Properties

Label 8003.2.a.b.1.16
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 1.16
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.36991 q^{2} -1.12262 q^{3} +3.61648 q^{4} +0.983312 q^{5} +2.66051 q^{6} +2.71051 q^{7} -3.83091 q^{8} -1.73972 q^{9} +O(q^{10})\) \(q-2.36991 q^{2} -1.12262 q^{3} +3.61648 q^{4} +0.983312 q^{5} +2.66051 q^{6} +2.71051 q^{7} -3.83091 q^{8} -1.73972 q^{9} -2.33036 q^{10} -1.16701 q^{11} -4.05993 q^{12} +3.98883 q^{13} -6.42368 q^{14} -1.10389 q^{15} +1.84596 q^{16} -4.49166 q^{17} +4.12299 q^{18} -7.69190 q^{19} +3.55613 q^{20} -3.04288 q^{21} +2.76571 q^{22} -0.541286 q^{23} +4.30066 q^{24} -4.03310 q^{25} -9.45317 q^{26} +5.32091 q^{27} +9.80251 q^{28} +6.32794 q^{29} +2.61611 q^{30} -9.15254 q^{31} +3.28705 q^{32} +1.31011 q^{33} +10.6448 q^{34} +2.66528 q^{35} -6.29168 q^{36} +5.19039 q^{37} +18.2291 q^{38} -4.47794 q^{39} -3.76698 q^{40} +1.05534 q^{41} +7.21135 q^{42} +3.56306 q^{43} -4.22046 q^{44} -1.71069 q^{45} +1.28280 q^{46} +13.5615 q^{47} -2.07232 q^{48} +0.346880 q^{49} +9.55809 q^{50} +5.04242 q^{51} +14.4255 q^{52} -1.00000 q^{53} -12.6101 q^{54} -1.14753 q^{55} -10.3837 q^{56} +8.63508 q^{57} -14.9967 q^{58} -2.11908 q^{59} -3.99218 q^{60} -1.28622 q^{61} +21.6907 q^{62} -4.71554 q^{63} -11.4820 q^{64} +3.92226 q^{65} -3.10484 q^{66} +14.7669 q^{67} -16.2440 q^{68} +0.607658 q^{69} -6.31647 q^{70} -6.06876 q^{71} +6.66473 q^{72} +4.45096 q^{73} -12.3008 q^{74} +4.52764 q^{75} -27.8176 q^{76} -3.16319 q^{77} +10.6123 q^{78} +5.53740 q^{79} +1.81516 q^{80} -0.754189 q^{81} -2.50106 q^{82} +3.68374 q^{83} -11.0045 q^{84} -4.41670 q^{85} -8.44413 q^{86} -7.10388 q^{87} +4.47071 q^{88} +7.35347 q^{89} +4.05418 q^{90} +10.8118 q^{91} -1.95755 q^{92} +10.2748 q^{93} -32.1395 q^{94} -7.56353 q^{95} -3.69011 q^{96} -16.9296 q^{97} -0.822076 q^{98} +2.03027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36991 −1.67578 −0.837890 0.545839i \(-0.816211\pi\)
−0.837890 + 0.545839i \(0.816211\pi\)
\(3\) −1.12262 −0.648145 −0.324073 0.946032i \(-0.605052\pi\)
−0.324073 + 0.946032i \(0.605052\pi\)
\(4\) 3.61648 1.80824
\(5\) 0.983312 0.439750 0.219875 0.975528i \(-0.429435\pi\)
0.219875 + 0.975528i \(0.429435\pi\)
\(6\) 2.66051 1.08615
\(7\) 2.71051 1.02448 0.512239 0.858843i \(-0.328816\pi\)
0.512239 + 0.858843i \(0.328816\pi\)
\(8\) −3.83091 −1.35443
\(9\) −1.73972 −0.579908
\(10\) −2.33036 −0.736925
\(11\) −1.16701 −0.351866 −0.175933 0.984402i \(-0.556294\pi\)
−0.175933 + 0.984402i \(0.556294\pi\)
\(12\) −4.05993 −1.17200
\(13\) 3.98883 1.10630 0.553151 0.833081i \(-0.313425\pi\)
0.553151 + 0.833081i \(0.313425\pi\)
\(14\) −6.42368 −1.71680
\(15\) −1.10389 −0.285022
\(16\) 1.84596 0.461491
\(17\) −4.49166 −1.08939 −0.544693 0.838635i \(-0.683354\pi\)
−0.544693 + 0.838635i \(0.683354\pi\)
\(18\) 4.12299 0.971798
\(19\) −7.69190 −1.76464 −0.882321 0.470648i \(-0.844020\pi\)
−0.882321 + 0.470648i \(0.844020\pi\)
\(20\) 3.55613 0.795174
\(21\) −3.04288 −0.664010
\(22\) 2.76571 0.589651
\(23\) −0.541286 −0.112866 −0.0564329 0.998406i \(-0.517973\pi\)
−0.0564329 + 0.998406i \(0.517973\pi\)
\(24\) 4.30066 0.877868
\(25\) −4.03310 −0.806620
\(26\) −9.45317 −1.85392
\(27\) 5.32091 1.02401
\(28\) 9.80251 1.85250
\(29\) 6.32794 1.17507 0.587535 0.809199i \(-0.300099\pi\)
0.587535 + 0.809199i \(0.300099\pi\)
\(30\) 2.61611 0.477634
\(31\) −9.15254 −1.64385 −0.821923 0.569599i \(-0.807099\pi\)
−0.821923 + 0.569599i \(0.807099\pi\)
\(32\) 3.28705 0.581075
\(33\) 1.31011 0.228060
\(34\) 10.6448 1.82557
\(35\) 2.66528 0.450514
\(36\) −6.29168 −1.04861
\(37\) 5.19039 0.853294 0.426647 0.904418i \(-0.359695\pi\)
0.426647 + 0.904418i \(0.359695\pi\)
\(38\) 18.2291 2.95715
\(39\) −4.47794 −0.717044
\(40\) −3.76698 −0.595612
\(41\) 1.05534 0.164817 0.0824083 0.996599i \(-0.473739\pi\)
0.0824083 + 0.996599i \(0.473739\pi\)
\(42\) 7.21135 1.11274
\(43\) 3.56306 0.543361 0.271681 0.962387i \(-0.412421\pi\)
0.271681 + 0.962387i \(0.412421\pi\)
\(44\) −4.22046 −0.636259
\(45\) −1.71069 −0.255015
\(46\) 1.28280 0.189138
\(47\) 13.5615 1.97815 0.989073 0.147429i \(-0.0470998\pi\)
0.989073 + 0.147429i \(0.0470998\pi\)
\(48\) −2.07232 −0.299113
\(49\) 0.346880 0.0495544
\(50\) 9.55809 1.35172
\(51\) 5.04242 0.706081
\(52\) 14.4255 2.00046
\(53\) −1.00000 −0.137361
\(54\) −12.6101 −1.71602
\(55\) −1.14753 −0.154733
\(56\) −10.3837 −1.38759
\(57\) 8.63508 1.14374
\(58\) −14.9967 −1.96916
\(59\) −2.11908 −0.275881 −0.137940 0.990441i \(-0.544048\pi\)
−0.137940 + 0.990441i \(0.544048\pi\)
\(60\) −3.99218 −0.515388
\(61\) −1.28622 −0.164683 −0.0823415 0.996604i \(-0.526240\pi\)
−0.0823415 + 0.996604i \(0.526240\pi\)
\(62\) 21.6907 2.75472
\(63\) −4.71554 −0.594103
\(64\) −11.4820 −1.43524
\(65\) 3.92226 0.486496
\(66\) −3.10484 −0.382179
\(67\) 14.7669 1.80407 0.902034 0.431665i \(-0.142074\pi\)
0.902034 + 0.431665i \(0.142074\pi\)
\(68\) −16.2440 −1.96987
\(69\) 0.607658 0.0731535
\(70\) −6.31647 −0.754963
\(71\) −6.06876 −0.720229 −0.360115 0.932908i \(-0.617262\pi\)
−0.360115 + 0.932908i \(0.617262\pi\)
\(72\) 6.66473 0.785446
\(73\) 4.45096 0.520945 0.260473 0.965481i \(-0.416122\pi\)
0.260473 + 0.965481i \(0.416122\pi\)
\(74\) −12.3008 −1.42993
\(75\) 4.52764 0.522807
\(76\) −27.8176 −3.19090
\(77\) −3.16319 −0.360479
\(78\) 10.6123 1.20161
\(79\) 5.53740 0.623006 0.311503 0.950245i \(-0.399168\pi\)
0.311503 + 0.950245i \(0.399168\pi\)
\(80\) 1.81516 0.202941
\(81\) −0.754189 −0.0837988
\(82\) −2.50106 −0.276196
\(83\) 3.68374 0.404343 0.202171 0.979350i \(-0.435200\pi\)
0.202171 + 0.979350i \(0.435200\pi\)
\(84\) −11.0045 −1.20069
\(85\) −4.41670 −0.479058
\(86\) −8.44413 −0.910554
\(87\) −7.10388 −0.761615
\(88\) 4.47071 0.476579
\(89\) 7.35347 0.779466 0.389733 0.920928i \(-0.372567\pi\)
0.389733 + 0.920928i \(0.372567\pi\)
\(90\) 4.05418 0.427349
\(91\) 10.8118 1.13338
\(92\) −1.95755 −0.204089
\(93\) 10.2748 1.06545
\(94\) −32.1395 −3.31494
\(95\) −7.56353 −0.776002
\(96\) −3.69011 −0.376621
\(97\) −16.9296 −1.71894 −0.859470 0.511187i \(-0.829206\pi\)
−0.859470 + 0.511187i \(0.829206\pi\)
\(98\) −0.822076 −0.0830422
\(99\) 2.03027 0.204050
\(100\) −14.5856 −1.45856
\(101\) −2.24894 −0.223777 −0.111889 0.993721i \(-0.535690\pi\)
−0.111889 + 0.993721i \(0.535690\pi\)
\(102\) −11.9501 −1.18324
\(103\) 0.513601 0.0506066 0.0253033 0.999680i \(-0.491945\pi\)
0.0253033 + 0.999680i \(0.491945\pi\)
\(104\) −15.2808 −1.49841
\(105\) −2.99210 −0.291999
\(106\) 2.36991 0.230186
\(107\) 1.93001 0.186581 0.0932907 0.995639i \(-0.470261\pi\)
0.0932907 + 0.995639i \(0.470261\pi\)
\(108\) 19.2430 1.85165
\(109\) 9.12126 0.873658 0.436829 0.899544i \(-0.356101\pi\)
0.436829 + 0.899544i \(0.356101\pi\)
\(110\) 2.71955 0.259299
\(111\) −5.82683 −0.553059
\(112\) 5.00351 0.472787
\(113\) 15.8955 1.49532 0.747661 0.664081i \(-0.231177\pi\)
0.747661 + 0.664081i \(0.231177\pi\)
\(114\) −20.4644 −1.91666
\(115\) −0.532253 −0.0496328
\(116\) 22.8849 2.12481
\(117\) −6.93946 −0.641553
\(118\) 5.02204 0.462316
\(119\) −12.1747 −1.11605
\(120\) 4.22889 0.386043
\(121\) −9.63809 −0.876190
\(122\) 3.04822 0.275973
\(123\) −1.18475 −0.106825
\(124\) −33.1000 −2.97247
\(125\) −8.88235 −0.794462
\(126\) 11.1754 0.995586
\(127\) −13.2914 −1.17942 −0.589709 0.807616i \(-0.700758\pi\)
−0.589709 + 0.807616i \(0.700758\pi\)
\(128\) 20.6371 1.82408
\(129\) −3.99996 −0.352177
\(130\) −9.29541 −0.815261
\(131\) 10.1842 0.889796 0.444898 0.895581i \(-0.353240\pi\)
0.444898 + 0.895581i \(0.353240\pi\)
\(132\) 4.73798 0.412388
\(133\) −20.8490 −1.80784
\(134\) −34.9963 −3.02322
\(135\) 5.23211 0.450309
\(136\) 17.2071 1.47550
\(137\) −13.7811 −1.17740 −0.588701 0.808351i \(-0.700360\pi\)
−0.588701 + 0.808351i \(0.700360\pi\)
\(138\) −1.44010 −0.122589
\(139\) −21.5588 −1.82859 −0.914297 0.405046i \(-0.867256\pi\)
−0.914297 + 0.405046i \(0.867256\pi\)
\(140\) 9.63893 0.814638
\(141\) −15.2244 −1.28213
\(142\) 14.3824 1.20695
\(143\) −4.65500 −0.389270
\(144\) −3.21147 −0.267622
\(145\) 6.22234 0.516737
\(146\) −10.5484 −0.872990
\(147\) −0.389415 −0.0321184
\(148\) 18.7709 1.54296
\(149\) 9.36635 0.767321 0.383661 0.923474i \(-0.374663\pi\)
0.383661 + 0.923474i \(0.374663\pi\)
\(150\) −10.7301 −0.876109
\(151\) −1.00000 −0.0813788
\(152\) 29.4670 2.39009
\(153\) 7.81424 0.631744
\(154\) 7.49648 0.604084
\(155\) −8.99980 −0.722882
\(156\) −16.1944 −1.29659
\(157\) −9.54420 −0.761710 −0.380855 0.924635i \(-0.624370\pi\)
−0.380855 + 0.924635i \(0.624370\pi\)
\(158\) −13.1231 −1.04402
\(159\) 1.12262 0.0890296
\(160\) 3.23220 0.255528
\(161\) −1.46716 −0.115629
\(162\) 1.78736 0.140428
\(163\) 23.7545 1.86060 0.930300 0.366800i \(-0.119547\pi\)
0.930300 + 0.366800i \(0.119547\pi\)
\(164\) 3.81662 0.298028
\(165\) 1.28824 0.100290
\(166\) −8.73013 −0.677589
\(167\) 10.3388 0.800039 0.400019 0.916507i \(-0.369003\pi\)
0.400019 + 0.916507i \(0.369003\pi\)
\(168\) 11.6570 0.899357
\(169\) 2.91074 0.223903
\(170\) 10.4672 0.802796
\(171\) 13.3818 1.02333
\(172\) 12.8857 0.982528
\(173\) −10.0843 −0.766692 −0.383346 0.923605i \(-0.625228\pi\)
−0.383346 + 0.923605i \(0.625228\pi\)
\(174\) 16.8356 1.27630
\(175\) −10.9318 −0.826364
\(176\) −2.15426 −0.162383
\(177\) 2.37892 0.178811
\(178\) −17.4271 −1.30621
\(179\) −0.651822 −0.0487195 −0.0243597 0.999703i \(-0.507755\pi\)
−0.0243597 + 0.999703i \(0.507755\pi\)
\(180\) −6.18668 −0.461128
\(181\) −8.09432 −0.601646 −0.300823 0.953680i \(-0.597261\pi\)
−0.300823 + 0.953680i \(0.597261\pi\)
\(182\) −25.6229 −1.89930
\(183\) 1.44393 0.106738
\(184\) 2.07362 0.152869
\(185\) 5.10377 0.375236
\(186\) −24.3504 −1.78546
\(187\) 5.24180 0.383319
\(188\) 49.0448 3.57696
\(189\) 14.4224 1.04907
\(190\) 17.9249 1.30041
\(191\) 5.73456 0.414939 0.207469 0.978242i \(-0.433477\pi\)
0.207469 + 0.978242i \(0.433477\pi\)
\(192\) 12.8899 0.930247
\(193\) −14.9959 −1.07943 −0.539716 0.841847i \(-0.681468\pi\)
−0.539716 + 0.841847i \(0.681468\pi\)
\(194\) 40.1216 2.88056
\(195\) −4.40321 −0.315320
\(196\) 1.25449 0.0896061
\(197\) −8.24257 −0.587259 −0.293629 0.955919i \(-0.594863\pi\)
−0.293629 + 0.955919i \(0.594863\pi\)
\(198\) −4.81157 −0.341943
\(199\) −15.5799 −1.10443 −0.552216 0.833701i \(-0.686218\pi\)
−0.552216 + 0.833701i \(0.686218\pi\)
\(200\) 15.4504 1.09251
\(201\) −16.5777 −1.16930
\(202\) 5.32978 0.375002
\(203\) 17.1520 1.20383
\(204\) 18.2358 1.27676
\(205\) 1.03773 0.0724781
\(206\) −1.21719 −0.0848055
\(207\) 0.941688 0.0654518
\(208\) 7.36323 0.510548
\(209\) 8.97651 0.620918
\(210\) 7.09100 0.489326
\(211\) −2.92004 −0.201024 −0.100512 0.994936i \(-0.532048\pi\)
−0.100512 + 0.994936i \(0.532048\pi\)
\(212\) −3.61648 −0.248381
\(213\) 6.81291 0.466813
\(214\) −4.57396 −0.312669
\(215\) 3.50360 0.238943
\(216\) −20.3839 −1.38695
\(217\) −24.8081 −1.68408
\(218\) −21.6166 −1.46406
\(219\) −4.99674 −0.337648
\(220\) −4.15003 −0.279795
\(221\) −17.9164 −1.20519
\(222\) 13.8091 0.926805
\(223\) −2.61809 −0.175321 −0.0876603 0.996150i \(-0.527939\pi\)
−0.0876603 + 0.996150i \(0.527939\pi\)
\(224\) 8.90960 0.595298
\(225\) 7.01648 0.467765
\(226\) −37.6709 −2.50583
\(227\) −24.5090 −1.62672 −0.813360 0.581761i \(-0.802364\pi\)
−0.813360 + 0.581761i \(0.802364\pi\)
\(228\) 31.2286 2.06816
\(229\) −3.84039 −0.253780 −0.126890 0.991917i \(-0.540500\pi\)
−0.126890 + 0.991917i \(0.540500\pi\)
\(230\) 1.26139 0.0831737
\(231\) 3.55106 0.233643
\(232\) −24.2418 −1.59155
\(233\) 4.39610 0.287998 0.143999 0.989578i \(-0.454004\pi\)
0.143999 + 0.989578i \(0.454004\pi\)
\(234\) 16.4459 1.07510
\(235\) 13.3352 0.869890
\(236\) −7.66362 −0.498859
\(237\) −6.21639 −0.403798
\(238\) 28.8529 1.87026
\(239\) −9.21626 −0.596150 −0.298075 0.954542i \(-0.596345\pi\)
−0.298075 + 0.954542i \(0.596345\pi\)
\(240\) −2.03773 −0.131535
\(241\) 9.96847 0.642126 0.321063 0.947058i \(-0.395960\pi\)
0.321063 + 0.947058i \(0.395960\pi\)
\(242\) 22.8414 1.46830
\(243\) −15.1161 −0.969696
\(244\) −4.65157 −0.297786
\(245\) 0.341092 0.0217915
\(246\) 2.80775 0.179015
\(247\) −30.6816 −1.95223
\(248\) 35.0626 2.22648
\(249\) −4.13544 −0.262073
\(250\) 21.0504 1.33134
\(251\) 7.17902 0.453136 0.226568 0.973995i \(-0.427249\pi\)
0.226568 + 0.973995i \(0.427249\pi\)
\(252\) −17.0537 −1.07428
\(253\) 0.631685 0.0397137
\(254\) 31.4994 1.97645
\(255\) 4.95827 0.310499
\(256\) −25.9442 −1.62151
\(257\) 15.6262 0.974739 0.487369 0.873196i \(-0.337957\pi\)
0.487369 + 0.873196i \(0.337957\pi\)
\(258\) 9.47955 0.590171
\(259\) 14.0686 0.874181
\(260\) 14.1848 0.879702
\(261\) −11.0089 −0.681432
\(262\) −24.1356 −1.49110
\(263\) −4.76886 −0.294061 −0.147030 0.989132i \(-0.546972\pi\)
−0.147030 + 0.989132i \(0.546972\pi\)
\(264\) −5.01891 −0.308892
\(265\) −0.983312 −0.0604043
\(266\) 49.4102 3.02954
\(267\) −8.25515 −0.505207
\(268\) 53.4043 3.26219
\(269\) 1.74684 0.106507 0.0532533 0.998581i \(-0.483041\pi\)
0.0532533 + 0.998581i \(0.483041\pi\)
\(270\) −12.3996 −0.754618
\(271\) −21.3661 −1.29790 −0.648948 0.760833i \(-0.724791\pi\)
−0.648948 + 0.760833i \(0.724791\pi\)
\(272\) −8.29143 −0.502742
\(273\) −12.1375 −0.734595
\(274\) 32.6600 1.97307
\(275\) 4.70666 0.283822
\(276\) 2.19758 0.132279
\(277\) −25.4291 −1.52789 −0.763944 0.645282i \(-0.776740\pi\)
−0.763944 + 0.645282i \(0.776740\pi\)
\(278\) 51.0924 3.06432
\(279\) 15.9229 0.953279
\(280\) −10.2104 −0.610191
\(281\) −25.1491 −1.50027 −0.750134 0.661286i \(-0.770011\pi\)
−0.750134 + 0.661286i \(0.770011\pi\)
\(282\) 36.0805 2.14856
\(283\) −12.1371 −0.721473 −0.360737 0.932668i \(-0.617475\pi\)
−0.360737 + 0.932668i \(0.617475\pi\)
\(284\) −21.9475 −1.30235
\(285\) 8.49097 0.502962
\(286\) 11.0319 0.652331
\(287\) 2.86052 0.168851
\(288\) −5.71857 −0.336970
\(289\) 3.17498 0.186763
\(290\) −14.7464 −0.865938
\(291\) 19.0055 1.11412
\(292\) 16.0968 0.941994
\(293\) 11.9117 0.695891 0.347945 0.937515i \(-0.386879\pi\)
0.347945 + 0.937515i \(0.386879\pi\)
\(294\) 0.922879 0.0538234
\(295\) −2.08372 −0.121319
\(296\) −19.8839 −1.15573
\(297\) −6.20955 −0.360315
\(298\) −22.1974 −1.28586
\(299\) −2.15910 −0.124864
\(300\) 16.3741 0.945360
\(301\) 9.65772 0.556662
\(302\) 2.36991 0.136373
\(303\) 2.52470 0.145040
\(304\) −14.1990 −0.814366
\(305\) −1.26475 −0.0724194
\(306\) −18.5191 −1.05866
\(307\) 2.40653 0.137348 0.0686739 0.997639i \(-0.478123\pi\)
0.0686739 + 0.997639i \(0.478123\pi\)
\(308\) −11.4396 −0.651833
\(309\) −0.576579 −0.0328004
\(310\) 21.3287 1.21139
\(311\) 1.75136 0.0993103 0.0496552 0.998766i \(-0.484188\pi\)
0.0496552 + 0.998766i \(0.484188\pi\)
\(312\) 17.1546 0.971187
\(313\) −33.2343 −1.87851 −0.939257 0.343215i \(-0.888484\pi\)
−0.939257 + 0.343215i \(0.888484\pi\)
\(314\) 22.6189 1.27646
\(315\) −4.63685 −0.261257
\(316\) 20.0259 1.12654
\(317\) −4.62324 −0.259667 −0.129833 0.991536i \(-0.541444\pi\)
−0.129833 + 0.991536i \(0.541444\pi\)
\(318\) −2.66051 −0.149194
\(319\) −7.38476 −0.413467
\(320\) −11.2903 −0.631149
\(321\) −2.16667 −0.120932
\(322\) 3.47704 0.193768
\(323\) 34.5494 1.92238
\(324\) −2.72751 −0.151528
\(325\) −16.0873 −0.892365
\(326\) −56.2962 −3.11796
\(327\) −10.2397 −0.566257
\(328\) −4.04292 −0.223233
\(329\) 36.7586 2.02657
\(330\) −3.05302 −0.168063
\(331\) 12.7582 0.701255 0.350628 0.936515i \(-0.385968\pi\)
0.350628 + 0.936515i \(0.385968\pi\)
\(332\) 13.3222 0.731148
\(333\) −9.02984 −0.494832
\(334\) −24.5020 −1.34069
\(335\) 14.5205 0.793339
\(336\) −5.61704 −0.306435
\(337\) 14.2594 0.776758 0.388379 0.921500i \(-0.373035\pi\)
0.388379 + 0.921500i \(0.373035\pi\)
\(338\) −6.89820 −0.375212
\(339\) −17.8446 −0.969185
\(340\) −15.9729 −0.866252
\(341\) 10.6811 0.578414
\(342\) −31.7136 −1.71488
\(343\) −18.0334 −0.973710
\(344\) −13.6498 −0.735946
\(345\) 0.597518 0.0321693
\(346\) 23.8988 1.28481
\(347\) 29.2819 1.57193 0.785967 0.618268i \(-0.212165\pi\)
0.785967 + 0.618268i \(0.212165\pi\)
\(348\) −25.6910 −1.37718
\(349\) 7.25835 0.388530 0.194265 0.980949i \(-0.437768\pi\)
0.194265 + 0.980949i \(0.437768\pi\)
\(350\) 25.9073 1.38480
\(351\) 21.2242 1.13286
\(352\) −3.83602 −0.204461
\(353\) −7.49718 −0.399034 −0.199517 0.979894i \(-0.563937\pi\)
−0.199517 + 0.979894i \(0.563937\pi\)
\(354\) −5.63784 −0.299648
\(355\) −5.96748 −0.316721
\(356\) 26.5937 1.40946
\(357\) 13.6676 0.723364
\(358\) 1.54476 0.0816431
\(359\) 28.0726 1.48161 0.740807 0.671718i \(-0.234443\pi\)
0.740807 + 0.671718i \(0.234443\pi\)
\(360\) 6.55351 0.345400
\(361\) 40.1653 2.11396
\(362\) 19.1828 1.00823
\(363\) 10.8199 0.567898
\(364\) 39.1005 2.04942
\(365\) 4.37668 0.229086
\(366\) −3.42199 −0.178870
\(367\) −13.4701 −0.703133 −0.351567 0.936163i \(-0.614351\pi\)
−0.351567 + 0.936163i \(0.614351\pi\)
\(368\) −0.999194 −0.0520866
\(369\) −1.83600 −0.0955784
\(370\) −12.0955 −0.628814
\(371\) −2.71051 −0.140723
\(372\) 37.1587 1.92659
\(373\) 30.9636 1.60324 0.801618 0.597836i \(-0.203973\pi\)
0.801618 + 0.597836i \(0.203973\pi\)
\(374\) −12.4226 −0.642358
\(375\) 9.97151 0.514926
\(376\) −51.9528 −2.67926
\(377\) 25.2411 1.29998
\(378\) −34.1798 −1.75802
\(379\) 26.6297 1.36788 0.683938 0.729541i \(-0.260266\pi\)
0.683938 + 0.729541i \(0.260266\pi\)
\(380\) −27.3533 −1.40320
\(381\) 14.9212 0.764434
\(382\) −13.5904 −0.695346
\(383\) −22.4532 −1.14731 −0.573653 0.819098i \(-0.694474\pi\)
−0.573653 + 0.819098i \(0.694474\pi\)
\(384\) −23.1676 −1.18227
\(385\) −3.11040 −0.158521
\(386\) 35.5390 1.80889
\(387\) −6.19874 −0.315100
\(388\) −61.2255 −3.10825
\(389\) −28.9292 −1.46677 −0.733385 0.679813i \(-0.762061\pi\)
−0.733385 + 0.679813i \(0.762061\pi\)
\(390\) 10.4352 0.528407
\(391\) 2.43127 0.122955
\(392\) −1.32887 −0.0671180
\(393\) −11.4330 −0.576717
\(394\) 19.5342 0.984116
\(395\) 5.44499 0.273967
\(396\) 7.34244 0.368971
\(397\) 24.8995 1.24967 0.624836 0.780756i \(-0.285166\pi\)
0.624836 + 0.780756i \(0.285166\pi\)
\(398\) 36.9231 1.85079
\(399\) 23.4055 1.17174
\(400\) −7.44495 −0.372248
\(401\) 11.8978 0.594147 0.297073 0.954855i \(-0.403989\pi\)
0.297073 + 0.954855i \(0.403989\pi\)
\(402\) 39.2876 1.95949
\(403\) −36.5079 −1.81859
\(404\) −8.13323 −0.404643
\(405\) −0.741603 −0.0368505
\(406\) −40.6486 −2.01736
\(407\) −6.05723 −0.300246
\(408\) −19.3171 −0.956338
\(409\) −26.5680 −1.31370 −0.656852 0.754020i \(-0.728112\pi\)
−0.656852 + 0.754020i \(0.728112\pi\)
\(410\) −2.45933 −0.121457
\(411\) 15.4710 0.763127
\(412\) 1.85743 0.0915089
\(413\) −5.74380 −0.282634
\(414\) −2.23172 −0.109683
\(415\) 3.62226 0.177810
\(416\) 13.1115 0.642844
\(417\) 24.2023 1.18519
\(418\) −21.2735 −1.04052
\(419\) −33.8122 −1.65183 −0.825917 0.563792i \(-0.809342\pi\)
−0.825917 + 0.563792i \(0.809342\pi\)
\(420\) −10.8209 −0.528004
\(421\) 29.9688 1.46059 0.730295 0.683132i \(-0.239383\pi\)
0.730295 + 0.683132i \(0.239383\pi\)
\(422\) 6.92023 0.336871
\(423\) −23.5932 −1.14714
\(424\) 3.83091 0.186046
\(425\) 18.1153 0.878721
\(426\) −16.1460 −0.782276
\(427\) −3.48630 −0.168714
\(428\) 6.97985 0.337384
\(429\) 5.22579 0.252304
\(430\) −8.30321 −0.400417
\(431\) −7.42622 −0.357708 −0.178854 0.983876i \(-0.557239\pi\)
−0.178854 + 0.983876i \(0.557239\pi\)
\(432\) 9.82221 0.472571
\(433\) −18.0839 −0.869057 −0.434529 0.900658i \(-0.643085\pi\)
−0.434529 + 0.900658i \(0.643085\pi\)
\(434\) 58.7930 2.82215
\(435\) −6.98532 −0.334921
\(436\) 32.9869 1.57978
\(437\) 4.16351 0.199168
\(438\) 11.8418 0.565824
\(439\) 22.7821 1.08733 0.543666 0.839302i \(-0.317036\pi\)
0.543666 + 0.839302i \(0.317036\pi\)
\(440\) 4.39610 0.209576
\(441\) −0.603476 −0.0287370
\(442\) 42.4604 2.01963
\(443\) 21.6143 1.02693 0.513464 0.858111i \(-0.328362\pi\)
0.513464 + 0.858111i \(0.328362\pi\)
\(444\) −21.0726 −1.00006
\(445\) 7.23075 0.342770
\(446\) 6.20465 0.293799
\(447\) −10.5149 −0.497335
\(448\) −31.1220 −1.47038
\(449\) −27.2867 −1.28774 −0.643869 0.765135i \(-0.722672\pi\)
−0.643869 + 0.765135i \(0.722672\pi\)
\(450\) −16.6284 −0.783872
\(451\) −1.23159 −0.0579934
\(452\) 57.4857 2.70390
\(453\) 1.12262 0.0527453
\(454\) 58.0842 2.72603
\(455\) 10.6313 0.498405
\(456\) −33.0802 −1.54912
\(457\) −31.8099 −1.48801 −0.744003 0.668176i \(-0.767075\pi\)
−0.744003 + 0.668176i \(0.767075\pi\)
\(458\) 9.10138 0.425279
\(459\) −23.8997 −1.11554
\(460\) −1.92488 −0.0897480
\(461\) −18.3939 −0.856687 −0.428344 0.903616i \(-0.640903\pi\)
−0.428344 + 0.903616i \(0.640903\pi\)
\(462\) −8.41570 −0.391534
\(463\) −5.82135 −0.270541 −0.135270 0.990809i \(-0.543190\pi\)
−0.135270 + 0.990809i \(0.543190\pi\)
\(464\) 11.6811 0.542284
\(465\) 10.1034 0.468532
\(466\) −10.4184 −0.482622
\(467\) −7.64472 −0.353755 −0.176878 0.984233i \(-0.556600\pi\)
−0.176878 + 0.984233i \(0.556600\pi\)
\(468\) −25.0964 −1.16008
\(469\) 40.0260 1.84823
\(470\) −31.6031 −1.45774
\(471\) 10.7145 0.493699
\(472\) 8.11802 0.373662
\(473\) −4.15812 −0.191191
\(474\) 14.7323 0.676677
\(475\) 31.0222 1.42339
\(476\) −44.0295 −2.01809
\(477\) 1.73972 0.0796565
\(478\) 21.8417 0.999017
\(479\) −20.0354 −0.915439 −0.457719 0.889097i \(-0.651334\pi\)
−0.457719 + 0.889097i \(0.651334\pi\)
\(480\) −3.62853 −0.165619
\(481\) 20.7036 0.944001
\(482\) −23.6244 −1.07606
\(483\) 1.64707 0.0749441
\(484\) −34.8560 −1.58436
\(485\) −16.6471 −0.755904
\(486\) 35.8237 1.62500
\(487\) −0.629141 −0.0285091 −0.0142545 0.999898i \(-0.504538\pi\)
−0.0142545 + 0.999898i \(0.504538\pi\)
\(488\) 4.92738 0.223052
\(489\) −26.6673 −1.20594
\(490\) −0.808357 −0.0365178
\(491\) −6.37157 −0.287545 −0.143772 0.989611i \(-0.545923\pi\)
−0.143772 + 0.989611i \(0.545923\pi\)
\(492\) −4.28461 −0.193165
\(493\) −28.4229 −1.28010
\(494\) 72.7128 3.27150
\(495\) 1.99639 0.0897311
\(496\) −16.8953 −0.758620
\(497\) −16.4495 −0.737859
\(498\) 9.80062 0.439176
\(499\) 21.4500 0.960235 0.480118 0.877204i \(-0.340594\pi\)
0.480118 + 0.877204i \(0.340594\pi\)
\(500\) −32.1228 −1.43658
\(501\) −11.6065 −0.518541
\(502\) −17.0137 −0.759356
\(503\) 38.6546 1.72352 0.861761 0.507314i \(-0.169362\pi\)
0.861761 + 0.507314i \(0.169362\pi\)
\(504\) 18.0648 0.804672
\(505\) −2.21140 −0.0984062
\(506\) −1.49704 −0.0665515
\(507\) −3.26766 −0.145122
\(508\) −48.0679 −2.13267
\(509\) −18.7062 −0.829137 −0.414568 0.910018i \(-0.636067\pi\)
−0.414568 + 0.910018i \(0.636067\pi\)
\(510\) −11.7507 −0.520328
\(511\) 12.0644 0.533697
\(512\) 20.2112 0.893219
\(513\) −40.9279 −1.80701
\(514\) −37.0328 −1.63345
\(515\) 0.505030 0.0222543
\(516\) −14.4658 −0.636820
\(517\) −15.8264 −0.696043
\(518\) −33.3414 −1.46494
\(519\) 11.3208 0.496927
\(520\) −15.0258 −0.658926
\(521\) −0.398041 −0.0174385 −0.00871925 0.999962i \(-0.502775\pi\)
−0.00871925 + 0.999962i \(0.502775\pi\)
\(522\) 26.0900 1.14193
\(523\) 3.76150 0.164479 0.0822395 0.996613i \(-0.473793\pi\)
0.0822395 + 0.996613i \(0.473793\pi\)
\(524\) 36.8309 1.60896
\(525\) 12.2722 0.535604
\(526\) 11.3018 0.492781
\(527\) 41.1101 1.79078
\(528\) 2.41841 0.105248
\(529\) −22.7070 −0.987261
\(530\) 2.33036 0.101224
\(531\) 3.68662 0.159986
\(532\) −75.3999 −3.26900
\(533\) 4.20957 0.182337
\(534\) 19.5640 0.846616
\(535\) 1.89780 0.0820492
\(536\) −56.5708 −2.44349
\(537\) 0.731748 0.0315773
\(538\) −4.13985 −0.178482
\(539\) −0.404813 −0.0174365
\(540\) 18.9218 0.814266
\(541\) −25.9551 −1.11590 −0.557948 0.829876i \(-0.688411\pi\)
−0.557948 + 0.829876i \(0.688411\pi\)
\(542\) 50.6357 2.17499
\(543\) 9.08685 0.389954
\(544\) −14.7643 −0.633015
\(545\) 8.96904 0.384192
\(546\) 28.7648 1.23102
\(547\) −22.3179 −0.954245 −0.477123 0.878837i \(-0.658320\pi\)
−0.477123 + 0.878837i \(0.658320\pi\)
\(548\) −49.8392 −2.12902
\(549\) 2.23766 0.0955010
\(550\) −11.1544 −0.475624
\(551\) −48.6739 −2.07358
\(552\) −2.32789 −0.0990814
\(553\) 15.0092 0.638256
\(554\) 60.2648 2.56041
\(555\) −5.72959 −0.243208
\(556\) −77.9669 −3.30653
\(557\) 19.4876 0.825716 0.412858 0.910795i \(-0.364531\pi\)
0.412858 + 0.910795i \(0.364531\pi\)
\(558\) −37.7359 −1.59749
\(559\) 14.2124 0.601122
\(560\) 4.92001 0.207908
\(561\) −5.88455 −0.248446
\(562\) 59.6011 2.51412
\(563\) −9.60392 −0.404757 −0.202379 0.979307i \(-0.564867\pi\)
−0.202379 + 0.979307i \(0.564867\pi\)
\(564\) −55.0587 −2.31839
\(565\) 15.6302 0.657568
\(566\) 28.7638 1.20903
\(567\) −2.04424 −0.0858500
\(568\) 23.2489 0.975502
\(569\) −29.3422 −1.23009 −0.615045 0.788492i \(-0.710862\pi\)
−0.615045 + 0.788492i \(0.710862\pi\)
\(570\) −20.1228 −0.842853
\(571\) −40.7553 −1.70555 −0.852777 0.522274i \(-0.825084\pi\)
−0.852777 + 0.522274i \(0.825084\pi\)
\(572\) −16.8347 −0.703894
\(573\) −6.43774 −0.268940
\(574\) −6.77917 −0.282957
\(575\) 2.18306 0.0910399
\(576\) 19.9754 0.832310
\(577\) 4.25234 0.177027 0.0885135 0.996075i \(-0.471788\pi\)
0.0885135 + 0.996075i \(0.471788\pi\)
\(578\) −7.52442 −0.312974
\(579\) 16.8347 0.699628
\(580\) 22.5030 0.934384
\(581\) 9.98481 0.414240
\(582\) −45.0413 −1.86702
\(583\) 1.16701 0.0483326
\(584\) −17.0512 −0.705585
\(585\) −6.82365 −0.282123
\(586\) −28.2297 −1.16616
\(587\) 25.1946 1.03989 0.519947 0.854199i \(-0.325952\pi\)
0.519947 + 0.854199i \(0.325952\pi\)
\(588\) −1.40831 −0.0580778
\(589\) 70.4004 2.90080
\(590\) 4.93823 0.203304
\(591\) 9.25327 0.380629
\(592\) 9.58127 0.393788
\(593\) −35.7256 −1.46707 −0.733537 0.679649i \(-0.762132\pi\)
−0.733537 + 0.679649i \(0.762132\pi\)
\(594\) 14.7161 0.603808
\(595\) −11.9715 −0.490784
\(596\) 33.8732 1.38750
\(597\) 17.4904 0.715832
\(598\) 5.11686 0.209244
\(599\) −4.26301 −0.174182 −0.0870909 0.996200i \(-0.527757\pi\)
−0.0870909 + 0.996200i \(0.527757\pi\)
\(600\) −17.3450 −0.708106
\(601\) −32.8171 −1.33864 −0.669319 0.742975i \(-0.733414\pi\)
−0.669319 + 0.742975i \(0.733414\pi\)
\(602\) −22.8879 −0.932843
\(603\) −25.6904 −1.04619
\(604\) −3.61648 −0.147152
\(605\) −9.47725 −0.385305
\(606\) −5.98332 −0.243056
\(607\) −9.88402 −0.401180 −0.200590 0.979675i \(-0.564286\pi\)
−0.200590 + 0.979675i \(0.564286\pi\)
\(608\) −25.2837 −1.02539
\(609\) −19.2551 −0.780258
\(610\) 2.99735 0.121359
\(611\) 54.0944 2.18843
\(612\) 28.2600 1.14234
\(613\) −12.8058 −0.517220 −0.258610 0.965982i \(-0.583264\pi\)
−0.258610 + 0.965982i \(0.583264\pi\)
\(614\) −5.70326 −0.230165
\(615\) −1.16498 −0.0469763
\(616\) 12.1179 0.488245
\(617\) 20.7771 0.836454 0.418227 0.908343i \(-0.362652\pi\)
0.418227 + 0.908343i \(0.362652\pi\)
\(618\) 1.36644 0.0549663
\(619\) 2.15920 0.0867857 0.0433929 0.999058i \(-0.486183\pi\)
0.0433929 + 0.999058i \(0.486183\pi\)
\(620\) −32.5476 −1.30714
\(621\) −2.88013 −0.115576
\(622\) −4.15056 −0.166422
\(623\) 19.9317 0.798545
\(624\) −8.26611 −0.330909
\(625\) 11.4314 0.457255
\(626\) 78.7624 3.14798
\(627\) −10.0772 −0.402445
\(628\) −34.5164 −1.37735
\(629\) −23.3134 −0.929568
\(630\) 10.9889 0.437809
\(631\) −16.7489 −0.666761 −0.333381 0.942792i \(-0.608189\pi\)
−0.333381 + 0.942792i \(0.608189\pi\)
\(632\) −21.2133 −0.843819
\(633\) 3.27809 0.130292
\(634\) 10.9567 0.435145
\(635\) −13.0696 −0.518649
\(636\) 4.05993 0.160987
\(637\) 1.38365 0.0548221
\(638\) 17.5012 0.692880
\(639\) 10.5580 0.417667
\(640\) 20.2927 0.802140
\(641\) −17.3573 −0.685571 −0.342785 0.939414i \(-0.611370\pi\)
−0.342785 + 0.939414i \(0.611370\pi\)
\(642\) 5.13482 0.202655
\(643\) −1.78770 −0.0705002 −0.0352501 0.999379i \(-0.511223\pi\)
−0.0352501 + 0.999379i \(0.511223\pi\)
\(644\) −5.30596 −0.209084
\(645\) −3.93321 −0.154870
\(646\) −81.8789 −3.22148
\(647\) −22.2521 −0.874821 −0.437411 0.899262i \(-0.644104\pi\)
−0.437411 + 0.899262i \(0.644104\pi\)
\(648\) 2.88923 0.113500
\(649\) 2.47299 0.0970732
\(650\) 38.1255 1.49541
\(651\) 27.8501 1.09153
\(652\) 85.9078 3.36441
\(653\) 19.4641 0.761688 0.380844 0.924639i \(-0.375633\pi\)
0.380844 + 0.924639i \(0.375633\pi\)
\(654\) 24.2672 0.948923
\(655\) 10.0142 0.391288
\(656\) 1.94812 0.0760613
\(657\) −7.74344 −0.302100
\(658\) −87.1145 −3.39608
\(659\) 6.04659 0.235542 0.117771 0.993041i \(-0.462425\pi\)
0.117771 + 0.993041i \(0.462425\pi\)
\(660\) 4.65891 0.181348
\(661\) 37.9723 1.47695 0.738475 0.674281i \(-0.235546\pi\)
0.738475 + 0.674281i \(0.235546\pi\)
\(662\) −30.2359 −1.17515
\(663\) 20.1134 0.781138
\(664\) −14.1121 −0.547655
\(665\) −20.5010 −0.794996
\(666\) 21.3999 0.829230
\(667\) −3.42523 −0.132625
\(668\) 37.3900 1.44666
\(669\) 2.93912 0.113633
\(670\) −34.4123 −1.32946
\(671\) 1.50102 0.0579464
\(672\) −10.0021 −0.385839
\(673\) −13.0726 −0.503912 −0.251956 0.967739i \(-0.581074\pi\)
−0.251956 + 0.967739i \(0.581074\pi\)
\(674\) −33.7935 −1.30168
\(675\) −21.4598 −0.825986
\(676\) 10.5266 0.404871
\(677\) 5.91181 0.227209 0.113605 0.993526i \(-0.463760\pi\)
0.113605 + 0.993526i \(0.463760\pi\)
\(678\) 42.2901 1.62414
\(679\) −45.8879 −1.76101
\(680\) 16.9200 0.648852
\(681\) 27.5143 1.05435
\(682\) −25.3133 −0.969295
\(683\) −29.7175 −1.13711 −0.568554 0.822646i \(-0.692497\pi\)
−0.568554 + 0.822646i \(0.692497\pi\)
\(684\) 48.3949 1.85043
\(685\) −13.5511 −0.517762
\(686\) 42.7375 1.63172
\(687\) 4.31130 0.164486
\(688\) 6.57728 0.250756
\(689\) −3.98883 −0.151962
\(690\) −1.41606 −0.0539086
\(691\) −17.1289 −0.651614 −0.325807 0.945436i \(-0.605636\pi\)
−0.325807 + 0.945436i \(0.605636\pi\)
\(692\) −36.4695 −1.38636
\(693\) 5.50308 0.209045
\(694\) −69.3955 −2.63422
\(695\) −21.1990 −0.804124
\(696\) 27.2143 1.03156
\(697\) −4.74023 −0.179549
\(698\) −17.2016 −0.651091
\(699\) −4.93515 −0.186665
\(700\) −39.5345 −1.49426
\(701\) −21.9772 −0.830066 −0.415033 0.909806i \(-0.636230\pi\)
−0.415033 + 0.909806i \(0.636230\pi\)
\(702\) −50.2994 −1.89843
\(703\) −39.9239 −1.50576
\(704\) 13.3995 0.505014
\(705\) −14.9703 −0.563815
\(706\) 17.7676 0.668694
\(707\) −6.09577 −0.229255
\(708\) 8.60333 0.323333
\(709\) 21.8867 0.821971 0.410985 0.911642i \(-0.365185\pi\)
0.410985 + 0.911642i \(0.365185\pi\)
\(710\) 14.1424 0.530755
\(711\) −9.63354 −0.361286
\(712\) −28.1705 −1.05573
\(713\) 4.95414 0.185534
\(714\) −32.3909 −1.21220
\(715\) −4.57731 −0.171182
\(716\) −2.35730 −0.0880964
\(717\) 10.3464 0.386392
\(718\) −66.5295 −2.48286
\(719\) −42.2807 −1.57681 −0.788403 0.615159i \(-0.789092\pi\)
−0.788403 + 0.615159i \(0.789092\pi\)
\(720\) −3.15787 −0.117687
\(721\) 1.39212 0.0518453
\(722\) −95.1881 −3.54253
\(723\) −11.1908 −0.416191
\(724\) −29.2729 −1.08792
\(725\) −25.5212 −0.947834
\(726\) −25.6422 −0.951673
\(727\) −21.4427 −0.795264 −0.397632 0.917545i \(-0.630168\pi\)
−0.397632 + 0.917545i \(0.630168\pi\)
\(728\) −41.4189 −1.53509
\(729\) 19.2322 0.712302
\(730\) −10.3723 −0.383898
\(731\) −16.0040 −0.591931
\(732\) 5.22195 0.193009
\(733\) −26.8627 −0.992196 −0.496098 0.868267i \(-0.665234\pi\)
−0.496098 + 0.868267i \(0.665234\pi\)
\(734\) 31.9229 1.17830
\(735\) −0.382916 −0.0141241
\(736\) −1.77924 −0.0655835
\(737\) −17.2331 −0.634791
\(738\) 4.35116 0.160168
\(739\) 1.75000 0.0643748 0.0321874 0.999482i \(-0.489753\pi\)
0.0321874 + 0.999482i \(0.489753\pi\)
\(740\) 18.4577 0.678517
\(741\) 34.4438 1.26533
\(742\) 6.42368 0.235821
\(743\) 3.76118 0.137984 0.0689921 0.997617i \(-0.478022\pi\)
0.0689921 + 0.997617i \(0.478022\pi\)
\(744\) −39.3620 −1.44308
\(745\) 9.21004 0.337430
\(746\) −73.3811 −2.68667
\(747\) −6.40868 −0.234481
\(748\) 18.9569 0.693132
\(749\) 5.23133 0.191148
\(750\) −23.6316 −0.862903
\(751\) 34.3160 1.25221 0.626105 0.779739i \(-0.284648\pi\)
0.626105 + 0.779739i \(0.284648\pi\)
\(752\) 25.0340 0.912896
\(753\) −8.05932 −0.293698
\(754\) −59.8191 −2.17848
\(755\) −0.983312 −0.0357864
\(756\) 52.1583 1.89698
\(757\) −24.5496 −0.892271 −0.446135 0.894966i \(-0.647200\pi\)
−0.446135 + 0.894966i \(0.647200\pi\)
\(758\) −63.1100 −2.29226
\(759\) −0.709143 −0.0257402
\(760\) 28.9752 1.05104
\(761\) 23.0877 0.836927 0.418464 0.908234i \(-0.362569\pi\)
0.418464 + 0.908234i \(0.362569\pi\)
\(762\) −35.3618 −1.28102
\(763\) 24.7233 0.895043
\(764\) 20.7389 0.750308
\(765\) 7.68383 0.277810
\(766\) 53.2122 1.92263
\(767\) −8.45265 −0.305208
\(768\) 29.1255 1.05098
\(769\) −48.4011 −1.74539 −0.872693 0.488269i \(-0.837629\pi\)
−0.872693 + 0.488269i \(0.837629\pi\)
\(770\) 7.37138 0.265646
\(771\) −17.5423 −0.631772
\(772\) −54.2325 −1.95187
\(773\) −1.22525 −0.0440690 −0.0220345 0.999757i \(-0.507014\pi\)
−0.0220345 + 0.999757i \(0.507014\pi\)
\(774\) 14.6905 0.528038
\(775\) 36.9131 1.32596
\(776\) 64.8558 2.32819
\(777\) −15.7937 −0.566596
\(778\) 68.5597 2.45798
\(779\) −8.11757 −0.290842
\(780\) −15.9241 −0.570175
\(781\) 7.08230 0.253424
\(782\) −5.76189 −0.206045
\(783\) 33.6704 1.20328
\(784\) 0.640329 0.0228689
\(785\) −9.38493 −0.334962
\(786\) 27.0951 0.966450
\(787\) −7.61598 −0.271480 −0.135740 0.990744i \(-0.543341\pi\)
−0.135740 + 0.990744i \(0.543341\pi\)
\(788\) −29.8091 −1.06190
\(789\) 5.35362 0.190594
\(790\) −12.9041 −0.459109
\(791\) 43.0849 1.53192
\(792\) −7.77780 −0.276372
\(793\) −5.13049 −0.182189
\(794\) −59.0097 −2.09418
\(795\) 1.10389 0.0391508
\(796\) −56.3445 −1.99708
\(797\) 12.5111 0.443168 0.221584 0.975141i \(-0.428877\pi\)
0.221584 + 0.975141i \(0.428877\pi\)
\(798\) −55.4689 −1.96358
\(799\) −60.9135 −2.15497
\(800\) −13.2570 −0.468706
\(801\) −12.7930 −0.452019
\(802\) −28.1967 −0.995659
\(803\) −5.19431 −0.183303
\(804\) −59.9527 −2.11437
\(805\) −1.44268 −0.0508477
\(806\) 86.5205 3.04756
\(807\) −1.96103 −0.0690317
\(808\) 8.61547 0.303091
\(809\) −9.90149 −0.348118 −0.174059 0.984735i \(-0.555688\pi\)
−0.174059 + 0.984735i \(0.555688\pi\)
\(810\) 1.75753 0.0617534
\(811\) 21.3543 0.749852 0.374926 0.927055i \(-0.377668\pi\)
0.374926 + 0.927055i \(0.377668\pi\)
\(812\) 62.0297 2.17682
\(813\) 23.9860 0.841225
\(814\) 14.3551 0.503146
\(815\) 23.3581 0.818199
\(816\) 9.30813 0.325850
\(817\) −27.4067 −0.958838
\(818\) 62.9638 2.20148
\(819\) −18.8095 −0.657257
\(820\) 3.75293 0.131058
\(821\) −7.50177 −0.261814 −0.130907 0.991395i \(-0.541789\pi\)
−0.130907 + 0.991395i \(0.541789\pi\)
\(822\) −36.6648 −1.27883
\(823\) 7.58769 0.264490 0.132245 0.991217i \(-0.457781\pi\)
0.132245 + 0.991217i \(0.457781\pi\)
\(824\) −1.96756 −0.0685432
\(825\) −5.28379 −0.183958
\(826\) 13.6123 0.473632
\(827\) 5.16163 0.179487 0.0897437 0.995965i \(-0.471395\pi\)
0.0897437 + 0.995965i \(0.471395\pi\)
\(828\) 3.40559 0.118353
\(829\) −40.0913 −1.39243 −0.696214 0.717834i \(-0.745133\pi\)
−0.696214 + 0.717834i \(0.745133\pi\)
\(830\) −8.58444 −0.297970
\(831\) 28.5473 0.990293
\(832\) −45.7995 −1.58781
\(833\) −1.55807 −0.0539839
\(834\) −57.3574 −1.98612
\(835\) 10.1662 0.351817
\(836\) 32.4634 1.12277
\(837\) −48.6999 −1.68331
\(838\) 80.1319 2.76811
\(839\) −7.91738 −0.273338 −0.136669 0.990617i \(-0.543640\pi\)
−0.136669 + 0.990617i \(0.543640\pi\)
\(840\) 11.4625 0.395492
\(841\) 11.0428 0.380788
\(842\) −71.0234 −2.44763
\(843\) 28.2329 0.972391
\(844\) −10.5603 −0.363499
\(845\) 2.86217 0.0984615
\(846\) 55.9139 1.92236
\(847\) −26.1242 −0.897637
\(848\) −1.84596 −0.0633906
\(849\) 13.6253 0.467619
\(850\) −42.9316 −1.47254
\(851\) −2.80948 −0.0963078
\(852\) 24.6388 0.844110
\(853\) −42.3846 −1.45122 −0.725610 0.688106i \(-0.758442\pi\)
−0.725610 + 0.688106i \(0.758442\pi\)
\(854\) 8.26223 0.282728
\(855\) 13.1585 0.450010
\(856\) −7.39371 −0.252712
\(857\) 45.8746 1.56705 0.783523 0.621363i \(-0.213421\pi\)
0.783523 + 0.621363i \(0.213421\pi\)
\(858\) −12.3847 −0.422805
\(859\) 15.1368 0.516459 0.258230 0.966084i \(-0.416861\pi\)
0.258230 + 0.966084i \(0.416861\pi\)
\(860\) 12.6707 0.432067
\(861\) −3.21127 −0.109440
\(862\) 17.5995 0.599441
\(863\) 7.19201 0.244819 0.122409 0.992480i \(-0.460938\pi\)
0.122409 + 0.992480i \(0.460938\pi\)
\(864\) 17.4901 0.595026
\(865\) −9.91596 −0.337153
\(866\) 42.8573 1.45635
\(867\) −3.56429 −0.121050
\(868\) −89.7179 −3.04523
\(869\) −6.46219 −0.219215
\(870\) 16.5546 0.561253
\(871\) 58.9027 1.99584
\(872\) −34.9428 −1.18331
\(873\) 29.4528 0.996827
\(874\) −9.86716 −0.333762
\(875\) −24.0757 −0.813908
\(876\) −18.0706 −0.610549
\(877\) 46.3350 1.56462 0.782310 0.622889i \(-0.214041\pi\)
0.782310 + 0.622889i \(0.214041\pi\)
\(878\) −53.9916 −1.82213
\(879\) −13.3723 −0.451038
\(880\) −2.11830 −0.0714080
\(881\) 33.9098 1.14245 0.571226 0.820793i \(-0.306468\pi\)
0.571226 + 0.820793i \(0.306468\pi\)
\(882\) 1.43019 0.0481568
\(883\) −10.1550 −0.341744 −0.170872 0.985293i \(-0.554658\pi\)
−0.170872 + 0.985293i \(0.554658\pi\)
\(884\) −64.7944 −2.17927
\(885\) 2.33922 0.0786321
\(886\) −51.2241 −1.72091
\(887\) −51.0245 −1.71323 −0.856617 0.515952i \(-0.827438\pi\)
−0.856617 + 0.515952i \(0.827438\pi\)
\(888\) 22.3221 0.749080
\(889\) −36.0264 −1.20829
\(890\) −17.1362 −0.574408
\(891\) 0.880145 0.0294860
\(892\) −9.46828 −0.317022
\(893\) −104.313 −3.49072
\(894\) 24.9193 0.833425
\(895\) −0.640944 −0.0214244
\(896\) 55.9371 1.86873
\(897\) 2.42384 0.0809298
\(898\) 64.6670 2.15797
\(899\) −57.9168 −1.93163
\(900\) 25.3749 0.845832
\(901\) 4.49166 0.149639
\(902\) 2.91876 0.0971842
\(903\) −10.8419 −0.360797
\(904\) −60.8942 −2.02531
\(905\) −7.95924 −0.264574
\(906\) −2.66051 −0.0883895
\(907\) 3.85912 0.128140 0.0640700 0.997945i \(-0.479592\pi\)
0.0640700 + 0.997945i \(0.479592\pi\)
\(908\) −88.6363 −2.94150
\(909\) 3.91253 0.129770
\(910\) −25.1953 −0.835217
\(911\) −28.0357 −0.928864 −0.464432 0.885609i \(-0.653742\pi\)
−0.464432 + 0.885609i \(0.653742\pi\)
\(912\) 15.9400 0.527827
\(913\) −4.29895 −0.142275
\(914\) 75.3867 2.49357
\(915\) 1.41983 0.0469383
\(916\) −13.8887 −0.458895
\(917\) 27.6043 0.911576
\(918\) 56.6402 1.86940
\(919\) −50.1373 −1.65388 −0.826938 0.562293i \(-0.809919\pi\)
−0.826938 + 0.562293i \(0.809919\pi\)
\(920\) 2.03901 0.0672243
\(921\) −2.70162 −0.0890213
\(922\) 43.5918 1.43562
\(923\) −24.2072 −0.796791
\(924\) 12.8423 0.422482
\(925\) −20.9333 −0.688284
\(926\) 13.7961 0.453367
\(927\) −0.893524 −0.0293472
\(928\) 20.8003 0.682803
\(929\) −8.05560 −0.264296 −0.132148 0.991230i \(-0.542187\pi\)
−0.132148 + 0.991230i \(0.542187\pi\)
\(930\) −23.9441 −0.785157
\(931\) −2.66817 −0.0874457
\(932\) 15.8984 0.520770
\(933\) −1.96611 −0.0643675
\(934\) 18.1173 0.592816
\(935\) 5.15432 0.168564
\(936\) 26.5845 0.868940
\(937\) 32.2970 1.05510 0.527548 0.849525i \(-0.323111\pi\)
0.527548 + 0.849525i \(0.323111\pi\)
\(938\) −94.8580 −3.09722
\(939\) 37.3095 1.21755
\(940\) 48.2263 1.57297
\(941\) 4.04283 0.131793 0.0658963 0.997826i \(-0.479009\pi\)
0.0658963 + 0.997826i \(0.479009\pi\)
\(942\) −25.3924 −0.827331
\(943\) −0.571241 −0.0186022
\(944\) −3.91175 −0.127317
\(945\) 14.1817 0.461331
\(946\) 9.85438 0.320393
\(947\) −24.8884 −0.808764 −0.404382 0.914590i \(-0.632513\pi\)
−0.404382 + 0.914590i \(0.632513\pi\)
\(948\) −22.4815 −0.730164
\(949\) 17.7541 0.576323
\(950\) −73.5198 −2.38530
\(951\) 5.19014 0.168302
\(952\) 46.6402 1.51162
\(953\) −20.1417 −0.652452 −0.326226 0.945292i \(-0.605777\pi\)
−0.326226 + 0.945292i \(0.605777\pi\)
\(954\) −4.12299 −0.133487
\(955\) 5.63886 0.182469
\(956\) −33.3304 −1.07798
\(957\) 8.29028 0.267987
\(958\) 47.4820 1.53407
\(959\) −37.3539 −1.20622
\(960\) 12.6748 0.409076
\(961\) 52.7691 1.70223
\(962\) −49.0656 −1.58194
\(963\) −3.35769 −0.108200
\(964\) 36.0508 1.16112
\(965\) −14.7457 −0.474680
\(966\) −3.90340 −0.125590
\(967\) 21.5490 0.692970 0.346485 0.938056i \(-0.387375\pi\)
0.346485 + 0.938056i \(0.387375\pi\)
\(968\) 36.9227 1.18674
\(969\) −38.7858 −1.24598
\(970\) 39.4521 1.26673
\(971\) −14.5288 −0.466252 −0.233126 0.972447i \(-0.574895\pi\)
−0.233126 + 0.972447i \(0.574895\pi\)
\(972\) −54.6669 −1.75344
\(973\) −58.4354 −1.87335
\(974\) 1.49101 0.0477750
\(975\) 18.0600 0.578382
\(976\) −2.37431 −0.0759997
\(977\) −54.7312 −1.75101 −0.875503 0.483212i \(-0.839470\pi\)
−0.875503 + 0.483212i \(0.839470\pi\)
\(978\) 63.1992 2.02089
\(979\) −8.58156 −0.274268
\(980\) 1.23355 0.0394043
\(981\) −15.8685 −0.506641
\(982\) 15.1000 0.481862
\(983\) 3.50474 0.111784 0.0558919 0.998437i \(-0.482200\pi\)
0.0558919 + 0.998437i \(0.482200\pi\)
\(984\) 4.53866 0.144687
\(985\) −8.10501 −0.258247
\(986\) 67.3598 2.14517
\(987\) −41.2659 −1.31351
\(988\) −110.960 −3.53009
\(989\) −1.92863 −0.0613270
\(990\) −4.73127 −0.150370
\(991\) −18.1278 −0.575847 −0.287924 0.957653i \(-0.592965\pi\)
−0.287924 + 0.957653i \(0.592965\pi\)
\(992\) −30.0849 −0.955197
\(993\) −14.3226 −0.454515
\(994\) 38.9837 1.23649
\(995\) −15.3199 −0.485674
\(996\) −14.9557 −0.473890
\(997\) 23.1100 0.731901 0.365951 0.930634i \(-0.380744\pi\)
0.365951 + 0.930634i \(0.380744\pi\)
\(998\) −50.8347 −1.60914
\(999\) 27.6176 0.873782
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.1.16 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.16 153 1.1 even 1 trivial