Properties

Label 6037.2.a.b.1.9
Level $6037$
Weight $2$
Character 6037.1
Self dual yes
Analytic conductor $48.206$
Analytic rank $0$
Dimension $259$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.58809 q^{2} -2.19108 q^{3} +4.69820 q^{4} +0.221659 q^{5} +5.67071 q^{6} +0.704833 q^{7} -6.98319 q^{8} +1.80083 q^{9} +O(q^{10})\) \(q-2.58809 q^{2} -2.19108 q^{3} +4.69820 q^{4} +0.221659 q^{5} +5.67071 q^{6} +0.704833 q^{7} -6.98319 q^{8} +1.80083 q^{9} -0.573673 q^{10} +5.84789 q^{11} -10.2941 q^{12} +4.53018 q^{13} -1.82417 q^{14} -0.485672 q^{15} +8.67672 q^{16} +1.50986 q^{17} -4.66070 q^{18} -3.56997 q^{19} +1.04140 q^{20} -1.54435 q^{21} -15.1349 q^{22} -1.45557 q^{23} +15.3007 q^{24} -4.95087 q^{25} -11.7245 q^{26} +2.62748 q^{27} +3.31145 q^{28} +0.0946853 q^{29} +1.25696 q^{30} +1.02206 q^{31} -8.48973 q^{32} -12.8132 q^{33} -3.90765 q^{34} +0.156233 q^{35} +8.46065 q^{36} +8.86741 q^{37} +9.23941 q^{38} -9.92599 q^{39} -1.54789 q^{40} +1.54403 q^{41} +3.99690 q^{42} +0.515830 q^{43} +27.4746 q^{44} +0.399169 q^{45} +3.76715 q^{46} +9.35593 q^{47} -19.0114 q^{48} -6.50321 q^{49} +12.8133 q^{50} -3.30822 q^{51} +21.2837 q^{52} -0.0346419 q^{53} -6.80016 q^{54} +1.29624 q^{55} -4.92199 q^{56} +7.82209 q^{57} -0.245054 q^{58} -3.03560 q^{59} -2.28179 q^{60} +8.23193 q^{61} -2.64519 q^{62} +1.26928 q^{63} +4.61875 q^{64} +1.00416 q^{65} +33.1617 q^{66} +6.07412 q^{67} +7.09362 q^{68} +3.18927 q^{69} -0.404344 q^{70} +10.3162 q^{71} -12.5755 q^{72} +3.27118 q^{73} -22.9497 q^{74} +10.8477 q^{75} -16.7725 q^{76} +4.12178 q^{77} +25.6893 q^{78} -13.1027 q^{79} +1.92327 q^{80} -11.1595 q^{81} -3.99608 q^{82} +5.80581 q^{83} -7.25565 q^{84} +0.334674 q^{85} -1.33501 q^{86} -0.207463 q^{87} -40.8369 q^{88} -1.97381 q^{89} -1.03309 q^{90} +3.19302 q^{91} -6.83858 q^{92} -2.23942 q^{93} -24.2140 q^{94} -0.791317 q^{95} +18.6017 q^{96} +10.8935 q^{97} +16.8309 q^{98} +10.5310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58809 −1.83006 −0.915028 0.403391i \(-0.867831\pi\)
−0.915028 + 0.403391i \(0.867831\pi\)
\(3\) −2.19108 −1.26502 −0.632510 0.774552i \(-0.717975\pi\)
−0.632510 + 0.774552i \(0.717975\pi\)
\(4\) 4.69820 2.34910
\(5\) 0.221659 0.0991289 0.0495645 0.998771i \(-0.484217\pi\)
0.0495645 + 0.998771i \(0.484217\pi\)
\(6\) 5.67071 2.31506
\(7\) 0.704833 0.266402 0.133201 0.991089i \(-0.457474\pi\)
0.133201 + 0.991089i \(0.457474\pi\)
\(8\) −6.98319 −2.46893
\(9\) 1.80083 0.600276
\(10\) −0.573673 −0.181411
\(11\) 5.84789 1.76320 0.881602 0.471993i \(-0.156465\pi\)
0.881602 + 0.471993i \(0.156465\pi\)
\(12\) −10.2941 −2.97166
\(13\) 4.53018 1.25645 0.628223 0.778033i \(-0.283782\pi\)
0.628223 + 0.778033i \(0.283782\pi\)
\(14\) −1.82417 −0.487530
\(15\) −0.485672 −0.125400
\(16\) 8.67672 2.16918
\(17\) 1.50986 0.366194 0.183097 0.983095i \(-0.441388\pi\)
0.183097 + 0.983095i \(0.441388\pi\)
\(18\) −4.66070 −1.09854
\(19\) −3.56997 −0.819008 −0.409504 0.912308i \(-0.634298\pi\)
−0.409504 + 0.912308i \(0.634298\pi\)
\(20\) 1.04140 0.232864
\(21\) −1.54435 −0.337004
\(22\) −15.1349 −3.22676
\(23\) −1.45557 −0.303508 −0.151754 0.988418i \(-0.548492\pi\)
−0.151754 + 0.988418i \(0.548492\pi\)
\(24\) 15.3007 3.12325
\(25\) −4.95087 −0.990173
\(26\) −11.7245 −2.29937
\(27\) 2.62748 0.505659
\(28\) 3.31145 0.625805
\(29\) 0.0946853 0.0175826 0.00879131 0.999961i \(-0.497202\pi\)
0.00879131 + 0.999961i \(0.497202\pi\)
\(30\) 1.25696 0.229489
\(31\) 1.02206 0.183568 0.0917840 0.995779i \(-0.470743\pi\)
0.0917840 + 0.995779i \(0.470743\pi\)
\(32\) −8.48973 −1.50079
\(33\) −12.8132 −2.23049
\(34\) −3.90765 −0.670156
\(35\) 0.156233 0.0264081
\(36\) 8.46065 1.41011
\(37\) 8.86741 1.45779 0.728897 0.684624i \(-0.240033\pi\)
0.728897 + 0.684624i \(0.240033\pi\)
\(38\) 9.23941 1.49883
\(39\) −9.92599 −1.58943
\(40\) −1.54789 −0.244743
\(41\) 1.54403 0.241137 0.120568 0.992705i \(-0.461528\pi\)
0.120568 + 0.992705i \(0.461528\pi\)
\(42\) 3.99690 0.616735
\(43\) 0.515830 0.0786633 0.0393316 0.999226i \(-0.487477\pi\)
0.0393316 + 0.999226i \(0.487477\pi\)
\(44\) 27.4746 4.14195
\(45\) 0.399169 0.0595047
\(46\) 3.76715 0.555436
\(47\) 9.35593 1.36470 0.682351 0.731024i \(-0.260957\pi\)
0.682351 + 0.731024i \(0.260957\pi\)
\(48\) −19.0114 −2.74406
\(49\) −6.50321 −0.929030
\(50\) 12.8133 1.81207
\(51\) −3.30822 −0.463243
\(52\) 21.2837 2.95152
\(53\) −0.0346419 −0.00475843 −0.00237921 0.999997i \(-0.500757\pi\)
−0.00237921 + 0.999997i \(0.500757\pi\)
\(54\) −6.80016 −0.925385
\(55\) 1.29624 0.174785
\(56\) −4.92199 −0.657728
\(57\) 7.82209 1.03606
\(58\) −0.245054 −0.0321772
\(59\) −3.03560 −0.395201 −0.197600 0.980283i \(-0.563315\pi\)
−0.197600 + 0.980283i \(0.563315\pi\)
\(60\) −2.28179 −0.294578
\(61\) 8.23193 1.05399 0.526995 0.849868i \(-0.323319\pi\)
0.526995 + 0.849868i \(0.323319\pi\)
\(62\) −2.64519 −0.335940
\(63\) 1.26928 0.159915
\(64\) 4.61875 0.577344
\(65\) 1.00416 0.124550
\(66\) 33.1617 4.08192
\(67\) 6.07412 0.742072 0.371036 0.928618i \(-0.379003\pi\)
0.371036 + 0.928618i \(0.379003\pi\)
\(68\) 7.09362 0.860228
\(69\) 3.18927 0.383943
\(70\) −0.404344 −0.0483283
\(71\) 10.3162 1.22431 0.612153 0.790739i \(-0.290304\pi\)
0.612153 + 0.790739i \(0.290304\pi\)
\(72\) −12.5755 −1.48204
\(73\) 3.27118 0.382863 0.191431 0.981506i \(-0.438687\pi\)
0.191431 + 0.981506i \(0.438687\pi\)
\(74\) −22.9497 −2.66784
\(75\) 10.8477 1.25259
\(76\) −16.7725 −1.92393
\(77\) 4.12178 0.469721
\(78\) 25.6893 2.90874
\(79\) −13.1027 −1.47417 −0.737085 0.675800i \(-0.763798\pi\)
−0.737085 + 0.675800i \(0.763798\pi\)
\(80\) 1.92327 0.215028
\(81\) −11.1595 −1.23994
\(82\) −3.99608 −0.441293
\(83\) 5.80581 0.637270 0.318635 0.947877i \(-0.396776\pi\)
0.318635 + 0.947877i \(0.396776\pi\)
\(84\) −7.25565 −0.791656
\(85\) 0.334674 0.0363005
\(86\) −1.33501 −0.143958
\(87\) −0.207463 −0.0222424
\(88\) −40.8369 −4.35323
\(89\) −1.97381 −0.209224 −0.104612 0.994513i \(-0.533360\pi\)
−0.104612 + 0.994513i \(0.533360\pi\)
\(90\) −1.03309 −0.108897
\(91\) 3.19302 0.334720
\(92\) −6.83858 −0.712971
\(93\) −2.23942 −0.232217
\(94\) −24.2140 −2.49748
\(95\) −0.791317 −0.0811874
\(96\) 18.6017 1.89853
\(97\) 10.8935 1.10606 0.553032 0.833160i \(-0.313471\pi\)
0.553032 + 0.833160i \(0.313471\pi\)
\(98\) 16.8309 1.70018
\(99\) 10.5310 1.05841
\(100\) −23.2602 −2.32602
\(101\) 5.43235 0.540539 0.270269 0.962785i \(-0.412887\pi\)
0.270269 + 0.962785i \(0.412887\pi\)
\(102\) 8.56196 0.847761
\(103\) 9.21047 0.907535 0.453767 0.891120i \(-0.350080\pi\)
0.453767 + 0.891120i \(0.350080\pi\)
\(104\) −31.6351 −3.10208
\(105\) −0.342318 −0.0334068
\(106\) 0.0896562 0.00870818
\(107\) −6.49127 −0.627534 −0.313767 0.949500i \(-0.601591\pi\)
−0.313767 + 0.949500i \(0.601591\pi\)
\(108\) 12.3445 1.18785
\(109\) −8.81516 −0.844339 −0.422170 0.906517i \(-0.638731\pi\)
−0.422170 + 0.906517i \(0.638731\pi\)
\(110\) −3.35478 −0.319865
\(111\) −19.4292 −1.84414
\(112\) 6.11564 0.577874
\(113\) 10.8309 1.01888 0.509441 0.860506i \(-0.329852\pi\)
0.509441 + 0.860506i \(0.329852\pi\)
\(114\) −20.2443 −1.89605
\(115\) −0.322641 −0.0300864
\(116\) 0.444851 0.0413034
\(117\) 8.15807 0.754214
\(118\) 7.85639 0.723240
\(119\) 1.06420 0.0975549
\(120\) 3.39154 0.309604
\(121\) 23.1978 2.10889
\(122\) −21.3050 −1.92886
\(123\) −3.38309 −0.305043
\(124\) 4.80186 0.431220
\(125\) −2.20570 −0.197284
\(126\) −3.28502 −0.292652
\(127\) 11.3700 1.00892 0.504461 0.863435i \(-0.331691\pi\)
0.504461 + 0.863435i \(0.331691\pi\)
\(128\) 5.02574 0.444216
\(129\) −1.13022 −0.0995106
\(130\) −2.59884 −0.227934
\(131\) 7.95476 0.695010 0.347505 0.937678i \(-0.387029\pi\)
0.347505 + 0.937678i \(0.387029\pi\)
\(132\) −60.1989 −5.23965
\(133\) −2.51624 −0.218185
\(134\) −15.7204 −1.35803
\(135\) 0.582405 0.0501255
\(136\) −10.5436 −0.904109
\(137\) 13.7214 1.17229 0.586147 0.810205i \(-0.300644\pi\)
0.586147 + 0.810205i \(0.300644\pi\)
\(138\) −8.25412 −0.702638
\(139\) 2.18059 0.184955 0.0924776 0.995715i \(-0.470521\pi\)
0.0924776 + 0.995715i \(0.470521\pi\)
\(140\) 0.734013 0.0620354
\(141\) −20.4996 −1.72638
\(142\) −26.6992 −2.24055
\(143\) 26.4920 2.21537
\(144\) 15.6253 1.30211
\(145\) 0.0209879 0.00174295
\(146\) −8.46611 −0.700660
\(147\) 14.2490 1.17524
\(148\) 41.6609 3.42451
\(149\) −5.85503 −0.479663 −0.239831 0.970815i \(-0.577092\pi\)
−0.239831 + 0.970815i \(0.577092\pi\)
\(150\) −28.0749 −2.29231
\(151\) 1.33704 0.108807 0.0544035 0.998519i \(-0.482674\pi\)
0.0544035 + 0.998519i \(0.482674\pi\)
\(152\) 24.9298 2.02208
\(153\) 2.71899 0.219818
\(154\) −10.6675 −0.859615
\(155\) 0.226550 0.0181969
\(156\) −46.6343 −3.73373
\(157\) −11.8154 −0.942968 −0.471484 0.881875i \(-0.656281\pi\)
−0.471484 + 0.881875i \(0.656281\pi\)
\(158\) 33.9110 2.69781
\(159\) 0.0759030 0.00601950
\(160\) −1.88183 −0.148771
\(161\) −1.02594 −0.0808551
\(162\) 28.8818 2.26917
\(163\) −22.7825 −1.78446 −0.892231 0.451579i \(-0.850861\pi\)
−0.892231 + 0.451579i \(0.850861\pi\)
\(164\) 7.25416 0.566454
\(165\) −2.84016 −0.221106
\(166\) −15.0260 −1.16624
\(167\) 15.1206 1.17007 0.585033 0.811010i \(-0.301082\pi\)
0.585033 + 0.811010i \(0.301082\pi\)
\(168\) 10.7845 0.832039
\(169\) 7.52255 0.578658
\(170\) −0.866165 −0.0664318
\(171\) −6.42890 −0.491631
\(172\) 2.42347 0.184788
\(173\) 16.9143 1.28597 0.642986 0.765878i \(-0.277695\pi\)
0.642986 + 0.765878i \(0.277695\pi\)
\(174\) 0.536933 0.0407048
\(175\) −3.48954 −0.263784
\(176\) 50.7405 3.82471
\(177\) 6.65123 0.499937
\(178\) 5.10841 0.382891
\(179\) −18.4652 −1.38015 −0.690077 0.723736i \(-0.742423\pi\)
−0.690077 + 0.723736i \(0.742423\pi\)
\(180\) 1.87538 0.139783
\(181\) −22.9648 −1.70696 −0.853479 0.521127i \(-0.825512\pi\)
−0.853479 + 0.521127i \(0.825512\pi\)
\(182\) −8.26383 −0.612556
\(183\) −18.0368 −1.33332
\(184\) 10.1645 0.749340
\(185\) 1.96554 0.144509
\(186\) 5.79582 0.424970
\(187\) 8.82948 0.645675
\(188\) 43.9561 3.20583
\(189\) 1.85194 0.134709
\(190\) 2.04800 0.148577
\(191\) 11.5845 0.838227 0.419113 0.907934i \(-0.362341\pi\)
0.419113 + 0.907934i \(0.362341\pi\)
\(192\) −10.1200 −0.730351
\(193\) −13.4307 −0.966761 −0.483381 0.875410i \(-0.660591\pi\)
−0.483381 + 0.875410i \(0.660591\pi\)
\(194\) −28.1933 −2.02416
\(195\) −2.20018 −0.157558
\(196\) −30.5534 −2.18239
\(197\) −25.3382 −1.80527 −0.902634 0.430408i \(-0.858370\pi\)
−0.902634 + 0.430408i \(0.858370\pi\)
\(198\) −27.2552 −1.93695
\(199\) −2.57866 −0.182796 −0.0913982 0.995814i \(-0.529134\pi\)
−0.0913982 + 0.995814i \(0.529134\pi\)
\(200\) 34.5729 2.44467
\(201\) −13.3089 −0.938736
\(202\) −14.0594 −0.989216
\(203\) 0.0667374 0.00468405
\(204\) −15.5427 −1.08821
\(205\) 0.342248 0.0239036
\(206\) −23.8375 −1.66084
\(207\) −2.62123 −0.182188
\(208\) 39.3071 2.72546
\(209\) −20.8768 −1.44408
\(210\) 0.885949 0.0611363
\(211\) 19.8440 1.36612 0.683058 0.730364i \(-0.260650\pi\)
0.683058 + 0.730364i \(0.260650\pi\)
\(212\) −0.162755 −0.0111780
\(213\) −22.6036 −1.54877
\(214\) 16.8000 1.14842
\(215\) 0.114338 0.00779781
\(216\) −18.3482 −1.24844
\(217\) 0.720384 0.0489029
\(218\) 22.8144 1.54519
\(219\) −7.16742 −0.484329
\(220\) 6.08999 0.410587
\(221\) 6.83993 0.460104
\(222\) 50.2845 3.37487
\(223\) −25.4849 −1.70660 −0.853299 0.521423i \(-0.825402\pi\)
−0.853299 + 0.521423i \(0.825402\pi\)
\(224\) −5.98385 −0.399813
\(225\) −8.91565 −0.594377
\(226\) −28.0312 −1.86461
\(227\) −24.5526 −1.62961 −0.814807 0.579732i \(-0.803157\pi\)
−0.814807 + 0.579732i \(0.803157\pi\)
\(228\) 36.7498 2.43381
\(229\) 7.31160 0.483164 0.241582 0.970380i \(-0.422334\pi\)
0.241582 + 0.970380i \(0.422334\pi\)
\(230\) 0.835023 0.0550598
\(231\) −9.03116 −0.594206
\(232\) −0.661206 −0.0434103
\(233\) 22.9836 1.50571 0.752853 0.658189i \(-0.228677\pi\)
0.752853 + 0.658189i \(0.228677\pi\)
\(234\) −21.1138 −1.38025
\(235\) 2.07383 0.135282
\(236\) −14.2619 −0.928368
\(237\) 28.7091 1.86485
\(238\) −2.75424 −0.178531
\(239\) 8.59001 0.555642 0.277821 0.960633i \(-0.410388\pi\)
0.277821 + 0.960633i \(0.410388\pi\)
\(240\) −4.21404 −0.272015
\(241\) −27.7512 −1.78761 −0.893806 0.448453i \(-0.851975\pi\)
−0.893806 + 0.448453i \(0.851975\pi\)
\(242\) −60.0379 −3.85938
\(243\) 16.5689 1.06290
\(244\) 38.6753 2.47593
\(245\) −1.44150 −0.0920937
\(246\) 8.75573 0.558245
\(247\) −16.1726 −1.02904
\(248\) −7.13727 −0.453217
\(249\) −12.7210 −0.806160
\(250\) 5.70855 0.361040
\(251\) 18.5685 1.17203 0.586016 0.810299i \(-0.300695\pi\)
0.586016 + 0.810299i \(0.300695\pi\)
\(252\) 5.96335 0.375656
\(253\) −8.51202 −0.535146
\(254\) −29.4265 −1.84638
\(255\) −0.733296 −0.0459208
\(256\) −22.2445 −1.39028
\(257\) 22.6728 1.41429 0.707146 0.707067i \(-0.249982\pi\)
0.707146 + 0.707067i \(0.249982\pi\)
\(258\) 2.92512 0.182110
\(259\) 6.25005 0.388359
\(260\) 4.71773 0.292581
\(261\) 0.170512 0.0105544
\(262\) −20.5876 −1.27191
\(263\) 16.7885 1.03522 0.517611 0.855616i \(-0.326822\pi\)
0.517611 + 0.855616i \(0.326822\pi\)
\(264\) 89.4769 5.50692
\(265\) −0.00767868 −0.000471698 0
\(266\) 6.51224 0.399291
\(267\) 4.32478 0.264672
\(268\) 28.5375 1.74320
\(269\) −2.41380 −0.147172 −0.0735859 0.997289i \(-0.523444\pi\)
−0.0735859 + 0.997289i \(0.523444\pi\)
\(270\) −1.50732 −0.0917324
\(271\) 7.65409 0.464953 0.232476 0.972602i \(-0.425317\pi\)
0.232476 + 0.972602i \(0.425317\pi\)
\(272\) 13.1006 0.794342
\(273\) −6.99617 −0.423427
\(274\) −35.5121 −2.14536
\(275\) −28.9521 −1.74588
\(276\) 14.9839 0.901922
\(277\) 14.5968 0.877039 0.438519 0.898722i \(-0.355503\pi\)
0.438519 + 0.898722i \(0.355503\pi\)
\(278\) −5.64356 −0.338478
\(279\) 1.84056 0.110191
\(280\) −1.09100 −0.0651999
\(281\) 13.2342 0.789488 0.394744 0.918791i \(-0.370833\pi\)
0.394744 + 0.918791i \(0.370833\pi\)
\(282\) 53.0547 3.15936
\(283\) −6.14852 −0.365491 −0.182746 0.983160i \(-0.558498\pi\)
−0.182746 + 0.983160i \(0.558498\pi\)
\(284\) 48.4675 2.87602
\(285\) 1.73384 0.102704
\(286\) −68.5636 −4.05425
\(287\) 1.08828 0.0642392
\(288\) −15.2885 −0.900886
\(289\) −14.7203 −0.865902
\(290\) −0.0543184 −0.00318969
\(291\) −23.8685 −1.39919
\(292\) 15.3687 0.899384
\(293\) −28.5901 −1.67025 −0.835127 0.550057i \(-0.814606\pi\)
−0.835127 + 0.550057i \(0.814606\pi\)
\(294\) −36.8778 −2.15076
\(295\) −0.672867 −0.0391758
\(296\) −61.9229 −3.59919
\(297\) 15.3652 0.891581
\(298\) 15.1533 0.877809
\(299\) −6.59401 −0.381341
\(300\) 50.9649 2.94246
\(301\) 0.363574 0.0209561
\(302\) −3.46038 −0.199123
\(303\) −11.9027 −0.683792
\(304\) −30.9757 −1.77658
\(305\) 1.82468 0.104481
\(306\) −7.03700 −0.402278
\(307\) −21.7103 −1.23907 −0.619536 0.784968i \(-0.712679\pi\)
−0.619536 + 0.784968i \(0.712679\pi\)
\(308\) 19.3650 1.10342
\(309\) −20.1809 −1.14805
\(310\) −0.586330 −0.0333013
\(311\) −15.7994 −0.895902 −0.447951 0.894058i \(-0.647846\pi\)
−0.447951 + 0.894058i \(0.647846\pi\)
\(312\) 69.3151 3.92419
\(313\) −12.0213 −0.679485 −0.339743 0.940518i \(-0.610340\pi\)
−0.339743 + 0.940518i \(0.610340\pi\)
\(314\) 30.5792 1.72568
\(315\) 0.281348 0.0158522
\(316\) −61.5592 −3.46298
\(317\) −22.8885 −1.28555 −0.642773 0.766057i \(-0.722216\pi\)
−0.642773 + 0.766057i \(0.722216\pi\)
\(318\) −0.196444 −0.0110160
\(319\) 0.553709 0.0310018
\(320\) 1.02379 0.0572314
\(321\) 14.2229 0.793843
\(322\) 2.65521 0.147969
\(323\) −5.39015 −0.299916
\(324\) −52.4296 −2.91276
\(325\) −22.4283 −1.24410
\(326\) 58.9631 3.26566
\(327\) 19.3147 1.06811
\(328\) −10.7822 −0.595350
\(329\) 6.59437 0.363559
\(330\) 7.35058 0.404636
\(331\) −17.1450 −0.942375 −0.471187 0.882033i \(-0.656174\pi\)
−0.471187 + 0.882033i \(0.656174\pi\)
\(332\) 27.2769 1.49701
\(333\) 15.9687 0.875078
\(334\) −39.1334 −2.14128
\(335\) 1.34638 0.0735608
\(336\) −13.3999 −0.731022
\(337\) −23.5025 −1.28026 −0.640130 0.768266i \(-0.721120\pi\)
−0.640130 + 0.768266i \(0.721120\pi\)
\(338\) −19.4690 −1.05898
\(339\) −23.7313 −1.28891
\(340\) 1.57237 0.0852735
\(341\) 5.97691 0.323668
\(342\) 16.6386 0.899711
\(343\) −9.51751 −0.513897
\(344\) −3.60214 −0.194214
\(345\) 0.706931 0.0380599
\(346\) −43.7758 −2.35340
\(347\) 10.0773 0.540980 0.270490 0.962723i \(-0.412814\pi\)
0.270490 + 0.962723i \(0.412814\pi\)
\(348\) −0.974704 −0.0522496
\(349\) 23.0316 1.23285 0.616426 0.787413i \(-0.288580\pi\)
0.616426 + 0.787413i \(0.288580\pi\)
\(350\) 9.03123 0.482739
\(351\) 11.9030 0.635334
\(352\) −49.6470 −2.64619
\(353\) 10.5780 0.563008 0.281504 0.959560i \(-0.409167\pi\)
0.281504 + 0.959560i \(0.409167\pi\)
\(354\) −17.2140 −0.914913
\(355\) 2.28667 0.121364
\(356\) −9.27339 −0.491488
\(357\) −2.33174 −0.123409
\(358\) 47.7896 2.52576
\(359\) −13.5404 −0.714635 −0.357317 0.933983i \(-0.616309\pi\)
−0.357317 + 0.933983i \(0.616309\pi\)
\(360\) −2.78748 −0.146913
\(361\) −6.25529 −0.329226
\(362\) 59.4349 3.12383
\(363\) −50.8282 −2.66779
\(364\) 15.0015 0.786291
\(365\) 0.725087 0.0379528
\(366\) 46.6809 2.44005
\(367\) −4.72279 −0.246527 −0.123264 0.992374i \(-0.539336\pi\)
−0.123264 + 0.992374i \(0.539336\pi\)
\(368\) −12.6296 −0.658363
\(369\) 2.78053 0.144748
\(370\) −5.08700 −0.264460
\(371\) −0.0244167 −0.00126765
\(372\) −10.5213 −0.545502
\(373\) 11.4775 0.594285 0.297142 0.954833i \(-0.403966\pi\)
0.297142 + 0.954833i \(0.403966\pi\)
\(374\) −22.8515 −1.18162
\(375\) 4.83286 0.249568
\(376\) −65.3343 −3.36936
\(377\) 0.428942 0.0220916
\(378\) −4.79298 −0.246524
\(379\) −5.44052 −0.279461 −0.139730 0.990190i \(-0.544624\pi\)
−0.139730 + 0.990190i \(0.544624\pi\)
\(380\) −3.71777 −0.190717
\(381\) −24.9125 −1.27631
\(382\) −29.9818 −1.53400
\(383\) −3.62836 −0.185400 −0.0927002 0.995694i \(-0.529550\pi\)
−0.0927002 + 0.995694i \(0.529550\pi\)
\(384\) −11.0118 −0.561943
\(385\) 0.913631 0.0465629
\(386\) 34.7598 1.76923
\(387\) 0.928920 0.0472197
\(388\) 51.1798 2.59826
\(389\) −29.6586 −1.50375 −0.751874 0.659306i \(-0.770850\pi\)
−0.751874 + 0.659306i \(0.770850\pi\)
\(390\) 5.69427 0.288341
\(391\) −2.19771 −0.111143
\(392\) 45.4132 2.29371
\(393\) −17.4295 −0.879202
\(394\) 65.5774 3.30374
\(395\) −2.90433 −0.146133
\(396\) 49.4769 2.48631
\(397\) 27.2954 1.36991 0.684957 0.728583i \(-0.259821\pi\)
0.684957 + 0.728583i \(0.259821\pi\)
\(398\) 6.67380 0.334527
\(399\) 5.51327 0.276009
\(400\) −42.9573 −2.14786
\(401\) 7.41740 0.370407 0.185204 0.982700i \(-0.440706\pi\)
0.185204 + 0.982700i \(0.440706\pi\)
\(402\) 34.4446 1.71794
\(403\) 4.63013 0.230643
\(404\) 25.5223 1.26978
\(405\) −2.47360 −0.122914
\(406\) −0.172722 −0.00857206
\(407\) 51.8556 2.57039
\(408\) 23.1019 1.14372
\(409\) −18.8556 −0.932350 −0.466175 0.884693i \(-0.654368\pi\)
−0.466175 + 0.884693i \(0.654368\pi\)
\(410\) −0.885767 −0.0437449
\(411\) −30.0646 −1.48298
\(412\) 43.2727 2.13189
\(413\) −2.13959 −0.105282
\(414\) 6.78399 0.333415
\(415\) 1.28691 0.0631719
\(416\) −38.4600 −1.88566
\(417\) −4.77785 −0.233972
\(418\) 54.0310 2.64274
\(419\) 30.9639 1.51269 0.756343 0.654175i \(-0.226984\pi\)
0.756343 + 0.654175i \(0.226984\pi\)
\(420\) −1.60828 −0.0784760
\(421\) 29.4432 1.43498 0.717488 0.696571i \(-0.245292\pi\)
0.717488 + 0.696571i \(0.245292\pi\)
\(422\) −51.3580 −2.50007
\(423\) 16.8484 0.819198
\(424\) 0.241911 0.0117482
\(425\) −7.47511 −0.362596
\(426\) 58.5001 2.83434
\(427\) 5.80214 0.280785
\(428\) −30.4973 −1.47414
\(429\) −58.0460 −2.80249
\(430\) −0.295918 −0.0142704
\(431\) 0.567480 0.0273345 0.0136673 0.999907i \(-0.495649\pi\)
0.0136673 + 0.999907i \(0.495649\pi\)
\(432\) 22.7979 1.09687
\(433\) −22.2777 −1.07060 −0.535300 0.844662i \(-0.679801\pi\)
−0.535300 + 0.844662i \(0.679801\pi\)
\(434\) −1.86442 −0.0894950
\(435\) −0.0459861 −0.00220486
\(436\) −41.4154 −1.98344
\(437\) 5.19635 0.248575
\(438\) 18.5499 0.886349
\(439\) 25.0143 1.19387 0.596935 0.802290i \(-0.296385\pi\)
0.596935 + 0.802290i \(0.296385\pi\)
\(440\) −9.05187 −0.431531
\(441\) −11.7112 −0.557674
\(442\) −17.7024 −0.842015
\(443\) 8.87131 0.421489 0.210744 0.977541i \(-0.432411\pi\)
0.210744 + 0.977541i \(0.432411\pi\)
\(444\) −91.2824 −4.33207
\(445\) −0.437514 −0.0207401
\(446\) 65.9573 3.12317
\(447\) 12.8288 0.606783
\(448\) 3.25545 0.153805
\(449\) −24.8325 −1.17192 −0.585959 0.810341i \(-0.699282\pi\)
−0.585959 + 0.810341i \(0.699282\pi\)
\(450\) 23.0745 1.08774
\(451\) 9.02930 0.425173
\(452\) 50.8856 2.39346
\(453\) −2.92956 −0.137643
\(454\) 63.5444 2.98229
\(455\) 0.707762 0.0331804
\(456\) −54.6232 −2.55797
\(457\) −9.62760 −0.450360 −0.225180 0.974317i \(-0.572297\pi\)
−0.225180 + 0.974317i \(0.572297\pi\)
\(458\) −18.9231 −0.884217
\(459\) 3.96713 0.185170
\(460\) −1.51583 −0.0706760
\(461\) −13.6020 −0.633506 −0.316753 0.948508i \(-0.602593\pi\)
−0.316753 + 0.948508i \(0.602593\pi\)
\(462\) 23.3734 1.08743
\(463\) 23.9242 1.11185 0.555925 0.831232i \(-0.312364\pi\)
0.555925 + 0.831232i \(0.312364\pi\)
\(464\) 0.821558 0.0381399
\(465\) −0.496388 −0.0230194
\(466\) −59.4836 −2.75552
\(467\) 26.0348 1.20475 0.602373 0.798215i \(-0.294222\pi\)
0.602373 + 0.798215i \(0.294222\pi\)
\(468\) 38.3283 1.77173
\(469\) 4.28124 0.197689
\(470\) −5.36725 −0.247573
\(471\) 25.8884 1.19287
\(472\) 21.1982 0.975724
\(473\) 3.01651 0.138699
\(474\) −74.3016 −3.41279
\(475\) 17.6745 0.810960
\(476\) 4.99982 0.229166
\(477\) −0.0623840 −0.00285637
\(478\) −22.2317 −1.01685
\(479\) 31.9145 1.45821 0.729105 0.684402i \(-0.239937\pi\)
0.729105 + 0.684402i \(0.239937\pi\)
\(480\) 4.12323 0.188199
\(481\) 40.1710 1.83164
\(482\) 71.8226 3.27143
\(483\) 2.24791 0.102283
\(484\) 108.988 4.95400
\(485\) 2.41464 0.109643
\(486\) −42.8818 −1.94516
\(487\) −0.470712 −0.0213300 −0.0106650 0.999943i \(-0.503395\pi\)
−0.0106650 + 0.999943i \(0.503395\pi\)
\(488\) −57.4852 −2.60223
\(489\) 49.9182 2.25738
\(490\) 3.73072 0.168537
\(491\) 15.9299 0.718907 0.359453 0.933163i \(-0.382963\pi\)
0.359453 + 0.933163i \(0.382963\pi\)
\(492\) −15.8944 −0.716576
\(493\) 0.142961 0.00643866
\(494\) 41.8562 1.88320
\(495\) 2.33430 0.104919
\(496\) 8.86816 0.398192
\(497\) 7.27119 0.326157
\(498\) 32.9230 1.47532
\(499\) −0.238983 −0.0106983 −0.00534917 0.999986i \(-0.501703\pi\)
−0.00534917 + 0.999986i \(0.501703\pi\)
\(500\) −10.3628 −0.463440
\(501\) −33.1304 −1.48016
\(502\) −48.0569 −2.14488
\(503\) 8.24796 0.367759 0.183879 0.982949i \(-0.441134\pi\)
0.183879 + 0.982949i \(0.441134\pi\)
\(504\) −8.86365 −0.394818
\(505\) 1.20413 0.0535830
\(506\) 22.0299 0.979347
\(507\) −16.4825 −0.732014
\(508\) 53.4184 2.37006
\(509\) 4.01036 0.177756 0.0888780 0.996043i \(-0.471672\pi\)
0.0888780 + 0.996043i \(0.471672\pi\)
\(510\) 1.89784 0.0840376
\(511\) 2.30564 0.101995
\(512\) 47.5194 2.10008
\(513\) −9.38005 −0.414139
\(514\) −58.6793 −2.58823
\(515\) 2.04158 0.0899630
\(516\) −5.31002 −0.233761
\(517\) 54.7124 2.40625
\(518\) −16.1757 −0.710718
\(519\) −37.0606 −1.62678
\(520\) −7.01221 −0.307506
\(521\) 20.9766 0.918999 0.459500 0.888178i \(-0.348029\pi\)
0.459500 + 0.888178i \(0.348029\pi\)
\(522\) −0.441300 −0.0193152
\(523\) 11.8473 0.518048 0.259024 0.965871i \(-0.416599\pi\)
0.259024 + 0.965871i \(0.416599\pi\)
\(524\) 37.3731 1.63265
\(525\) 7.64585 0.333692
\(526\) −43.4501 −1.89451
\(527\) 1.54317 0.0672216
\(528\) −111.176 −4.83833
\(529\) −20.8813 −0.907883
\(530\) 0.0198731 0.000863233 0
\(531\) −5.46658 −0.237229
\(532\) −11.8218 −0.512540
\(533\) 6.99473 0.302975
\(534\) −11.1929 −0.484365
\(535\) −1.43885 −0.0622068
\(536\) −42.4168 −1.83213
\(537\) 40.4587 1.74592
\(538\) 6.24712 0.269333
\(539\) −38.0300 −1.63807
\(540\) 2.73626 0.117750
\(541\) 35.1486 1.51116 0.755578 0.655058i \(-0.227356\pi\)
0.755578 + 0.655058i \(0.227356\pi\)
\(542\) −19.8095 −0.850889
\(543\) 50.3176 2.15934
\(544\) −12.8183 −0.549580
\(545\) −1.95396 −0.0836985
\(546\) 18.1067 0.774895
\(547\) 28.2611 1.20836 0.604180 0.796848i \(-0.293501\pi\)
0.604180 + 0.796848i \(0.293501\pi\)
\(548\) 64.4657 2.75384
\(549\) 14.8243 0.632685
\(550\) 74.9306 3.19505
\(551\) −0.338024 −0.0144003
\(552\) −22.2713 −0.947930
\(553\) −9.23522 −0.392722
\(554\) −37.7779 −1.60503
\(555\) −4.30666 −0.182807
\(556\) 10.2449 0.434479
\(557\) −9.06621 −0.384148 −0.192074 0.981380i \(-0.561521\pi\)
−0.192074 + 0.981380i \(0.561521\pi\)
\(558\) −4.76353 −0.201656
\(559\) 2.33680 0.0988362
\(560\) 1.35559 0.0572840
\(561\) −19.3461 −0.816792
\(562\) −34.2514 −1.44481
\(563\) −31.0160 −1.30717 −0.653583 0.756854i \(-0.726735\pi\)
−0.653583 + 0.756854i \(0.726735\pi\)
\(564\) −96.3112 −4.05543
\(565\) 2.40076 0.101001
\(566\) 15.9129 0.668869
\(567\) −7.86559 −0.330324
\(568\) −72.0399 −3.02273
\(569\) 6.01559 0.252187 0.126093 0.992018i \(-0.459756\pi\)
0.126093 + 0.992018i \(0.459756\pi\)
\(570\) −4.48733 −0.187953
\(571\) −38.1201 −1.59528 −0.797638 0.603137i \(-0.793917\pi\)
−0.797638 + 0.603137i \(0.793917\pi\)
\(572\) 124.465 5.20414
\(573\) −25.3826 −1.06037
\(574\) −2.81657 −0.117561
\(575\) 7.20635 0.300525
\(576\) 8.31757 0.346565
\(577\) −9.22344 −0.383977 −0.191988 0.981397i \(-0.561494\pi\)
−0.191988 + 0.981397i \(0.561494\pi\)
\(578\) 38.0975 1.58465
\(579\) 29.4277 1.22297
\(580\) 0.0986053 0.00409436
\(581\) 4.09213 0.169770
\(582\) 61.7737 2.56060
\(583\) −0.202582 −0.00839008
\(584\) −22.8433 −0.945262
\(585\) 1.80831 0.0747644
\(586\) 73.9938 3.05666
\(587\) −20.0466 −0.827412 −0.413706 0.910411i \(-0.635766\pi\)
−0.413706 + 0.910411i \(0.635766\pi\)
\(588\) 66.9449 2.76076
\(589\) −3.64874 −0.150344
\(590\) 1.74144 0.0716940
\(591\) 55.5179 2.28370
\(592\) 76.9400 3.16222
\(593\) −10.4139 −0.427649 −0.213824 0.976872i \(-0.568592\pi\)
−0.213824 + 0.976872i \(0.568592\pi\)
\(594\) −39.7666 −1.63164
\(595\) 0.235889 0.00967051
\(596\) −27.5081 −1.12678
\(597\) 5.65005 0.231241
\(598\) 17.0659 0.697876
\(599\) 27.2274 1.11248 0.556241 0.831021i \(-0.312243\pi\)
0.556241 + 0.831021i \(0.312243\pi\)
\(600\) −75.7519 −3.09256
\(601\) 15.7871 0.643967 0.321984 0.946745i \(-0.395650\pi\)
0.321984 + 0.946745i \(0.395650\pi\)
\(602\) −0.940962 −0.0383507
\(603\) 10.9384 0.445448
\(604\) 6.28170 0.255599
\(605\) 5.14200 0.209052
\(606\) 30.8052 1.25138
\(607\) −13.9950 −0.568039 −0.284020 0.958818i \(-0.591668\pi\)
−0.284020 + 0.958818i \(0.591668\pi\)
\(608\) 30.3081 1.22916
\(609\) −0.146227 −0.00592541
\(610\) −4.72244 −0.191206
\(611\) 42.3841 1.71468
\(612\) 12.7744 0.516374
\(613\) −12.1958 −0.492585 −0.246293 0.969196i \(-0.579212\pi\)
−0.246293 + 0.969196i \(0.579212\pi\)
\(614\) 56.1882 2.26757
\(615\) −0.749891 −0.0302385
\(616\) −28.7832 −1.15971
\(617\) −5.31506 −0.213976 −0.106988 0.994260i \(-0.534121\pi\)
−0.106988 + 0.994260i \(0.534121\pi\)
\(618\) 52.2299 2.10099
\(619\) 17.3359 0.696789 0.348395 0.937348i \(-0.386727\pi\)
0.348395 + 0.937348i \(0.386727\pi\)
\(620\) 1.06438 0.0427464
\(621\) −3.82449 −0.153472
\(622\) 40.8903 1.63955
\(623\) −1.39121 −0.0557377
\(624\) −86.1250 −3.44776
\(625\) 24.2654 0.970617
\(626\) 31.1123 1.24350
\(627\) 45.7427 1.82679
\(628\) −55.5109 −2.21513
\(629\) 13.3885 0.533836
\(630\) −0.728153 −0.0290103
\(631\) 22.8286 0.908791 0.454395 0.890800i \(-0.349855\pi\)
0.454395 + 0.890800i \(0.349855\pi\)
\(632\) 91.4988 3.63963
\(633\) −43.4797 −1.72816
\(634\) 59.2374 2.35262
\(635\) 2.52025 0.100013
\(636\) 0.356608 0.0141404
\(637\) −29.4607 −1.16728
\(638\) −1.43305 −0.0567349
\(639\) 18.5777 0.734921
\(640\) 1.11400 0.0440347
\(641\) 3.22736 0.127473 0.0637364 0.997967i \(-0.479698\pi\)
0.0637364 + 0.997967i \(0.479698\pi\)
\(642\) −36.8101 −1.45278
\(643\) −2.43874 −0.0961744 −0.0480872 0.998843i \(-0.515313\pi\)
−0.0480872 + 0.998843i \(0.515313\pi\)
\(644\) −4.82006 −0.189937
\(645\) −0.250524 −0.00986438
\(646\) 13.9502 0.548863
\(647\) 24.2512 0.953415 0.476707 0.879062i \(-0.341830\pi\)
0.476707 + 0.879062i \(0.341830\pi\)
\(648\) 77.9290 3.06134
\(649\) −17.7518 −0.696820
\(650\) 58.0465 2.27677
\(651\) −1.57842 −0.0618631
\(652\) −107.037 −4.19188
\(653\) 36.1003 1.41272 0.706358 0.707855i \(-0.250337\pi\)
0.706358 + 0.707855i \(0.250337\pi\)
\(654\) −49.9882 −1.95469
\(655\) 1.76324 0.0688956
\(656\) 13.3971 0.523069
\(657\) 5.89083 0.229823
\(658\) −17.0668 −0.665334
\(659\) −35.2138 −1.37173 −0.685867 0.727727i \(-0.740577\pi\)
−0.685867 + 0.727727i \(0.740577\pi\)
\(660\) −13.3436 −0.519400
\(661\) −20.4794 −0.796557 −0.398278 0.917265i \(-0.630392\pi\)
−0.398278 + 0.917265i \(0.630392\pi\)
\(662\) 44.3728 1.72460
\(663\) −14.9868 −0.582040
\(664\) −40.5431 −1.57338
\(665\) −0.557746 −0.0216285
\(666\) −41.3283 −1.60144
\(667\) −0.137821 −0.00533646
\(668\) 71.0396 2.74860
\(669\) 55.8395 2.15888
\(670\) −3.48456 −0.134620
\(671\) 48.1394 1.85840
\(672\) 13.1111 0.505771
\(673\) 32.7243 1.26143 0.630715 0.776014i \(-0.282762\pi\)
0.630715 + 0.776014i \(0.282762\pi\)
\(674\) 60.8265 2.34295
\(675\) −13.0083 −0.500691
\(676\) 35.3425 1.35933
\(677\) −4.42624 −0.170114 −0.0850571 0.996376i \(-0.527107\pi\)
−0.0850571 + 0.996376i \(0.527107\pi\)
\(678\) 61.4187 2.35877
\(679\) 7.67808 0.294658
\(680\) −2.33709 −0.0896234
\(681\) 53.7967 2.06150
\(682\) −15.4688 −0.592330
\(683\) −11.2770 −0.431503 −0.215752 0.976448i \(-0.569220\pi\)
−0.215752 + 0.976448i \(0.569220\pi\)
\(684\) −30.2043 −1.15489
\(685\) 3.04146 0.116208
\(686\) 24.6322 0.940460
\(687\) −16.0203 −0.611213
\(688\) 4.47571 0.170635
\(689\) −0.156934 −0.00597871
\(690\) −1.82960 −0.0696517
\(691\) 27.2380 1.03618 0.518092 0.855325i \(-0.326643\pi\)
0.518092 + 0.855325i \(0.326643\pi\)
\(692\) 79.4670 3.02088
\(693\) 7.42262 0.281962
\(694\) −26.0811 −0.990023
\(695\) 0.483348 0.0183344
\(696\) 1.44875 0.0549149
\(697\) 2.33126 0.0883029
\(698\) −59.6078 −2.25619
\(699\) −50.3589 −1.90475
\(700\) −16.3946 −0.619656
\(701\) 28.5116 1.07687 0.538433 0.842668i \(-0.319016\pi\)
0.538433 + 0.842668i \(0.319016\pi\)
\(702\) −30.8060 −1.16270
\(703\) −31.6564 −1.19394
\(704\) 27.0099 1.01797
\(705\) −4.54392 −0.171134
\(706\) −27.3767 −1.03034
\(707\) 3.82890 0.144001
\(708\) 31.2488 1.17440
\(709\) −11.5797 −0.434885 −0.217443 0.976073i \(-0.569771\pi\)
−0.217443 + 0.976073i \(0.569771\pi\)
\(710\) −5.91812 −0.222103
\(711\) −23.5957 −0.884908
\(712\) 13.7835 0.516560
\(713\) −1.48769 −0.0557143
\(714\) 6.03476 0.225845
\(715\) 5.87219 0.219607
\(716\) −86.7533 −3.24212
\(717\) −18.8214 −0.702898
\(718\) 35.0437 1.30782
\(719\) 39.8732 1.48702 0.743511 0.668724i \(-0.233159\pi\)
0.743511 + 0.668724i \(0.233159\pi\)
\(720\) 3.46348 0.129076
\(721\) 6.49185 0.241769
\(722\) 16.1893 0.602502
\(723\) 60.8051 2.26137
\(724\) −107.893 −4.00982
\(725\) −0.468775 −0.0174099
\(726\) 131.548 4.88220
\(727\) 32.4888 1.20494 0.602471 0.798141i \(-0.294183\pi\)
0.602471 + 0.798141i \(0.294183\pi\)
\(728\) −22.2975 −0.826400
\(729\) −2.82526 −0.104639
\(730\) −1.87659 −0.0694557
\(731\) 0.778830 0.0288061
\(732\) −84.7406 −3.13210
\(733\) 46.1342 1.70401 0.852003 0.523537i \(-0.175388\pi\)
0.852003 + 0.523537i \(0.175388\pi\)
\(734\) 12.2230 0.451159
\(735\) 3.15843 0.116500
\(736\) 12.3574 0.455501
\(737\) 35.5208 1.30842
\(738\) −7.19625 −0.264898
\(739\) 10.9428 0.402538 0.201269 0.979536i \(-0.435493\pi\)
0.201269 + 0.979536i \(0.435493\pi\)
\(740\) 9.23452 0.339468
\(741\) 35.4355 1.30176
\(742\) 0.0631927 0.00231988
\(743\) −3.56653 −0.130843 −0.0654216 0.997858i \(-0.520839\pi\)
−0.0654216 + 0.997858i \(0.520839\pi\)
\(744\) 15.6383 0.573329
\(745\) −1.29782 −0.0475484
\(746\) −29.7049 −1.08757
\(747\) 10.4553 0.382538
\(748\) 41.4827 1.51676
\(749\) −4.57526 −0.167176
\(750\) −12.5079 −0.456723
\(751\) −15.5350 −0.566879 −0.283439 0.958990i \(-0.591475\pi\)
−0.283439 + 0.958990i \(0.591475\pi\)
\(752\) 81.1788 2.96029
\(753\) −40.6850 −1.48264
\(754\) −1.11014 −0.0404289
\(755\) 0.296367 0.0107859
\(756\) 8.70078 0.316444
\(757\) 1.48658 0.0540306 0.0270153 0.999635i \(-0.491400\pi\)
0.0270153 + 0.999635i \(0.491400\pi\)
\(758\) 14.0806 0.511429
\(759\) 18.6505 0.676971
\(760\) 5.52592 0.200446
\(761\) −19.4897 −0.706501 −0.353251 0.935529i \(-0.614924\pi\)
−0.353251 + 0.935529i \(0.614924\pi\)
\(762\) 64.4757 2.33571
\(763\) −6.21322 −0.224934
\(764\) 54.4265 1.96908
\(765\) 0.602689 0.0217903
\(766\) 9.39051 0.339293
\(767\) −13.7518 −0.496549
\(768\) 48.7396 1.75874
\(769\) −11.8389 −0.426920 −0.213460 0.976952i \(-0.568473\pi\)
−0.213460 + 0.976952i \(0.568473\pi\)
\(770\) −2.36456 −0.0852127
\(771\) −49.6780 −1.78911
\(772\) −63.1001 −2.27102
\(773\) −1.90972 −0.0686879 −0.0343439 0.999410i \(-0.510934\pi\)
−0.0343439 + 0.999410i \(0.510934\pi\)
\(774\) −2.40413 −0.0864146
\(775\) −5.06010 −0.181764
\(776\) −76.0713 −2.73080
\(777\) −13.6943 −0.491282
\(778\) 76.7590 2.75194
\(779\) −5.51214 −0.197493
\(780\) −10.3369 −0.370121
\(781\) 60.3279 2.15870
\(782\) 5.68786 0.203398
\(783\) 0.248784 0.00889082
\(784\) −56.4265 −2.01523
\(785\) −2.61898 −0.0934754
\(786\) 45.1091 1.60899
\(787\) −40.7722 −1.45337 −0.726686 0.686970i \(-0.758940\pi\)
−0.726686 + 0.686970i \(0.758940\pi\)
\(788\) −119.044 −4.24076
\(789\) −36.7849 −1.30958
\(790\) 7.51667 0.267431
\(791\) 7.63395 0.271432
\(792\) −73.5402 −2.61314
\(793\) 37.2921 1.32428
\(794\) −70.6428 −2.50702
\(795\) 0.0168246 0.000596707 0
\(796\) −12.1151 −0.429407
\(797\) 1.20819 0.0427961 0.0213981 0.999771i \(-0.493188\pi\)
0.0213981 + 0.999771i \(0.493188\pi\)
\(798\) −14.2688 −0.505111
\(799\) 14.1261 0.499746
\(800\) 42.0315 1.48604
\(801\) −3.55450 −0.125592
\(802\) −19.1969 −0.677865
\(803\) 19.1295 0.675065
\(804\) −62.5279 −2.20519
\(805\) −0.227408 −0.00801507
\(806\) −11.9832 −0.422090
\(807\) 5.28882 0.186175
\(808\) −37.9351 −1.33455
\(809\) 12.5969 0.442885 0.221442 0.975173i \(-0.428924\pi\)
0.221442 + 0.975173i \(0.428924\pi\)
\(810\) 6.40191 0.224940
\(811\) 5.00382 0.175708 0.0878540 0.996133i \(-0.471999\pi\)
0.0878540 + 0.996133i \(0.471999\pi\)
\(812\) 0.313546 0.0110033
\(813\) −16.7707 −0.588174
\(814\) −134.207 −4.70395
\(815\) −5.04994 −0.176892
\(816\) −28.7045 −1.00486
\(817\) −1.84150 −0.0644259
\(818\) 48.8000 1.70625
\(819\) 5.75008 0.200924
\(820\) 1.60795 0.0561520
\(821\) −13.9475 −0.486772 −0.243386 0.969930i \(-0.578258\pi\)
−0.243386 + 0.969930i \(0.578258\pi\)
\(822\) 77.8098 2.71393
\(823\) −36.4653 −1.27110 −0.635550 0.772059i \(-0.719227\pi\)
−0.635550 + 0.772059i \(0.719227\pi\)
\(824\) −64.3185 −2.24064
\(825\) 63.4364 2.20857
\(826\) 5.53745 0.192672
\(827\) 16.3115 0.567207 0.283604 0.958942i \(-0.408470\pi\)
0.283604 + 0.958942i \(0.408470\pi\)
\(828\) −12.3151 −0.427979
\(829\) −42.4834 −1.47551 −0.737756 0.675068i \(-0.764114\pi\)
−0.737756 + 0.675068i \(0.764114\pi\)
\(830\) −3.33064 −0.115608
\(831\) −31.9828 −1.10947
\(832\) 20.9238 0.725401
\(833\) −9.81893 −0.340206
\(834\) 12.3655 0.428182
\(835\) 3.35161 0.115987
\(836\) −98.0835 −3.39229
\(837\) 2.68545 0.0928229
\(838\) −80.1373 −2.76830
\(839\) 50.1047 1.72981 0.864903 0.501938i \(-0.167380\pi\)
0.864903 + 0.501938i \(0.167380\pi\)
\(840\) 2.39047 0.0824792
\(841\) −28.9910 −0.999691
\(842\) −76.2017 −2.62608
\(843\) −28.9972 −0.998718
\(844\) 93.2311 3.20915
\(845\) 1.66744 0.0573617
\(846\) −43.6052 −1.49918
\(847\) 16.3506 0.561812
\(848\) −0.300578 −0.0103219
\(849\) 13.4719 0.462354
\(850\) 19.3462 0.663571
\(851\) −12.9072 −0.442452
\(852\) −106.196 −3.63822
\(853\) −41.2506 −1.41239 −0.706196 0.708016i \(-0.749590\pi\)
−0.706196 + 0.708016i \(0.749590\pi\)
\(854\) −15.0164 −0.513852
\(855\) −1.42502 −0.0487348
\(856\) 45.3298 1.54934
\(857\) −23.7106 −0.809940 −0.404970 0.914330i \(-0.632718\pi\)
−0.404970 + 0.914330i \(0.632718\pi\)
\(858\) 150.228 5.12871
\(859\) 51.1339 1.74467 0.872333 0.488913i \(-0.162606\pi\)
0.872333 + 0.488913i \(0.162606\pi\)
\(860\) 0.537185 0.0183178
\(861\) −2.38451 −0.0812639
\(862\) −1.46869 −0.0500237
\(863\) 34.2499 1.16588 0.582941 0.812515i \(-0.301902\pi\)
0.582941 + 0.812515i \(0.301902\pi\)
\(864\) −22.3066 −0.758887
\(865\) 3.74921 0.127477
\(866\) 57.6568 1.95926
\(867\) 32.2534 1.09538
\(868\) 3.38451 0.114878
\(869\) −76.6232 −2.59926
\(870\) 0.119016 0.00403502
\(871\) 27.5169 0.932374
\(872\) 61.5580 2.08462
\(873\) 19.6173 0.663944
\(874\) −13.4486 −0.454907
\(875\) −1.55465 −0.0525568
\(876\) −33.6740 −1.13774
\(877\) 51.5335 1.74016 0.870081 0.492910i \(-0.164067\pi\)
0.870081 + 0.492910i \(0.164067\pi\)
\(878\) −64.7394 −2.18485
\(879\) 62.6433 2.11290
\(880\) 11.2471 0.379139
\(881\) −38.2008 −1.28702 −0.643510 0.765438i \(-0.722522\pi\)
−0.643510 + 0.765438i \(0.722522\pi\)
\(882\) 30.3095 1.02057
\(883\) 29.9756 1.00876 0.504380 0.863482i \(-0.331721\pi\)
0.504380 + 0.863482i \(0.331721\pi\)
\(884\) 32.1354 1.08083
\(885\) 1.47431 0.0495582
\(886\) −22.9597 −0.771348
\(887\) −55.8702 −1.87594 −0.937968 0.346721i \(-0.887295\pi\)
−0.937968 + 0.346721i \(0.887295\pi\)
\(888\) 135.678 4.55305
\(889\) 8.01393 0.268779
\(890\) 1.13232 0.0379556
\(891\) −65.2595 −2.18628
\(892\) −119.733 −4.00897
\(893\) −33.4004 −1.11770
\(894\) −33.2022 −1.11045
\(895\) −4.09298 −0.136813
\(896\) 3.54231 0.118340
\(897\) 14.4480 0.482404
\(898\) 64.2687 2.14467
\(899\) 0.0967744 0.00322761
\(900\) −41.8876 −1.39625
\(901\) −0.0523043 −0.00174251
\(902\) −23.3686 −0.778090
\(903\) −0.796619 −0.0265098
\(904\) −75.6340 −2.51555
\(905\) −5.09035 −0.169209
\(906\) 7.58197 0.251894
\(907\) 32.0009 1.06257 0.531286 0.847193i \(-0.321709\pi\)
0.531286 + 0.847193i \(0.321709\pi\)
\(908\) −115.353 −3.82813
\(909\) 9.78271 0.324472
\(910\) −1.83175 −0.0607220
\(911\) 29.0415 0.962189 0.481094 0.876669i \(-0.340239\pi\)
0.481094 + 0.876669i \(0.340239\pi\)
\(912\) 67.8701 2.24740
\(913\) 33.9517 1.12364
\(914\) 24.9171 0.824184
\(915\) −3.99802 −0.132170
\(916\) 34.3514 1.13500
\(917\) 5.60678 0.185152
\(918\) −10.2673 −0.338871
\(919\) −4.72429 −0.155840 −0.0779200 0.996960i \(-0.524828\pi\)
−0.0779200 + 0.996960i \(0.524828\pi\)
\(920\) 2.25306 0.0742813
\(921\) 47.5690 1.56745
\(922\) 35.2031 1.15935
\(923\) 46.7342 1.53827
\(924\) −42.4302 −1.39585
\(925\) −43.9014 −1.44347
\(926\) −61.9179 −2.03475
\(927\) 16.5865 0.544771
\(928\) −0.803853 −0.0263878
\(929\) −30.8910 −1.01350 −0.506751 0.862093i \(-0.669153\pi\)
−0.506751 + 0.862093i \(0.669153\pi\)
\(930\) 1.28470 0.0421269
\(931\) 23.2163 0.760883
\(932\) 107.982 3.53706
\(933\) 34.6178 1.13333
\(934\) −67.3803 −2.20475
\(935\) 1.95713 0.0640051
\(936\) −56.9694 −1.86210
\(937\) −25.3378 −0.827750 −0.413875 0.910334i \(-0.635825\pi\)
−0.413875 + 0.910334i \(0.635825\pi\)
\(938\) −11.0802 −0.361783
\(939\) 26.3397 0.859562
\(940\) 9.74326 0.317790
\(941\) −47.0802 −1.53477 −0.767385 0.641187i \(-0.778442\pi\)
−0.767385 + 0.641187i \(0.778442\pi\)
\(942\) −67.0014 −2.18302
\(943\) −2.24744 −0.0731868
\(944\) −26.3390 −0.857262
\(945\) 0.410499 0.0133535
\(946\) −7.80701 −0.253828
\(947\) 0.217403 0.00706465 0.00353232 0.999994i \(-0.498876\pi\)
0.00353232 + 0.999994i \(0.498876\pi\)
\(948\) 134.881 4.38073
\(949\) 14.8190 0.481047
\(950\) −45.7431 −1.48410
\(951\) 50.1505 1.62624
\(952\) −7.43150 −0.240856
\(953\) 4.28728 0.138879 0.0694393 0.997586i \(-0.477879\pi\)
0.0694393 + 0.997586i \(0.477879\pi\)
\(954\) 0.161455 0.00522731
\(955\) 2.56781 0.0830925
\(956\) 40.3576 1.30526
\(957\) −1.21322 −0.0392178
\(958\) −82.5975 −2.66860
\(959\) 9.67127 0.312301
\(960\) −2.24320 −0.0723989
\(961\) −29.9554 −0.966303
\(962\) −103.966 −3.35200
\(963\) −11.6896 −0.376694
\(964\) −130.381 −4.19929
\(965\) −2.97703 −0.0958340
\(966\) −5.81778 −0.187184
\(967\) 5.40073 0.173676 0.0868378 0.996222i \(-0.472324\pi\)
0.0868378 + 0.996222i \(0.472324\pi\)
\(968\) −161.995 −5.20670
\(969\) 11.8103 0.379400
\(970\) −6.24930 −0.200653
\(971\) −6.58018 −0.211168 −0.105584 0.994410i \(-0.533671\pi\)
−0.105584 + 0.994410i \(0.533671\pi\)
\(972\) 77.8441 2.49685
\(973\) 1.53695 0.0492724
\(974\) 1.21824 0.0390351
\(975\) 49.1422 1.57381
\(976\) 71.4261 2.28630
\(977\) −18.6673 −0.597219 −0.298609 0.954375i \(-0.596523\pi\)
−0.298609 + 0.954375i \(0.596523\pi\)
\(978\) −129.193 −4.13113
\(979\) −11.5426 −0.368905
\(980\) −6.77244 −0.216338
\(981\) −15.8746 −0.506836
\(982\) −41.2280 −1.31564
\(983\) 16.4237 0.523835 0.261918 0.965090i \(-0.415645\pi\)
0.261918 + 0.965090i \(0.415645\pi\)
\(984\) 23.6247 0.753129
\(985\) −5.61643 −0.178954
\(986\) −0.369997 −0.0117831
\(987\) −14.4488 −0.459910
\(988\) −75.9823 −2.41732
\(989\) −0.750827 −0.0238749
\(990\) −6.04137 −0.192007
\(991\) 25.8923 0.822495 0.411248 0.911524i \(-0.365093\pi\)
0.411248 + 0.911524i \(0.365093\pi\)
\(992\) −8.67705 −0.275497
\(993\) 37.5661 1.19212
\(994\) −18.8185 −0.596886
\(995\) −0.571583 −0.0181204
\(996\) −59.7658 −1.89375
\(997\) 14.3871 0.455645 0.227822 0.973703i \(-0.426839\pi\)
0.227822 + 0.973703i \(0.426839\pi\)
\(998\) 0.618508 0.0195785
\(999\) 23.2990 0.737147
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 6037.2.a.b.1.9 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.9 259 1.1 even 1 trivial