) −1.82417 −0.0603051
\(916\) −115.336 −3.81080
\(917\) −26.3664 −0.870697
\(918\) −51.1090 −1.68685
\(919\) −25.8843 −0.853843 −0.426922 0.904289i \(-0.640402\pi\)
−0.426922 + 0.904289i \(0.640402\pi\)
\(920\) −4.55005 −0.150011
\(921\) 27.9257 0.920182
\(922\) −65.5003 −2.15714
\(923\) −64.0302 −2.10758
\(924\) −134.203 −4.41495
\(925\) −14.9128 −0.490328
\(926\) 50.3200 1.65362
\(927\) 56.9899 1.87179
\(928\) 19.5135 0.640561
\(929\) −10.9990 −0.360864 −0.180432 0.983587i \(-0.557750\pi\)
−0.180432 + 0.983587i \(0.557750\pi\)
\(930\) 3.64435 0.119503
\(931\) −0.839959 −0.0275286
\(932\) −15.3506 −0.502825
\(933\) −44.9867 −1.47280
\(934\) 15.9751 0.522722
\(935\) −1.65180 −0.0540197
\(936\) 173.703 5.67767
\(937\) 8.73378 0.285320 0.142660 0.989772i \(-0.454434\pi\)
0.142660 + 0.989772i \(0.454434\pi\)
\(938\) 9.83350 0.321075
\(939\) 70.2595 2.29283
\(940\) −1.74631 −0.0569584
\(941\) 17.3878 0.566825 0.283412 0.958998i \(-0.408533\pi\)
0.283412 + 0.958998i \(0.408533\pi\)
\(942\) −149.786 −4.88029
\(943\) −96.8631 −3.15430
\(944\) 106.255 3.45830
\(945\) −0.895141 −0.0291189
\(946\) −8.25181 −0.268289
\(947\) 42.6828 1.38700 0.693502 0.720455i \(-0.256067\pi\)
0.693502 + 0.720455i \(0.256067\pi\)
\(948\) −119.951 −3.89584
\(949\) −0.847722 −0.0275182
\(950\) 15.6535 0.507868
\(951\) −1.11257 −0.0360774
\(952\) −73.3628 −2.37770
\(953\) −15.6047 −0.505484 −0.252742 0.967534i \(-0.581332\pi\)
−0.252742 + 0.967534i \(0.581332\pi\)
\(954\) 11.6395 0.376844
\(955\) 0.827073 0.0267634
\(956\) 121.084 3.91613
\(957\) −43.1088 −1.39351
\(958\) 93.1289 3.00886
\(959\) −25.1878 −0.813358
\(960\) −0.0904038 −0.00291777
\(961\) 9.09487 0.293383
\(962\) 45.8327 1.47770
\(963\) −41.2347 −1.32877
\(964\) −53.0123 −1.70741
\(965\) −0.126539 −0.00407343
\(966\) 154.780 4.97997
\(967\) 44.5276 1.43191 0.715955 0.698146i \(-0.245992\pi\)
0.715955 + 0.698146i \(0.245992\pi\)
\(968\) −49.0953 −1.57798
\(969\) 15.7184 0.504948
\(970\) 1.69687 0.0544832
\(971\) 9.85220 0.316172 0.158086 0.987425i \(-0.449468\pi\)
0.158086 + 0.987425i \(0.449468\pi\)
\(972\) 80.3046 2.57577
\(973\) 4.53858 0.145500
\(974\) 53.2029 1.70473
\(975\) −82.8814 −2.65433
\(976\) −57.0302 −1.82549
\(977\) 19.0304 0.608837 0.304418 0.952538i \(-0.401538\pi\)
0.304418 + 0.952538i \(0.401538\pi\)
\(978\) −42.5616 −1.36097
\(979\) 4.59036 0.146709
\(980\) 0.250707 0.00800854
\(981\) 0.261570 0.00835129
\(982\) −77.9158 −2.48639
\(983\) −19.9750 −0.637104 −0.318552 0.947905i \(-0.603196\pi\)
−0.318552 + 0.947905i \(0.603196\pi\)
\(984\) 190.881 6.08507
\(985\) −1.77465 −0.0565451
\(986\) −42.6132 −1.35708
\(987\) 32.8517 1.04568
\(988\) −33.2480 −1.05776
\(989\) 6.57717 0.209142
\(990\) −4.14752 −0.131817
\(991\) −19.6606 −0.624539 −0.312270 0.949994i \(-0.601089\pi\)
−0.312270 + 0.949994i \(0.601089\pi\)
\(992\) 34.2011 1.08589
\(993\) −65.1079 −2.06614
\(994\) 67.9021 2.15372
\(995\) −0.817189 −0.0259066
\(996\) −97.7405 −3.09703
\(997\) 16.2073 0.513291 0.256646 0.966506i \(-0.417383\pi\)
0.256646 + 0.966506i \(0.417383\pi\)
\(998\) 78.2116 2.47574
\(999\) −12.9410 −0.409435
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.1.9 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.9 153 1.1 even 1 trivial