Properties

Label 8007.2.a.f.1.43
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.43
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.37316 q^{2} -1.00000 q^{3} +3.63190 q^{4} -3.39062 q^{5} -2.37316 q^{6} -2.72468 q^{7} +3.87278 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.37316 q^{2} -1.00000 q^{3} +3.63190 q^{4} -3.39062 q^{5} -2.37316 q^{6} -2.72468 q^{7} +3.87278 q^{8} +1.00000 q^{9} -8.04650 q^{10} +0.191904 q^{11} -3.63190 q^{12} +3.63167 q^{13} -6.46611 q^{14} +3.39062 q^{15} +1.92692 q^{16} -1.00000 q^{17} +2.37316 q^{18} +6.06019 q^{19} -12.3144 q^{20} +2.72468 q^{21} +0.455420 q^{22} +7.64992 q^{23} -3.87278 q^{24} +6.49632 q^{25} +8.61855 q^{26} -1.00000 q^{27} -9.89578 q^{28} -5.48562 q^{29} +8.04650 q^{30} -6.85276 q^{31} -3.17265 q^{32} -0.191904 q^{33} -2.37316 q^{34} +9.23837 q^{35} +3.63190 q^{36} +2.95555 q^{37} +14.3818 q^{38} -3.63167 q^{39} -13.1311 q^{40} +5.70226 q^{41} +6.46611 q^{42} -1.32018 q^{43} +0.696977 q^{44} -3.39062 q^{45} +18.1545 q^{46} +2.64382 q^{47} -1.92692 q^{48} +0.423888 q^{49} +15.4168 q^{50} +1.00000 q^{51} +13.1899 q^{52} -5.38691 q^{53} -2.37316 q^{54} -0.650674 q^{55} -10.5521 q^{56} -6.06019 q^{57} -13.0183 q^{58} -7.04781 q^{59} +12.3144 q^{60} -1.28646 q^{61} -16.2627 q^{62} -2.72468 q^{63} -11.3831 q^{64} -12.3136 q^{65} -0.455420 q^{66} -8.81575 q^{67} -3.63190 q^{68} -7.64992 q^{69} +21.9242 q^{70} -6.29632 q^{71} +3.87278 q^{72} -7.91126 q^{73} +7.01400 q^{74} -6.49632 q^{75} +22.0100 q^{76} -0.522877 q^{77} -8.61855 q^{78} -5.71367 q^{79} -6.53347 q^{80} +1.00000 q^{81} +13.5324 q^{82} -0.273284 q^{83} +9.89578 q^{84} +3.39062 q^{85} -3.13301 q^{86} +5.48562 q^{87} +0.743201 q^{88} +8.77053 q^{89} -8.04650 q^{90} -9.89515 q^{91} +27.7838 q^{92} +6.85276 q^{93} +6.27421 q^{94} -20.5478 q^{95} +3.17265 q^{96} +3.56633 q^{97} +1.00595 q^{98} +0.191904 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.37316 1.67808 0.839040 0.544070i \(-0.183117\pi\)
0.839040 + 0.544070i \(0.183117\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.63190 1.81595
\(5\) −3.39062 −1.51633 −0.758166 0.652061i \(-0.773904\pi\)
−0.758166 + 0.652061i \(0.773904\pi\)
\(6\) −2.37316 −0.968840
\(7\) −2.72468 −1.02983 −0.514916 0.857240i \(-0.672177\pi\)
−0.514916 + 0.857240i \(0.672177\pi\)
\(8\) 3.87278 1.36923
\(9\) 1.00000 0.333333
\(10\) −8.04650 −2.54453
\(11\) 0.191904 0.0578612 0.0289306 0.999581i \(-0.490790\pi\)
0.0289306 + 0.999581i \(0.490790\pi\)
\(12\) −3.63190 −1.04844
\(13\) 3.63167 1.00724 0.503622 0.863924i \(-0.332000\pi\)
0.503622 + 0.863924i \(0.332000\pi\)
\(14\) −6.46611 −1.72814
\(15\) 3.39062 0.875455
\(16\) 1.92692 0.481731
\(17\) −1.00000 −0.242536
\(18\) 2.37316 0.559360
\(19\) 6.06019 1.39030 0.695152 0.718863i \(-0.255337\pi\)
0.695152 + 0.718863i \(0.255337\pi\)
\(20\) −12.3144 −2.75359
\(21\) 2.72468 0.594574
\(22\) 0.455420 0.0970958
\(23\) 7.64992 1.59512 0.797559 0.603241i \(-0.206124\pi\)
0.797559 + 0.603241i \(0.206124\pi\)
\(24\) −3.87278 −0.790527
\(25\) 6.49632 1.29926
\(26\) 8.61855 1.69024
\(27\) −1.00000 −0.192450
\(28\) −9.89578 −1.87013
\(29\) −5.48562 −1.01865 −0.509327 0.860573i \(-0.670106\pi\)
−0.509327 + 0.860573i \(0.670106\pi\)
\(30\) 8.04650 1.46908
\(31\) −6.85276 −1.23079 −0.615396 0.788218i \(-0.711004\pi\)
−0.615396 + 0.788218i \(0.711004\pi\)
\(32\) −3.17265 −0.560851
\(33\) −0.191904 −0.0334062
\(34\) −2.37316 −0.406994
\(35\) 9.23837 1.56157
\(36\) 3.63190 0.605317
\(37\) 2.95555 0.485889 0.242945 0.970040i \(-0.421887\pi\)
0.242945 + 0.970040i \(0.421887\pi\)
\(38\) 14.3818 2.33304
\(39\) −3.63167 −0.581533
\(40\) −13.1311 −2.07621
\(41\) 5.70226 0.890544 0.445272 0.895395i \(-0.353107\pi\)
0.445272 + 0.895395i \(0.353107\pi\)
\(42\) 6.46611 0.997743
\(43\) −1.32018 −0.201326 −0.100663 0.994921i \(-0.532096\pi\)
−0.100663 + 0.994921i \(0.532096\pi\)
\(44\) 0.696977 0.105073
\(45\) −3.39062 −0.505444
\(46\) 18.1545 2.67674
\(47\) 2.64382 0.385640 0.192820 0.981234i \(-0.438237\pi\)
0.192820 + 0.981234i \(0.438237\pi\)
\(48\) −1.92692 −0.278127
\(49\) 0.423888 0.0605554
\(50\) 15.4168 2.18027
\(51\) 1.00000 0.140028
\(52\) 13.1899 1.82911
\(53\) −5.38691 −0.739949 −0.369975 0.929042i \(-0.620634\pi\)
−0.369975 + 0.929042i \(0.620634\pi\)
\(54\) −2.37316 −0.322947
\(55\) −0.650674 −0.0877369
\(56\) −10.5521 −1.41008
\(57\) −6.06019 −0.802692
\(58\) −13.0183 −1.70938
\(59\) −7.04781 −0.917547 −0.458773 0.888553i \(-0.651711\pi\)
−0.458773 + 0.888553i \(0.651711\pi\)
\(60\) 12.3144 1.58978
\(61\) −1.28646 −0.164715 −0.0823573 0.996603i \(-0.526245\pi\)
−0.0823573 + 0.996603i \(0.526245\pi\)
\(62\) −16.2627 −2.06537
\(63\) −2.72468 −0.343278
\(64\) −11.3831 −1.42288
\(65\) −12.3136 −1.52732
\(66\) −0.455420 −0.0560583
\(67\) −8.81575 −1.07702 −0.538508 0.842621i \(-0.681012\pi\)
−0.538508 + 0.842621i \(0.681012\pi\)
\(68\) −3.63190 −0.440433
\(69\) −7.64992 −0.920942
\(70\) 21.9242 2.62044
\(71\) −6.29632 −0.747235 −0.373618 0.927583i \(-0.621883\pi\)
−0.373618 + 0.927583i \(0.621883\pi\)
\(72\) 3.87278 0.456411
\(73\) −7.91126 −0.925943 −0.462971 0.886373i \(-0.653217\pi\)
−0.462971 + 0.886373i \(0.653217\pi\)
\(74\) 7.01400 0.815361
\(75\) −6.49632 −0.750131
\(76\) 22.0100 2.52472
\(77\) −0.522877 −0.0595874
\(78\) −8.61855 −0.975859
\(79\) −5.71367 −0.642838 −0.321419 0.946937i \(-0.604160\pi\)
−0.321419 + 0.946937i \(0.604160\pi\)
\(80\) −6.53347 −0.730464
\(81\) 1.00000 0.111111
\(82\) 13.5324 1.49440
\(83\) −0.273284 −0.0299968 −0.0149984 0.999888i \(-0.504774\pi\)
−0.0149984 + 0.999888i \(0.504774\pi\)
\(84\) 9.89578 1.07972
\(85\) 3.39062 0.367765
\(86\) −3.13301 −0.337841
\(87\) 5.48562 0.588121
\(88\) 0.743201 0.0792255
\(89\) 8.77053 0.929674 0.464837 0.885396i \(-0.346113\pi\)
0.464837 + 0.885396i \(0.346113\pi\)
\(90\) −8.04650 −0.848176
\(91\) −9.89515 −1.03729
\(92\) 27.7838 2.89666
\(93\) 6.85276 0.710599
\(94\) 6.27421 0.647135
\(95\) −20.5478 −2.10816
\(96\) 3.17265 0.323807
\(97\) 3.56633 0.362106 0.181053 0.983473i \(-0.442049\pi\)
0.181053 + 0.983473i \(0.442049\pi\)
\(98\) 1.00595 0.101617
\(99\) 0.191904 0.0192871
\(100\) 23.5940 2.35940
\(101\) 0.332282 0.0330633 0.0165317 0.999863i \(-0.494738\pi\)
0.0165317 + 0.999863i \(0.494738\pi\)
\(102\) 2.37316 0.234978
\(103\) 7.78283 0.766865 0.383433 0.923569i \(-0.374742\pi\)
0.383433 + 0.923569i \(0.374742\pi\)
\(104\) 14.0647 1.37915
\(105\) −9.23837 −0.901572
\(106\) −12.7840 −1.24169
\(107\) 8.27010 0.799501 0.399750 0.916624i \(-0.369097\pi\)
0.399750 + 0.916624i \(0.369097\pi\)
\(108\) −3.63190 −0.349480
\(109\) −16.7955 −1.60872 −0.804361 0.594142i \(-0.797492\pi\)
−0.804361 + 0.594142i \(0.797492\pi\)
\(110\) −1.54416 −0.147229
\(111\) −2.95555 −0.280528
\(112\) −5.25025 −0.496102
\(113\) −12.1634 −1.14423 −0.572117 0.820172i \(-0.693878\pi\)
−0.572117 + 0.820172i \(0.693878\pi\)
\(114\) −14.3818 −1.34698
\(115\) −25.9380 −2.41873
\(116\) −19.9233 −1.84983
\(117\) 3.63167 0.335748
\(118\) −16.7256 −1.53972
\(119\) 2.72468 0.249771
\(120\) 13.1311 1.19870
\(121\) −10.9632 −0.996652
\(122\) −3.05298 −0.276404
\(123\) −5.70226 −0.514156
\(124\) −24.8886 −2.23506
\(125\) −5.07346 −0.453784
\(126\) −6.46611 −0.576047
\(127\) −5.12275 −0.454571 −0.227285 0.973828i \(-0.572985\pi\)
−0.227285 + 0.973828i \(0.572985\pi\)
\(128\) −20.6686 −1.82686
\(129\) 1.32018 0.116236
\(130\) −29.2223 −2.56296
\(131\) −8.14562 −0.711686 −0.355843 0.934546i \(-0.615806\pi\)
−0.355843 + 0.934546i \(0.615806\pi\)
\(132\) −0.696977 −0.0606641
\(133\) −16.5121 −1.43178
\(134\) −20.9212 −1.80732
\(135\) 3.39062 0.291818
\(136\) −3.87278 −0.332088
\(137\) −1.37856 −0.117778 −0.0588892 0.998265i \(-0.518756\pi\)
−0.0588892 + 0.998265i \(0.518756\pi\)
\(138\) −18.1545 −1.54541
\(139\) −10.5415 −0.894118 −0.447059 0.894504i \(-0.647529\pi\)
−0.447059 + 0.894504i \(0.647529\pi\)
\(140\) 33.5529 2.83573
\(141\) −2.64382 −0.222649
\(142\) −14.9422 −1.25392
\(143\) 0.696933 0.0582804
\(144\) 1.92692 0.160577
\(145\) 18.5997 1.54462
\(146\) −18.7747 −1.55381
\(147\) −0.423888 −0.0349617
\(148\) 10.7343 0.882352
\(149\) −4.28942 −0.351403 −0.175701 0.984444i \(-0.556219\pi\)
−0.175701 + 0.984444i \(0.556219\pi\)
\(150\) −15.4168 −1.25878
\(151\) −2.93543 −0.238882 −0.119441 0.992841i \(-0.538110\pi\)
−0.119441 + 0.992841i \(0.538110\pi\)
\(152\) 23.4698 1.90365
\(153\) −1.00000 −0.0808452
\(154\) −1.24087 −0.0999924
\(155\) 23.2351 1.86629
\(156\) −13.1899 −1.05604
\(157\) −1.00000 −0.0798087
\(158\) −13.5595 −1.07873
\(159\) 5.38691 0.427210
\(160\) 10.7573 0.850436
\(161\) −20.8436 −1.64271
\(162\) 2.37316 0.186453
\(163\) −3.34783 −0.262222 −0.131111 0.991368i \(-0.541854\pi\)
−0.131111 + 0.991368i \(0.541854\pi\)
\(164\) 20.7101 1.61718
\(165\) 0.650674 0.0506549
\(166\) −0.648547 −0.0503370
\(167\) 0.761191 0.0589027 0.0294514 0.999566i \(-0.490624\pi\)
0.0294514 + 0.999566i \(0.490624\pi\)
\(168\) 10.5521 0.814111
\(169\) 0.189051 0.0145424
\(170\) 8.04650 0.617139
\(171\) 6.06019 0.463434
\(172\) −4.79478 −0.365598
\(173\) 14.2672 1.08471 0.542357 0.840148i \(-0.317532\pi\)
0.542357 + 0.840148i \(0.317532\pi\)
\(174\) 13.0183 0.986913
\(175\) −17.7004 −1.33803
\(176\) 0.369784 0.0278735
\(177\) 7.04781 0.529746
\(178\) 20.8139 1.56007
\(179\) 9.48174 0.708698 0.354349 0.935113i \(-0.384702\pi\)
0.354349 + 0.935113i \(0.384702\pi\)
\(180\) −12.3144 −0.917863
\(181\) −10.5384 −0.783312 −0.391656 0.920112i \(-0.628098\pi\)
−0.391656 + 0.920112i \(0.628098\pi\)
\(182\) −23.4828 −1.74066
\(183\) 1.28646 0.0950980
\(184\) 29.6264 2.18409
\(185\) −10.0212 −0.736770
\(186\) 16.2627 1.19244
\(187\) −0.191904 −0.0140334
\(188\) 9.60209 0.700304
\(189\) 2.72468 0.198191
\(190\) −48.7633 −3.53766
\(191\) −14.1219 −1.02183 −0.510914 0.859632i \(-0.670693\pi\)
−0.510914 + 0.859632i \(0.670693\pi\)
\(192\) 11.3831 0.821502
\(193\) −19.2420 −1.38507 −0.692534 0.721385i \(-0.743506\pi\)
−0.692534 + 0.721385i \(0.743506\pi\)
\(194\) 8.46349 0.607643
\(195\) 12.3136 0.881798
\(196\) 1.53952 0.109966
\(197\) 23.4939 1.67387 0.836934 0.547303i \(-0.184346\pi\)
0.836934 + 0.547303i \(0.184346\pi\)
\(198\) 0.455420 0.0323653
\(199\) −12.3584 −0.876062 −0.438031 0.898960i \(-0.644324\pi\)
−0.438031 + 0.898960i \(0.644324\pi\)
\(200\) 25.1588 1.77900
\(201\) 8.81575 0.621815
\(202\) 0.788560 0.0554829
\(203\) 14.9466 1.04904
\(204\) 3.63190 0.254284
\(205\) −19.3342 −1.35036
\(206\) 18.4699 1.28686
\(207\) 7.64992 0.531706
\(208\) 6.99796 0.485221
\(209\) 1.16298 0.0804447
\(210\) −21.9242 −1.51291
\(211\) −14.4101 −0.992033 −0.496017 0.868313i \(-0.665205\pi\)
−0.496017 + 0.868313i \(0.665205\pi\)
\(212\) −19.5648 −1.34371
\(213\) 6.29632 0.431417
\(214\) 19.6263 1.34163
\(215\) 4.47624 0.305277
\(216\) −3.87278 −0.263509
\(217\) 18.6716 1.26751
\(218\) −39.8586 −2.69956
\(219\) 7.91126 0.534593
\(220\) −2.36319 −0.159326
\(221\) −3.63167 −0.244293
\(222\) −7.01400 −0.470749
\(223\) 19.8049 1.32623 0.663116 0.748517i \(-0.269234\pi\)
0.663116 + 0.748517i \(0.269234\pi\)
\(224\) 8.64446 0.577582
\(225\) 6.49632 0.433088
\(226\) −28.8657 −1.92012
\(227\) −18.6053 −1.23487 −0.617437 0.786620i \(-0.711829\pi\)
−0.617437 + 0.786620i \(0.711829\pi\)
\(228\) −22.0100 −1.45765
\(229\) 22.3431 1.47647 0.738236 0.674543i \(-0.235659\pi\)
0.738236 + 0.674543i \(0.235659\pi\)
\(230\) −61.5551 −4.05882
\(231\) 0.522877 0.0344028
\(232\) −21.2446 −1.39478
\(233\) 5.62788 0.368695 0.184347 0.982861i \(-0.440983\pi\)
0.184347 + 0.982861i \(0.440983\pi\)
\(234\) 8.61855 0.563413
\(235\) −8.96418 −0.584759
\(236\) −25.5970 −1.66622
\(237\) 5.71367 0.371143
\(238\) 6.46611 0.419136
\(239\) 5.73694 0.371092 0.185546 0.982636i \(-0.440595\pi\)
0.185546 + 0.982636i \(0.440595\pi\)
\(240\) 6.53347 0.421734
\(241\) −13.9510 −0.898664 −0.449332 0.893365i \(-0.648338\pi\)
−0.449332 + 0.893365i \(0.648338\pi\)
\(242\) −26.0174 −1.67246
\(243\) −1.00000 −0.0641500
\(244\) −4.67231 −0.299114
\(245\) −1.43724 −0.0918221
\(246\) −13.5324 −0.862794
\(247\) 22.0086 1.40038
\(248\) −26.5392 −1.68524
\(249\) 0.273284 0.0173187
\(250\) −12.0402 −0.761487
\(251\) 25.4006 1.60327 0.801636 0.597813i \(-0.203963\pi\)
0.801636 + 0.597813i \(0.203963\pi\)
\(252\) −9.89578 −0.623376
\(253\) 1.46805 0.0922955
\(254\) −12.1571 −0.762806
\(255\) −3.39062 −0.212329
\(256\) −26.2838 −1.64274
\(257\) −28.5674 −1.78198 −0.890991 0.454021i \(-0.849989\pi\)
−0.890991 + 0.454021i \(0.849989\pi\)
\(258\) 3.13301 0.195053
\(259\) −8.05293 −0.500385
\(260\) −44.7219 −2.77354
\(261\) −5.48562 −0.339552
\(262\) −19.3309 −1.19427
\(263\) −5.67725 −0.350074 −0.175037 0.984562i \(-0.556005\pi\)
−0.175037 + 0.984562i \(0.556005\pi\)
\(264\) −0.743201 −0.0457409
\(265\) 18.2650 1.12201
\(266\) −39.1859 −2.40264
\(267\) −8.77053 −0.536748
\(268\) −32.0180 −1.95581
\(269\) 17.9223 1.09274 0.546369 0.837544i \(-0.316009\pi\)
0.546369 + 0.837544i \(0.316009\pi\)
\(270\) 8.04650 0.489695
\(271\) −21.3728 −1.29831 −0.649154 0.760657i \(-0.724877\pi\)
−0.649154 + 0.760657i \(0.724877\pi\)
\(272\) −1.92692 −0.116837
\(273\) 9.89515 0.598882
\(274\) −3.27155 −0.197641
\(275\) 1.24667 0.0751770
\(276\) −27.7838 −1.67239
\(277\) 21.9877 1.32111 0.660555 0.750778i \(-0.270321\pi\)
0.660555 + 0.750778i \(0.270321\pi\)
\(278\) −25.0167 −1.50040
\(279\) −6.85276 −0.410264
\(280\) 35.7781 2.13815
\(281\) −6.01868 −0.359044 −0.179522 0.983754i \(-0.557455\pi\)
−0.179522 + 0.983754i \(0.557455\pi\)
\(282\) −6.27421 −0.373624
\(283\) −25.6402 −1.52415 −0.762076 0.647488i \(-0.775820\pi\)
−0.762076 + 0.647488i \(0.775820\pi\)
\(284\) −22.8676 −1.35694
\(285\) 20.5478 1.21715
\(286\) 1.65394 0.0977992
\(287\) −15.5368 −0.917111
\(288\) −3.17265 −0.186950
\(289\) 1.00000 0.0588235
\(290\) 44.1401 2.59199
\(291\) −3.56633 −0.209062
\(292\) −28.7329 −1.68147
\(293\) −15.7560 −0.920474 −0.460237 0.887796i \(-0.652236\pi\)
−0.460237 + 0.887796i \(0.652236\pi\)
\(294\) −1.00595 −0.0586684
\(295\) 23.8965 1.39131
\(296\) 11.4462 0.665296
\(297\) −0.191904 −0.0111354
\(298\) −10.1795 −0.589682
\(299\) 27.7820 1.60667
\(300\) −23.5940 −1.36220
\(301\) 3.59708 0.207332
\(302\) −6.96625 −0.400863
\(303\) −0.332282 −0.0190891
\(304\) 11.6775 0.669752
\(305\) 4.36191 0.249762
\(306\) −2.37316 −0.135665
\(307\) 15.5196 0.885748 0.442874 0.896584i \(-0.353959\pi\)
0.442874 + 0.896584i \(0.353959\pi\)
\(308\) −1.89904 −0.108208
\(309\) −7.78283 −0.442750
\(310\) 55.1408 3.13179
\(311\) 1.09937 0.0623396 0.0311698 0.999514i \(-0.490077\pi\)
0.0311698 + 0.999514i \(0.490077\pi\)
\(312\) −14.0647 −0.796255
\(313\) 19.2900 1.09034 0.545168 0.838327i \(-0.316466\pi\)
0.545168 + 0.838327i \(0.316466\pi\)
\(314\) −2.37316 −0.133925
\(315\) 9.23837 0.520523
\(316\) −20.7515 −1.16736
\(317\) −14.9672 −0.840642 −0.420321 0.907376i \(-0.638082\pi\)
−0.420321 + 0.907376i \(0.638082\pi\)
\(318\) 12.7840 0.716892
\(319\) −1.05271 −0.0589406
\(320\) 38.5957 2.15756
\(321\) −8.27010 −0.461592
\(322\) −49.4652 −2.75659
\(323\) −6.06019 −0.337198
\(324\) 3.63190 0.201772
\(325\) 23.5925 1.30868
\(326\) −7.94494 −0.440030
\(327\) 16.7955 0.928796
\(328\) 22.0836 1.21936
\(329\) −7.20355 −0.397145
\(330\) 1.54416 0.0850030
\(331\) −7.89985 −0.434215 −0.217108 0.976148i \(-0.569662\pi\)
−0.217108 + 0.976148i \(0.569662\pi\)
\(332\) −0.992540 −0.0544727
\(333\) 2.95555 0.161963
\(334\) 1.80643 0.0988435
\(335\) 29.8909 1.63311
\(336\) 5.25025 0.286425
\(337\) 16.1420 0.879308 0.439654 0.898167i \(-0.355101\pi\)
0.439654 + 0.898167i \(0.355101\pi\)
\(338\) 0.448649 0.0244033
\(339\) 12.1634 0.660624
\(340\) 12.3144 0.667843
\(341\) −1.31507 −0.0712152
\(342\) 14.3818 0.777680
\(343\) 17.9178 0.967471
\(344\) −5.11277 −0.275662
\(345\) 25.9380 1.39645
\(346\) 33.8584 1.82024
\(347\) −30.2270 −1.62267 −0.811335 0.584581i \(-0.801259\pi\)
−0.811335 + 0.584581i \(0.801259\pi\)
\(348\) 19.9233 1.06800
\(349\) −16.4799 −0.882147 −0.441073 0.897471i \(-0.645402\pi\)
−0.441073 + 0.897471i \(0.645402\pi\)
\(350\) −42.0060 −2.24531
\(351\) −3.63167 −0.193844
\(352\) −0.608844 −0.0324515
\(353\) −4.56441 −0.242939 −0.121470 0.992595i \(-0.538761\pi\)
−0.121470 + 0.992595i \(0.538761\pi\)
\(354\) 16.7256 0.888956
\(355\) 21.3484 1.13306
\(356\) 31.8537 1.68824
\(357\) −2.72468 −0.144205
\(358\) 22.5017 1.18925
\(359\) −3.05799 −0.161395 −0.0806974 0.996739i \(-0.525715\pi\)
−0.0806974 + 0.996739i \(0.525715\pi\)
\(360\) −13.1311 −0.692071
\(361\) 17.7259 0.932943
\(362\) −25.0093 −1.31446
\(363\) 10.9632 0.575417
\(364\) −35.9383 −1.88368
\(365\) 26.8241 1.40404
\(366\) 3.05298 0.159582
\(367\) 2.71249 0.141591 0.0707953 0.997491i \(-0.477446\pi\)
0.0707953 + 0.997491i \(0.477446\pi\)
\(368\) 14.7408 0.768418
\(369\) 5.70226 0.296848
\(370\) −23.7818 −1.23636
\(371\) 14.6776 0.762024
\(372\) 24.8886 1.29041
\(373\) −5.55810 −0.287787 −0.143894 0.989593i \(-0.545962\pi\)
−0.143894 + 0.989593i \(0.545962\pi\)
\(374\) −0.455420 −0.0235492
\(375\) 5.07346 0.261993
\(376\) 10.2389 0.528031
\(377\) −19.9220 −1.02603
\(378\) 6.46611 0.332581
\(379\) −2.69896 −0.138636 −0.0693181 0.997595i \(-0.522082\pi\)
−0.0693181 + 0.997595i \(0.522082\pi\)
\(380\) −74.6277 −3.82832
\(381\) 5.12275 0.262447
\(382\) −33.5137 −1.71471
\(383\) −3.35029 −0.171192 −0.0855958 0.996330i \(-0.527279\pi\)
−0.0855958 + 0.996330i \(0.527279\pi\)
\(384\) 20.6686 1.05474
\(385\) 1.77288 0.0903543
\(386\) −45.6644 −2.32426
\(387\) −1.32018 −0.0671087
\(388\) 12.9526 0.657568
\(389\) −5.22188 −0.264760 −0.132380 0.991199i \(-0.542262\pi\)
−0.132380 + 0.991199i \(0.542262\pi\)
\(390\) 29.2223 1.47973
\(391\) −7.64992 −0.386873
\(392\) 1.64162 0.0829144
\(393\) 8.14562 0.410892
\(394\) 55.7548 2.80889
\(395\) 19.3729 0.974756
\(396\) 0.696977 0.0350244
\(397\) −26.9283 −1.35149 −0.675746 0.737134i \(-0.736178\pi\)
−0.675746 + 0.737134i \(0.736178\pi\)
\(398\) −29.3285 −1.47010
\(399\) 16.5121 0.826638
\(400\) 12.5179 0.625896
\(401\) −3.13136 −0.156373 −0.0781864 0.996939i \(-0.524913\pi\)
−0.0781864 + 0.996939i \(0.524913\pi\)
\(402\) 20.9212 1.04346
\(403\) −24.8870 −1.23971
\(404\) 1.20682 0.0600414
\(405\) −3.39062 −0.168481
\(406\) 35.4707 1.76038
\(407\) 0.567182 0.0281142
\(408\) 3.87278 0.191731
\(409\) 25.0095 1.23664 0.618321 0.785926i \(-0.287813\pi\)
0.618321 + 0.785926i \(0.287813\pi\)
\(410\) −45.8833 −2.26601
\(411\) 1.37856 0.0679994
\(412\) 28.2665 1.39259
\(413\) 19.2030 0.944920
\(414\) 18.1545 0.892245
\(415\) 0.926602 0.0454851
\(416\) −11.5220 −0.564914
\(417\) 10.5415 0.516219
\(418\) 2.75993 0.134993
\(419\) −18.6931 −0.913215 −0.456608 0.889668i \(-0.650936\pi\)
−0.456608 + 0.889668i \(0.650936\pi\)
\(420\) −33.5529 −1.63721
\(421\) 13.5966 0.662657 0.331328 0.943516i \(-0.392503\pi\)
0.331328 + 0.943516i \(0.392503\pi\)
\(422\) −34.1976 −1.66471
\(423\) 2.64382 0.128547
\(424\) −20.8623 −1.01316
\(425\) −6.49632 −0.315118
\(426\) 14.9422 0.723952
\(427\) 3.50520 0.169628
\(428\) 30.0362 1.45186
\(429\) −0.696933 −0.0336482
\(430\) 10.6229 0.512280
\(431\) 0.429543 0.0206904 0.0103452 0.999946i \(-0.496707\pi\)
0.0103452 + 0.999946i \(0.496707\pi\)
\(432\) −1.92692 −0.0927092
\(433\) −40.7644 −1.95901 −0.979506 0.201417i \(-0.935445\pi\)
−0.979506 + 0.201417i \(0.935445\pi\)
\(434\) 44.3108 2.12698
\(435\) −18.5997 −0.891786
\(436\) −60.9998 −2.92136
\(437\) 46.3600 2.21770
\(438\) 18.7747 0.897090
\(439\) −12.4056 −0.592085 −0.296043 0.955175i \(-0.595667\pi\)
−0.296043 + 0.955175i \(0.595667\pi\)
\(440\) −2.51992 −0.120132
\(441\) 0.423888 0.0201851
\(442\) −8.61855 −0.409943
\(443\) −13.1699 −0.625722 −0.312861 0.949799i \(-0.601287\pi\)
−0.312861 + 0.949799i \(0.601287\pi\)
\(444\) −10.7343 −0.509426
\(445\) −29.7376 −1.40970
\(446\) 47.0002 2.22552
\(447\) 4.28942 0.202883
\(448\) 31.0152 1.46533
\(449\) 18.5882 0.877231 0.438615 0.898675i \(-0.355469\pi\)
0.438615 + 0.898675i \(0.355469\pi\)
\(450\) 15.4168 0.726757
\(451\) 1.09429 0.0515279
\(452\) −44.1762 −2.07788
\(453\) 2.93543 0.137918
\(454\) −44.1533 −2.07222
\(455\) 33.5507 1.57288
\(456\) −23.4698 −1.09907
\(457\) −2.93771 −0.137420 −0.0687102 0.997637i \(-0.521888\pi\)
−0.0687102 + 0.997637i \(0.521888\pi\)
\(458\) 53.0238 2.47764
\(459\) 1.00000 0.0466760
\(460\) −94.2043 −4.39230
\(461\) 32.0428 1.49238 0.746190 0.665733i \(-0.231881\pi\)
0.746190 + 0.665733i \(0.231881\pi\)
\(462\) 1.24087 0.0577306
\(463\) −26.9135 −1.25078 −0.625388 0.780314i \(-0.715059\pi\)
−0.625388 + 0.780314i \(0.715059\pi\)
\(464\) −10.5704 −0.490717
\(465\) −23.2351 −1.07750
\(466\) 13.3559 0.618700
\(467\) 42.7441 1.97796 0.988981 0.148039i \(-0.0472962\pi\)
0.988981 + 0.148039i \(0.0472962\pi\)
\(468\) 13.1899 0.609703
\(469\) 24.0201 1.10915
\(470\) −21.2735 −0.981272
\(471\) 1.00000 0.0460776
\(472\) −27.2946 −1.25634
\(473\) −0.253348 −0.0116490
\(474\) 13.5595 0.622807
\(475\) 39.3690 1.80637
\(476\) 9.89578 0.453572
\(477\) −5.38691 −0.246650
\(478\) 13.6147 0.622722
\(479\) 23.5351 1.07535 0.537673 0.843153i \(-0.319303\pi\)
0.537673 + 0.843153i \(0.319303\pi\)
\(480\) −10.7573 −0.490999
\(481\) 10.7336 0.489410
\(482\) −33.1080 −1.50803
\(483\) 20.8436 0.948416
\(484\) −39.8172 −1.80987
\(485\) −12.0921 −0.549073
\(486\) −2.37316 −0.107649
\(487\) 12.3847 0.561204 0.280602 0.959824i \(-0.409466\pi\)
0.280602 + 0.959824i \(0.409466\pi\)
\(488\) −4.98218 −0.225533
\(489\) 3.34783 0.151394
\(490\) −3.41081 −0.154085
\(491\) 26.6924 1.20461 0.602306 0.798266i \(-0.294249\pi\)
0.602306 + 0.798266i \(0.294249\pi\)
\(492\) −20.7101 −0.933682
\(493\) 5.48562 0.247060
\(494\) 52.2301 2.34994
\(495\) −0.650674 −0.0292456
\(496\) −13.2048 −0.592911
\(497\) 17.1555 0.769527
\(498\) 0.648547 0.0290621
\(499\) −42.6461 −1.90910 −0.954551 0.298048i \(-0.903664\pi\)
−0.954551 + 0.298048i \(0.903664\pi\)
\(500\) −18.4263 −0.824051
\(501\) −0.761191 −0.0340075
\(502\) 60.2798 2.69042
\(503\) 28.7603 1.28236 0.641178 0.767392i \(-0.278446\pi\)
0.641178 + 0.767392i \(0.278446\pi\)
\(504\) −10.5521 −0.470027
\(505\) −1.12664 −0.0501350
\(506\) 3.48392 0.154879
\(507\) −0.189051 −0.00839604
\(508\) −18.6053 −0.825479
\(509\) 29.6347 1.31353 0.656767 0.754094i \(-0.271924\pi\)
0.656767 + 0.754094i \(0.271924\pi\)
\(510\) −8.04650 −0.356305
\(511\) 21.5557 0.953566
\(512\) −21.0385 −0.929781
\(513\) −6.06019 −0.267564
\(514\) −67.7950 −2.99031
\(515\) −26.3886 −1.16282
\(516\) 4.79478 0.211078
\(517\) 0.507359 0.0223136
\(518\) −19.1109 −0.839686
\(519\) −14.2672 −0.626260
\(520\) −47.6880 −2.09126
\(521\) −31.3579 −1.37382 −0.686908 0.726745i \(-0.741032\pi\)
−0.686908 + 0.726745i \(0.741032\pi\)
\(522\) −13.0183 −0.569795
\(523\) 1.96648 0.0859881 0.0429941 0.999075i \(-0.486310\pi\)
0.0429941 + 0.999075i \(0.486310\pi\)
\(524\) −29.5841 −1.29239
\(525\) 17.7004 0.772509
\(526\) −13.4730 −0.587453
\(527\) 6.85276 0.298511
\(528\) −0.369784 −0.0160928
\(529\) 35.5213 1.54440
\(530\) 43.3458 1.88282
\(531\) −7.04781 −0.305849
\(532\) −59.9703 −2.60004
\(533\) 20.7087 0.896995
\(534\) −20.8139 −0.900705
\(535\) −28.0408 −1.21231
\(536\) −34.1414 −1.47469
\(537\) −9.48174 −0.409167
\(538\) 42.5324 1.83370
\(539\) 0.0813457 0.00350381
\(540\) 12.3144 0.529928
\(541\) 40.3332 1.73406 0.867029 0.498258i \(-0.166027\pi\)
0.867029 + 0.498258i \(0.166027\pi\)
\(542\) −50.7212 −2.17866
\(543\) 10.5384 0.452245
\(544\) 3.17265 0.136026
\(545\) 56.9473 2.43936
\(546\) 23.4828 1.00497
\(547\) 10.0861 0.431249 0.215624 0.976476i \(-0.430821\pi\)
0.215624 + 0.976476i \(0.430821\pi\)
\(548\) −5.00680 −0.213880
\(549\) −1.28646 −0.0549048
\(550\) 2.95855 0.126153
\(551\) −33.2439 −1.41624
\(552\) −29.6264 −1.26098
\(553\) 15.5679 0.662015
\(554\) 52.1803 2.21693
\(555\) 10.0212 0.425374
\(556\) −38.2857 −1.62368
\(557\) −42.4211 −1.79744 −0.898720 0.438524i \(-0.855502\pi\)
−0.898720 + 0.438524i \(0.855502\pi\)
\(558\) −16.2627 −0.688456
\(559\) −4.79447 −0.202785
\(560\) 17.8016 0.752256
\(561\) 0.191904 0.00810219
\(562\) −14.2833 −0.602505
\(563\) 2.14959 0.0905945 0.0452972 0.998974i \(-0.485577\pi\)
0.0452972 + 0.998974i \(0.485577\pi\)
\(564\) −9.60209 −0.404321
\(565\) 41.2414 1.73504
\(566\) −60.8484 −2.55765
\(567\) −2.72468 −0.114426
\(568\) −24.3842 −1.02314
\(569\) 14.5936 0.611796 0.305898 0.952064i \(-0.401043\pi\)
0.305898 + 0.952064i \(0.401043\pi\)
\(570\) 48.7633 2.04247
\(571\) −12.6971 −0.531358 −0.265679 0.964062i \(-0.585596\pi\)
−0.265679 + 0.964062i \(0.585596\pi\)
\(572\) 2.53119 0.105835
\(573\) 14.1219 0.589953
\(574\) −36.8715 −1.53899
\(575\) 49.6963 2.07248
\(576\) −11.3831 −0.474294
\(577\) −43.6114 −1.81557 −0.907784 0.419439i \(-0.862227\pi\)
−0.907784 + 0.419439i \(0.862227\pi\)
\(578\) 2.37316 0.0987106
\(579\) 19.2420 0.799670
\(580\) 67.5523 2.80496
\(581\) 0.744611 0.0308917
\(582\) −8.46349 −0.350823
\(583\) −1.03377 −0.0428144
\(584\) −30.6385 −1.26783
\(585\) −12.3136 −0.509106
\(586\) −37.3915 −1.54463
\(587\) 33.8700 1.39797 0.698983 0.715138i \(-0.253636\pi\)
0.698983 + 0.715138i \(0.253636\pi\)
\(588\) −1.53952 −0.0634887
\(589\) −41.5291 −1.71118
\(590\) 56.7102 2.33472
\(591\) −23.4939 −0.966409
\(592\) 5.69512 0.234068
\(593\) −32.0023 −1.31418 −0.657088 0.753814i \(-0.728212\pi\)
−0.657088 + 0.753814i \(0.728212\pi\)
\(594\) −0.455420 −0.0186861
\(595\) −9.23837 −0.378736
\(596\) −15.5788 −0.638131
\(597\) 12.3584 0.505795
\(598\) 65.9312 2.69613
\(599\) 6.87403 0.280865 0.140433 0.990090i \(-0.455151\pi\)
0.140433 + 0.990090i \(0.455151\pi\)
\(600\) −25.1588 −1.02710
\(601\) 30.4331 1.24139 0.620696 0.784051i \(-0.286850\pi\)
0.620696 + 0.784051i \(0.286850\pi\)
\(602\) 8.53645 0.347920
\(603\) −8.81575 −0.359005
\(604\) −10.6612 −0.433798
\(605\) 37.1720 1.51126
\(606\) −0.788560 −0.0320330
\(607\) −1.57393 −0.0638838 −0.0319419 0.999490i \(-0.510169\pi\)
−0.0319419 + 0.999490i \(0.510169\pi\)
\(608\) −19.2269 −0.779752
\(609\) −14.9466 −0.605666
\(610\) 10.3515 0.419121
\(611\) 9.60147 0.388434
\(612\) −3.63190 −0.146811
\(613\) −25.6767 −1.03707 −0.518536 0.855056i \(-0.673523\pi\)
−0.518536 + 0.855056i \(0.673523\pi\)
\(614\) 36.8305 1.48636
\(615\) 19.3342 0.779631
\(616\) −2.02499 −0.0815891
\(617\) 14.7843 0.595194 0.297597 0.954692i \(-0.403815\pi\)
0.297597 + 0.954692i \(0.403815\pi\)
\(618\) −18.4699 −0.742969
\(619\) −8.67475 −0.348668 −0.174334 0.984687i \(-0.555777\pi\)
−0.174334 + 0.984687i \(0.555777\pi\)
\(620\) 84.3878 3.38910
\(621\) −7.64992 −0.306981
\(622\) 2.60898 0.104611
\(623\) −23.8969 −0.957409
\(624\) −6.99796 −0.280142
\(625\) −15.2794 −0.611176
\(626\) 45.7783 1.82967
\(627\) −1.16298 −0.0464447
\(628\) −3.63190 −0.144929
\(629\) −2.95555 −0.117846
\(630\) 21.9242 0.873479
\(631\) −0.279777 −0.0111377 −0.00556887 0.999984i \(-0.501773\pi\)
−0.00556887 + 0.999984i \(0.501773\pi\)
\(632\) −22.1278 −0.880195
\(633\) 14.4101 0.572751
\(634\) −35.5196 −1.41066
\(635\) 17.3693 0.689280
\(636\) 19.5648 0.775793
\(637\) 1.53942 0.0609941
\(638\) −2.49826 −0.0989071
\(639\) −6.29632 −0.249078
\(640\) 70.0793 2.77013
\(641\) −47.1913 −1.86395 −0.931973 0.362529i \(-0.881913\pi\)
−0.931973 + 0.362529i \(0.881913\pi\)
\(642\) −19.6263 −0.774588
\(643\) 24.2565 0.956581 0.478291 0.878202i \(-0.341257\pi\)
0.478291 + 0.878202i \(0.341257\pi\)
\(644\) −75.7019 −2.98307
\(645\) −4.47624 −0.176252
\(646\) −14.3818 −0.565845
\(647\) 12.2686 0.482330 0.241165 0.970484i \(-0.422471\pi\)
0.241165 + 0.970484i \(0.422471\pi\)
\(648\) 3.87278 0.152137
\(649\) −1.35250 −0.0530904
\(650\) 55.9889 2.19607
\(651\) −18.6716 −0.731798
\(652\) −12.1590 −0.476183
\(653\) −4.55672 −0.178318 −0.0891591 0.996017i \(-0.528418\pi\)
−0.0891591 + 0.996017i \(0.528418\pi\)
\(654\) 39.8586 1.55859
\(655\) 27.6187 1.07915
\(656\) 10.9878 0.429002
\(657\) −7.91126 −0.308648
\(658\) −17.0952 −0.666441
\(659\) 11.8468 0.461485 0.230743 0.973015i \(-0.425884\pi\)
0.230743 + 0.973015i \(0.425884\pi\)
\(660\) 2.36319 0.0919869
\(661\) −8.54857 −0.332501 −0.166251 0.986084i \(-0.553166\pi\)
−0.166251 + 0.986084i \(0.553166\pi\)
\(662\) −18.7476 −0.728648
\(663\) 3.63167 0.141043
\(664\) −1.05837 −0.0410726
\(665\) 55.9863 2.17105
\(666\) 7.01400 0.271787
\(667\) −41.9646 −1.62487
\(668\) 2.76457 0.106965
\(669\) −19.8049 −0.765701
\(670\) 70.9360 2.74050
\(671\) −0.246877 −0.00953058
\(672\) −8.64446 −0.333467
\(673\) −22.0835 −0.851255 −0.425628 0.904898i \(-0.639947\pi\)
−0.425628 + 0.904898i \(0.639947\pi\)
\(674\) 38.3075 1.47555
\(675\) −6.49632 −0.250044
\(676\) 0.686615 0.0264083
\(677\) 4.49547 0.172775 0.0863874 0.996262i \(-0.472468\pi\)
0.0863874 + 0.996262i \(0.472468\pi\)
\(678\) 28.8657 1.10858
\(679\) −9.71712 −0.372909
\(680\) 13.1311 0.503556
\(681\) 18.6053 0.712955
\(682\) −3.12088 −0.119505
\(683\) 20.7049 0.792251 0.396125 0.918196i \(-0.370355\pi\)
0.396125 + 0.918196i \(0.370355\pi\)
\(684\) 22.0100 0.841575
\(685\) 4.67418 0.178591
\(686\) 42.5219 1.62349
\(687\) −22.3431 −0.852441
\(688\) −2.54389 −0.0969850
\(689\) −19.5635 −0.745310
\(690\) 61.5551 2.34336
\(691\) 21.2809 0.809563 0.404781 0.914413i \(-0.367348\pi\)
0.404781 + 0.914413i \(0.367348\pi\)
\(692\) 51.8170 1.96979
\(693\) −0.522877 −0.0198625
\(694\) −71.7336 −2.72297
\(695\) 35.7422 1.35578
\(696\) 21.2446 0.805274
\(697\) −5.70226 −0.215989
\(698\) −39.1094 −1.48031
\(699\) −5.62788 −0.212866
\(700\) −64.2862 −2.42979
\(701\) −30.1948 −1.14044 −0.570220 0.821492i \(-0.693142\pi\)
−0.570220 + 0.821492i \(0.693142\pi\)
\(702\) −8.61855 −0.325286
\(703\) 17.9112 0.675534
\(704\) −2.18446 −0.0823298
\(705\) 8.96418 0.337611
\(706\) −10.8321 −0.407671
\(707\) −0.905363 −0.0340497
\(708\) 25.5970 0.961993
\(709\) 21.2486 0.798006 0.399003 0.916950i \(-0.369356\pi\)
0.399003 + 0.916950i \(0.369356\pi\)
\(710\) 50.6633 1.90136
\(711\) −5.71367 −0.214279
\(712\) 33.9663 1.27294
\(713\) −52.4231 −1.96326
\(714\) −6.46611 −0.241988
\(715\) −2.36304 −0.0883725
\(716\) 34.4368 1.28696
\(717\) −5.73694 −0.214250
\(718\) −7.25712 −0.270833
\(719\) 39.6830 1.47993 0.739964 0.672647i \(-0.234843\pi\)
0.739964 + 0.672647i \(0.234843\pi\)
\(720\) −6.53347 −0.243488
\(721\) −21.2057 −0.789743
\(722\) 42.0665 1.56555
\(723\) 13.9510 0.518844
\(724\) −38.2744 −1.42246
\(725\) −35.6364 −1.32350
\(726\) 26.0174 0.965596
\(727\) −13.7912 −0.511486 −0.255743 0.966745i \(-0.582320\pi\)
−0.255743 + 0.966745i \(0.582320\pi\)
\(728\) −38.3217 −1.42030
\(729\) 1.00000 0.0370370
\(730\) 63.6580 2.35609
\(731\) 1.32018 0.0488287
\(732\) 4.67231 0.172693
\(733\) 15.2325 0.562624 0.281312 0.959616i \(-0.409230\pi\)
0.281312 + 0.959616i \(0.409230\pi\)
\(734\) 6.43717 0.237600
\(735\) 1.43724 0.0530135
\(736\) −24.2705 −0.894623
\(737\) −1.69178 −0.0623174
\(738\) 13.5324 0.498134
\(739\) −5.74760 −0.211429 −0.105714 0.994397i \(-0.533713\pi\)
−0.105714 + 0.994397i \(0.533713\pi\)
\(740\) −36.3959 −1.33794
\(741\) −22.0086 −0.808507
\(742\) 34.8324 1.27874
\(743\) 35.4555 1.30074 0.650369 0.759619i \(-0.274614\pi\)
0.650369 + 0.759619i \(0.274614\pi\)
\(744\) 26.5392 0.972975
\(745\) 14.5438 0.532844
\(746\) −13.1903 −0.482930
\(747\) −0.273284 −0.00999893
\(748\) −0.696977 −0.0254840
\(749\) −22.5334 −0.823352
\(750\) 12.0402 0.439645
\(751\) −25.8075 −0.941730 −0.470865 0.882205i \(-0.656058\pi\)
−0.470865 + 0.882205i \(0.656058\pi\)
\(752\) 5.09443 0.185775
\(753\) −25.4006 −0.925649
\(754\) −47.2781 −1.72177
\(755\) 9.95293 0.362224
\(756\) 9.89578 0.359906
\(757\) −24.2778 −0.882391 −0.441195 0.897411i \(-0.645445\pi\)
−0.441195 + 0.897411i \(0.645445\pi\)
\(758\) −6.40507 −0.232643
\(759\) −1.46805 −0.0532868
\(760\) −79.5771 −2.88657
\(761\) −8.93062 −0.323735 −0.161867 0.986813i \(-0.551752\pi\)
−0.161867 + 0.986813i \(0.551752\pi\)
\(762\) 12.1571 0.440406
\(763\) 45.7625 1.65671
\(764\) −51.2896 −1.85559
\(765\) 3.39062 0.122588
\(766\) −7.95077 −0.287273
\(767\) −25.5953 −0.924194
\(768\) 26.2838 0.948434
\(769\) 26.4051 0.952193 0.476097 0.879393i \(-0.342051\pi\)
0.476097 + 0.879393i \(0.342051\pi\)
\(770\) 4.20733 0.151622
\(771\) 28.5674 1.02883
\(772\) −69.8851 −2.51522
\(773\) −47.6233 −1.71289 −0.856445 0.516238i \(-0.827332\pi\)
−0.856445 + 0.516238i \(0.827332\pi\)
\(774\) −3.13301 −0.112614
\(775\) −44.5178 −1.59913
\(776\) 13.8116 0.495808
\(777\) 8.05293 0.288897
\(778\) −12.3924 −0.444288
\(779\) 34.5568 1.23813
\(780\) 44.7219 1.60130
\(781\) −1.20829 −0.0432360
\(782\) −18.1545 −0.649204
\(783\) 5.48562 0.196040
\(784\) 0.816799 0.0291714
\(785\) 3.39062 0.121017
\(786\) 19.3309 0.689510
\(787\) 2.91188 0.103797 0.0518987 0.998652i \(-0.483473\pi\)
0.0518987 + 0.998652i \(0.483473\pi\)
\(788\) 85.3275 3.03967
\(789\) 5.67725 0.202116
\(790\) 45.9750 1.63572
\(791\) 33.1413 1.17837
\(792\) 0.743201 0.0264085
\(793\) −4.67201 −0.165908
\(794\) −63.9052 −2.26791
\(795\) −18.2650 −0.647792
\(796\) −44.8845 −1.59089
\(797\) 16.2468 0.575492 0.287746 0.957707i \(-0.407094\pi\)
0.287746 + 0.957707i \(0.407094\pi\)
\(798\) 39.1859 1.38717
\(799\) −2.64382 −0.0935315
\(800\) −20.6106 −0.728693
\(801\) 8.77053 0.309891
\(802\) −7.43124 −0.262406
\(803\) −1.51820 −0.0535762
\(804\) 32.0180 1.12919
\(805\) 70.6728 2.49089
\(806\) −59.0609 −2.08033
\(807\) −17.9223 −0.630893
\(808\) 1.28685 0.0452714
\(809\) −25.7473 −0.905226 −0.452613 0.891707i \(-0.649508\pi\)
−0.452613 + 0.891707i \(0.649508\pi\)
\(810\) −8.04650 −0.282725
\(811\) −32.3623 −1.13639 −0.568197 0.822892i \(-0.692359\pi\)
−0.568197 + 0.822892i \(0.692359\pi\)
\(812\) 54.2845 1.90501
\(813\) 21.3728 0.749578
\(814\) 1.34602 0.0471778
\(815\) 11.3512 0.397616
\(816\) 1.92692 0.0674558
\(817\) −8.00056 −0.279904
\(818\) 59.3517 2.07518
\(819\) −9.89515 −0.345765
\(820\) −70.2200 −2.45219
\(821\) −4.63571 −0.161787 −0.0808936 0.996723i \(-0.525777\pi\)
−0.0808936 + 0.996723i \(0.525777\pi\)
\(822\) 3.27155 0.114108
\(823\) 23.5333 0.820318 0.410159 0.912014i \(-0.365473\pi\)
0.410159 + 0.912014i \(0.365473\pi\)
\(824\) 30.1412 1.05002
\(825\) −1.24667 −0.0434035
\(826\) 45.5719 1.58565
\(827\) −5.60101 −0.194766 −0.0973831 0.995247i \(-0.531047\pi\)
−0.0973831 + 0.995247i \(0.531047\pi\)
\(828\) 27.7838 0.965553
\(829\) −4.83821 −0.168038 −0.0840189 0.996464i \(-0.526776\pi\)
−0.0840189 + 0.996464i \(0.526776\pi\)
\(830\) 2.19898 0.0763276
\(831\) −21.9877 −0.762743
\(832\) −41.3396 −1.43319
\(833\) −0.423888 −0.0146868
\(834\) 25.0167 0.866257
\(835\) −2.58091 −0.0893162
\(836\) 4.22381 0.146084
\(837\) 6.85276 0.236866
\(838\) −44.3617 −1.53245
\(839\) 13.5095 0.466401 0.233201 0.972429i \(-0.425080\pi\)
0.233201 + 0.972429i \(0.425080\pi\)
\(840\) −35.7781 −1.23446
\(841\) 1.09206 0.0376574
\(842\) 32.2669 1.11199
\(843\) 6.01868 0.207294
\(844\) −52.3362 −1.80149
\(845\) −0.641000 −0.0220511
\(846\) 6.27421 0.215712
\(847\) 29.8712 1.02638
\(848\) −10.3802 −0.356456
\(849\) 25.6402 0.879969
\(850\) −15.4168 −0.528793
\(851\) 22.6097 0.775051
\(852\) 22.8676 0.783432
\(853\) −3.82277 −0.130889 −0.0654445 0.997856i \(-0.520847\pi\)
−0.0654445 + 0.997856i \(0.520847\pi\)
\(854\) 8.31841 0.284650
\(855\) −20.5478 −0.702721
\(856\) 32.0283 1.09470
\(857\) −48.3635 −1.65207 −0.826033 0.563622i \(-0.809408\pi\)
−0.826033 + 0.563622i \(0.809408\pi\)
\(858\) −1.65394 −0.0564644
\(859\) 1.02138 0.0348490 0.0174245 0.999848i \(-0.494453\pi\)
0.0174245 + 0.999848i \(0.494453\pi\)
\(860\) 16.2573 0.554369
\(861\) 15.5368 0.529494
\(862\) 1.01938 0.0347201
\(863\) −52.8846 −1.80021 −0.900106 0.435671i \(-0.856511\pi\)
−0.900106 + 0.435671i \(0.856511\pi\)
\(864\) 3.17265 0.107936
\(865\) −48.3746 −1.64479
\(866\) −96.7405 −3.28738
\(867\) −1.00000 −0.0339618
\(868\) 67.8135 2.30174
\(869\) −1.09648 −0.0371954
\(870\) −44.1401 −1.49649
\(871\) −32.0159 −1.08482
\(872\) −65.0454 −2.20271
\(873\) 3.56633 0.120702
\(874\) 110.020 3.72148
\(875\) 13.8236 0.467322
\(876\) 28.7329 0.970796
\(877\) −17.3570 −0.586104 −0.293052 0.956097i \(-0.594671\pi\)
−0.293052 + 0.956097i \(0.594671\pi\)
\(878\) −29.4404 −0.993567
\(879\) 15.7560 0.531436
\(880\) −1.25380 −0.0422656
\(881\) 34.9333 1.17693 0.588467 0.808522i \(-0.299732\pi\)
0.588467 + 0.808522i \(0.299732\pi\)
\(882\) 1.00595 0.0338722
\(883\) −51.6710 −1.73887 −0.869434 0.494049i \(-0.835516\pi\)
−0.869434 + 0.494049i \(0.835516\pi\)
\(884\) −13.1899 −0.443624
\(885\) −23.8965 −0.803271
\(886\) −31.2544 −1.05001
\(887\) 53.1390 1.78423 0.892117 0.451804i \(-0.149219\pi\)
0.892117 + 0.451804i \(0.149219\pi\)
\(888\) −11.4462 −0.384109
\(889\) 13.9579 0.468132
\(890\) −70.5721 −2.36558
\(891\) 0.191904 0.00642903
\(892\) 71.9294 2.40837
\(893\) 16.0220 0.536157
\(894\) 10.1795 0.340453
\(895\) −32.1490 −1.07462
\(896\) 56.3153 1.88136
\(897\) −27.7820 −0.927614
\(898\) 44.1128 1.47206
\(899\) 37.5917 1.25375
\(900\) 23.5940 0.786468
\(901\) 5.38691 0.179464
\(902\) 2.59692 0.0864680
\(903\) −3.59708 −0.119703
\(904\) −47.1061 −1.56672
\(905\) 35.7317 1.18776
\(906\) 6.96625 0.231438
\(907\) −48.3648 −1.60593 −0.802964 0.596028i \(-0.796745\pi\)
−0.802964 + 0.596028i \(0.796745\pi\)
\(908\) −67.5725 −2.24247
\(909\) 0.332282 0.0110211
\(910\) 79.6214 2.63942
\(911\) 38.1072 1.26255 0.631273 0.775560i \(-0.282533\pi\)
0.631273 + 0.775560i \(0.282533\pi\)
\(912\) −11.6775 −0.386682
\(913\) −0.0524442 −0.00173565
\(914\) −6.97167 −0.230602
\(915\) −4.36191 −0.144200
\(916\) 81.1479 2.68120
\(917\) 22.1942 0.732918
\(918\) 2.37316 0.0783261
\(919\) 20.8793 0.688745 0.344373 0.938833i \(-0.388092\pi\)
0.344373 + 0.938833i \(0.388092\pi\)
\(920\) −100.452 −3.31181
\(921\) −15.5196 −0.511387
\(922\) 76.0427 2.50433
\(923\) −22.8662 −0.752649
\(924\) 1.89904 0.0624738
\(925\) 19.2002 0.631299
\(926\) −63.8701 −2.09890
\(927\) 7.78283 0.255622
\(928\) 17.4040 0.571313
\(929\) −19.2764 −0.632439 −0.316220 0.948686i \(-0.602414\pi\)
−0.316220 + 0.948686i \(0.602414\pi\)
\(930\) −55.1408 −1.80814
\(931\) 2.56884 0.0841903
\(932\) 20.4399 0.669533
\(933\) −1.09937 −0.0359918
\(934\) 101.439 3.31918
\(935\) 0.650674 0.0212793
\(936\) 14.0647 0.459718
\(937\) 43.6237 1.42512 0.712562 0.701609i \(-0.247535\pi\)
0.712562 + 0.701609i \(0.247535\pi\)
\(938\) 57.0036 1.86124
\(939\) −19.2900 −0.629506
\(940\) −32.5570 −1.06189
\(941\) −38.6703 −1.26062 −0.630308 0.776345i \(-0.717071\pi\)
−0.630308 + 0.776345i \(0.717071\pi\)
\(942\) 2.37316 0.0773218
\(943\) 43.6218 1.42052
\(944\) −13.5806 −0.442011
\(945\) −9.23837 −0.300524
\(946\) −0.601237 −0.0195479
\(947\) 5.94121 0.193063 0.0965317 0.995330i \(-0.469225\pi\)
0.0965317 + 0.995330i \(0.469225\pi\)
\(948\) 20.7515 0.673977
\(949\) −28.7311 −0.932651
\(950\) 93.4290 3.03124
\(951\) 14.9672 0.485345
\(952\) 10.5521 0.341995
\(953\) −26.0723 −0.844565 −0.422282 0.906464i \(-0.638771\pi\)
−0.422282 + 0.906464i \(0.638771\pi\)
\(954\) −12.7840 −0.413898
\(955\) 47.8822 1.54943
\(956\) 20.8360 0.673885
\(957\) 1.05271 0.0340294
\(958\) 55.8527 1.80452
\(959\) 3.75614 0.121292
\(960\) −38.5957 −1.24567
\(961\) 15.9604 0.514851
\(962\) 25.4726 0.821269
\(963\) 8.27010 0.266500
\(964\) −50.6687 −1.63193
\(965\) 65.2423 2.10022
\(966\) 49.4652 1.59152
\(967\) 21.1321 0.679563 0.339781 0.940504i \(-0.389647\pi\)
0.339781 + 0.940504i \(0.389647\pi\)
\(968\) −42.4579 −1.36465
\(969\) 6.06019 0.194681
\(970\) −28.6965 −0.921389
\(971\) −59.3368 −1.90421 −0.952104 0.305774i \(-0.901085\pi\)
−0.952104 + 0.305774i \(0.901085\pi\)
\(972\) −3.63190 −0.116493
\(973\) 28.7222 0.920792
\(974\) 29.3909 0.941746
\(975\) −23.5925 −0.755565
\(976\) −2.47891 −0.0793481
\(977\) 0.848607 0.0271494 0.0135747 0.999908i \(-0.495679\pi\)
0.0135747 + 0.999908i \(0.495679\pi\)
\(978\) 7.94494 0.254051
\(979\) 1.68310 0.0537921
\(980\) −5.21993 −0.166745
\(981\) −16.7955 −0.536240
\(982\) 63.3454 2.02143
\(983\) −15.2561 −0.486595 −0.243298 0.969952i \(-0.578229\pi\)
−0.243298 + 0.969952i \(0.578229\pi\)
\(984\) −22.0836 −0.703999
\(985\) −79.6588 −2.53814
\(986\) 13.0183 0.414587
\(987\) 7.20355 0.229292
\(988\) 79.9333 2.54302
\(989\) −10.0993 −0.321139
\(990\) −1.54416 −0.0490765
\(991\) 26.9241 0.855271 0.427636 0.903951i \(-0.359347\pi\)
0.427636 + 0.903951i \(0.359347\pi\)
\(992\) 21.7414 0.690291
\(993\) 7.89985 0.250694
\(994\) 40.7127 1.29133
\(995\) 41.9026 1.32840
\(996\) 0.992540 0.0314498
\(997\) 42.4673 1.34495 0.672476 0.740119i \(-0.265231\pi\)
0.672476 + 0.740119i \(0.265231\pi\)
\(998\) −101.206 −3.20363
\(999\) −2.95555 −0.0935095
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 8007.2.a.f.1.43 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.43 48 1.1 even 1 trivial