Properties

Label 6037.2.a.b.1.3
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 1.3
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65823 q^{2} -1.47107 q^{3} +5.06620 q^{4} -0.123247 q^{5} +3.91044 q^{6} -2.04180 q^{7} -8.15068 q^{8} -0.835960 q^{9} +O(q^{10})\) \(q-2.65823 q^{2} -1.47107 q^{3} +5.06620 q^{4} -0.123247 q^{5} +3.91044 q^{6} -2.04180 q^{7} -8.15068 q^{8} -0.835960 q^{9} +0.327620 q^{10} -1.27617 q^{11} -7.45273 q^{12} +1.33307 q^{13} +5.42757 q^{14} +0.181305 q^{15} +11.5340 q^{16} +2.50462 q^{17} +2.22218 q^{18} -0.794015 q^{19} -0.624396 q^{20} +3.00362 q^{21} +3.39235 q^{22} +6.36334 q^{23} +11.9902 q^{24} -4.98481 q^{25} -3.54361 q^{26} +5.64296 q^{27} -10.3442 q^{28} +5.26622 q^{29} -0.481951 q^{30} +4.00337 q^{31} -14.3587 q^{32} +1.87733 q^{33} -6.65786 q^{34} +0.251646 q^{35} -4.23514 q^{36} +6.53938 q^{37} +2.11068 q^{38} -1.96103 q^{39} +1.00455 q^{40} +5.59187 q^{41} -7.98432 q^{42} +9.30737 q^{43} -6.46532 q^{44} +0.103030 q^{45} -16.9152 q^{46} -1.09584 q^{47} -16.9673 q^{48} -2.83107 q^{49} +13.2508 q^{50} -3.68446 q^{51} +6.75360 q^{52} -3.14381 q^{53} -15.0003 q^{54} +0.157284 q^{55} +16.6420 q^{56} +1.16805 q^{57} -13.9988 q^{58} -8.64986 q^{59} +0.918528 q^{60} -13.0794 q^{61} -10.6419 q^{62} +1.70686 q^{63} +15.1008 q^{64} -0.164297 q^{65} -4.99038 q^{66} -7.37724 q^{67} +12.6889 q^{68} -9.36090 q^{69} -0.668933 q^{70} +3.68520 q^{71} +6.81364 q^{72} -12.4700 q^{73} -17.3832 q^{74} +7.33299 q^{75} -4.02264 q^{76} +2.60567 q^{77} +5.21289 q^{78} +10.4393 q^{79} -1.42154 q^{80} -5.79329 q^{81} -14.8645 q^{82} -2.55002 q^{83} +15.2169 q^{84} -0.308687 q^{85} -24.7412 q^{86} -7.74696 q^{87} +10.4016 q^{88} -4.05771 q^{89} -0.273877 q^{90} -2.72185 q^{91} +32.2380 q^{92} -5.88923 q^{93} +2.91300 q^{94} +0.0978602 q^{95} +21.1226 q^{96} +11.8973 q^{97} +7.52565 q^{98} +1.06682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65823 −1.87965 −0.939827 0.341650i \(-0.889014\pi\)
−0.939827 + 0.341650i \(0.889014\pi\)
\(3\) −1.47107 −0.849321 −0.424661 0.905353i \(-0.639607\pi\)
−0.424661 + 0.905353i \(0.639607\pi\)
\(4\) 5.06620 2.53310
\(5\) −0.123247 −0.0551179 −0.0275589 0.999620i \(-0.508773\pi\)
−0.0275589 + 0.999620i \(0.508773\pi\)
\(6\) 3.91044 1.59643
\(7\) −2.04180 −0.771726 −0.385863 0.922556i \(-0.626096\pi\)
−0.385863 + 0.922556i \(0.626096\pi\)
\(8\) −8.15068 −2.88170
\(9\) −0.835960 −0.278653
\(10\) 0.327620 0.103603
\(11\) −1.27617 −0.384779 −0.192389 0.981319i \(-0.561624\pi\)
−0.192389 + 0.981319i \(0.561624\pi\)
\(12\) −7.45273 −2.15142
\(13\) 1.33307 0.369727 0.184863 0.982764i \(-0.440816\pi\)
0.184863 + 0.982764i \(0.440816\pi\)
\(14\) 5.42757 1.45058
\(15\) 0.181305 0.0468128
\(16\) 11.5340 2.88350
\(17\) 2.50462 0.607459 0.303730 0.952758i \(-0.401768\pi\)
0.303730 + 0.952758i \(0.401768\pi\)
\(18\) 2.22218 0.523772
\(19\) −0.794015 −0.182160 −0.0910798 0.995844i \(-0.529032\pi\)
−0.0910798 + 0.995844i \(0.529032\pi\)
\(20\) −0.624396 −0.139619
\(21\) 3.00362 0.655443
\(22\) 3.39235 0.723251
\(23\) 6.36334 1.32685 0.663424 0.748244i \(-0.269103\pi\)
0.663424 + 0.748244i \(0.269103\pi\)
\(24\) 11.9902 2.44749
\(25\) −4.98481 −0.996962
\(26\) −3.54361 −0.694959
\(27\) 5.64296 1.08599
\(28\) −10.3442 −1.95486
\(29\) 5.26622 0.977912 0.488956 0.872309i \(-0.337378\pi\)
0.488956 + 0.872309i \(0.337378\pi\)
\(30\) −0.481951 −0.0879918
\(31\) 4.00337 0.719026 0.359513 0.933140i \(-0.382943\pi\)
0.359513 + 0.933140i \(0.382943\pi\)
\(32\) −14.3587 −2.53829
\(33\) 1.87733 0.326801
\(34\) −6.65786 −1.14181
\(35\) 0.251646 0.0425359
\(36\) −4.23514 −0.705857
\(37\) 6.53938 1.07507 0.537534 0.843242i \(-0.319356\pi\)
0.537534 + 0.843242i \(0.319356\pi\)
\(38\) 2.11068 0.342397
\(39\) −1.96103 −0.314017
\(40\) 1.00455 0.158833
\(41\) 5.59187 0.873303 0.436652 0.899631i \(-0.356164\pi\)
0.436652 + 0.899631i \(0.356164\pi\)
\(42\) −7.98432 −1.23201
\(43\) 9.30737 1.41936 0.709680 0.704524i \(-0.248839\pi\)
0.709680 + 0.704524i \(0.248839\pi\)
\(44\) −6.46532 −0.974684
\(45\) 0.103030 0.0153588
\(46\) −16.9152 −2.49402
\(47\) −1.09584 −0.159845 −0.0799224 0.996801i \(-0.525467\pi\)
−0.0799224 + 0.996801i \(0.525467\pi\)
\(48\) −16.9673 −2.44902
\(49\) −2.83107 −0.404439
\(50\) 13.2508 1.87394
\(51\) −3.68446 −0.515928
\(52\) 6.75360 0.936556
\(53\) −3.14381 −0.431836 −0.215918 0.976412i \(-0.569274\pi\)
−0.215918 + 0.976412i \(0.569274\pi\)
\(54\) −15.0003 −2.04128
\(55\) 0.157284 0.0212082
\(56\) 16.6420 2.22388
\(57\) 1.16805 0.154712
\(58\) −13.9988 −1.83814
\(59\) −8.64986 −1.12612 −0.563058 0.826418i \(-0.690375\pi\)
−0.563058 + 0.826418i \(0.690375\pi\)
\(60\) 0.918528 0.118581
\(61\) −13.0794 −1.67465 −0.837325 0.546705i \(-0.815882\pi\)
−0.837325 + 0.546705i \(0.815882\pi\)
\(62\) −10.6419 −1.35152
\(63\) 1.70686 0.215044
\(64\) 15.1008 1.88760
\(65\) −0.164297 −0.0203786
\(66\) −4.99038 −0.614273
\(67\) −7.37724 −0.901274 −0.450637 0.892707i \(-0.648803\pi\)
−0.450637 + 0.892707i \(0.648803\pi\)
\(68\) 12.6889 1.53876
\(69\) −9.36090 −1.12692
\(70\) −0.668933 −0.0799528
\(71\) 3.68520 0.437353 0.218677 0.975797i \(-0.429826\pi\)
0.218677 + 0.975797i \(0.429826\pi\)
\(72\) 6.81364 0.802996
\(73\) −12.4700 −1.45950 −0.729752 0.683712i \(-0.760364\pi\)
−0.729752 + 0.683712i \(0.760364\pi\)
\(74\) −17.3832 −2.02076
\(75\) 7.33299 0.846741
\(76\) −4.02264 −0.461429
\(77\) 2.60567 0.296944
\(78\) 5.21289 0.590243
\(79\) 10.4393 1.17451 0.587256 0.809401i \(-0.300208\pi\)
0.587256 + 0.809401i \(0.300208\pi\)
\(80\) −1.42154 −0.158932
\(81\) −5.79329 −0.643699
\(82\) −14.8645 −1.64151
\(83\) −2.55002 −0.279901 −0.139950 0.990159i \(-0.544694\pi\)
−0.139950 + 0.990159i \(0.544694\pi\)
\(84\) 15.2169 1.66030
\(85\) −0.308687 −0.0334818
\(86\) −24.7412 −2.66791
\(87\) −7.74696 −0.830561
\(88\) 10.4016 1.10882
\(89\) −4.05771 −0.430117 −0.215058 0.976601i \(-0.568994\pi\)
−0.215058 + 0.976601i \(0.568994\pi\)
\(90\) −0.273877 −0.0288692
\(91\) −2.72185 −0.285328
\(92\) 32.2380 3.36104
\(93\) −5.88923 −0.610684
\(94\) 2.91300 0.300453
\(95\) 0.0978602 0.0100402
\(96\) 21.1226 2.15582
\(97\) 11.8973 1.20798 0.603992 0.796990i \(-0.293576\pi\)
0.603992 + 0.796990i \(0.293576\pi\)
\(98\) 7.52565 0.760205
\(99\) 1.06682 0.107220
\(100\) −25.2541 −2.52541
\(101\) 14.0613 1.39915 0.699574 0.714560i \(-0.253373\pi\)
0.699574 + 0.714560i \(0.253373\pi\)
\(102\) 9.79416 0.969766
\(103\) −8.63753 −0.851082 −0.425541 0.904939i \(-0.639916\pi\)
−0.425541 + 0.904939i \(0.639916\pi\)
\(104\) −10.8654 −1.06544
\(105\) −0.370188 −0.0361266
\(106\) 8.35698 0.811702
\(107\) −7.53328 −0.728270 −0.364135 0.931346i \(-0.618635\pi\)
−0.364135 + 0.931346i \(0.618635\pi\)
\(108\) 28.5884 2.75092
\(109\) −10.7117 −1.02599 −0.512997 0.858391i \(-0.671465\pi\)
−0.512997 + 0.858391i \(0.671465\pi\)
\(110\) −0.418098 −0.0398641
\(111\) −9.61987 −0.913078
\(112\) −23.5501 −2.22527
\(113\) 5.82344 0.547823 0.273911 0.961755i \(-0.411682\pi\)
0.273911 + 0.961755i \(0.411682\pi\)
\(114\) −3.10495 −0.290805
\(115\) −0.784264 −0.0731330
\(116\) 26.6797 2.47715
\(117\) −1.11439 −0.103026
\(118\) 22.9933 2.11671
\(119\) −5.11392 −0.468792
\(120\) −1.47776 −0.134900
\(121\) −9.37140 −0.851945
\(122\) 34.7682 3.14776
\(123\) −8.22602 −0.741715
\(124\) 20.2819 1.82137
\(125\) 1.23060 0.110068
\(126\) −4.53723 −0.404209
\(127\) 2.17453 0.192958 0.0964791 0.995335i \(-0.469242\pi\)
0.0964791 + 0.995335i \(0.469242\pi\)
\(128\) −11.4240 −1.00975
\(129\) −13.6918 −1.20549
\(130\) 0.436740 0.0383046
\(131\) −12.7862 −1.11714 −0.558568 0.829459i \(-0.688649\pi\)
−0.558568 + 0.829459i \(0.688649\pi\)
\(132\) 9.51093 0.827820
\(133\) 1.62122 0.140577
\(134\) 19.6104 1.69408
\(135\) −0.695479 −0.0598573
\(136\) −20.4143 −1.75052
\(137\) 2.25089 0.192307 0.0961534 0.995367i \(-0.469346\pi\)
0.0961534 + 0.995367i \(0.469346\pi\)
\(138\) 24.8835 2.11822
\(139\) −21.9323 −1.86027 −0.930135 0.367218i \(-0.880310\pi\)
−0.930135 + 0.367218i \(0.880310\pi\)
\(140\) 1.27489 0.107748
\(141\) 1.61206 0.135760
\(142\) −9.79613 −0.822073
\(143\) −1.70122 −0.142263
\(144\) −9.64197 −0.803498
\(145\) −0.649047 −0.0539004
\(146\) 33.1482 2.74336
\(147\) 4.16470 0.343498
\(148\) 33.1298 2.72326
\(149\) 17.5974 1.44163 0.720817 0.693125i \(-0.243767\pi\)
0.720817 + 0.693125i \(0.243767\pi\)
\(150\) −19.4928 −1.59158
\(151\) −4.93173 −0.401339 −0.200669 0.979659i \(-0.564312\pi\)
−0.200669 + 0.979659i \(0.564312\pi\)
\(152\) 6.47177 0.524930
\(153\) −2.09376 −0.169270
\(154\) −6.92648 −0.558152
\(155\) −0.493404 −0.0396312
\(156\) −9.93500 −0.795437
\(157\) 14.2892 1.14040 0.570201 0.821505i \(-0.306865\pi\)
0.570201 + 0.821505i \(0.306865\pi\)
\(158\) −27.7501 −2.20768
\(159\) 4.62476 0.366767
\(160\) 1.76967 0.139905
\(161\) −12.9926 −1.02396
\(162\) 15.3999 1.20993
\(163\) 22.8863 1.79260 0.896298 0.443451i \(-0.146246\pi\)
0.896298 + 0.443451i \(0.146246\pi\)
\(164\) 28.3295 2.21217
\(165\) −0.231376 −0.0180126
\(166\) 6.77854 0.526117
\(167\) −6.70468 −0.518824 −0.259412 0.965767i \(-0.583529\pi\)
−0.259412 + 0.965767i \(0.583529\pi\)
\(168\) −24.4815 −1.88879
\(169\) −11.2229 −0.863302
\(170\) 0.820563 0.0629343
\(171\) 0.663765 0.0507594
\(172\) 47.1530 3.59538
\(173\) 1.94342 0.147755 0.0738777 0.997267i \(-0.476463\pi\)
0.0738777 + 0.997267i \(0.476463\pi\)
\(174\) 20.5932 1.56117
\(175\) 10.1780 0.769382
\(176\) −14.7193 −1.10951
\(177\) 12.7245 0.956434
\(178\) 10.7863 0.808471
\(179\) 21.5858 1.61340 0.806698 0.590965i \(-0.201253\pi\)
0.806698 + 0.590965i \(0.201253\pi\)
\(180\) 0.521970 0.0389053
\(181\) −4.25783 −0.316482 −0.158241 0.987400i \(-0.550582\pi\)
−0.158241 + 0.987400i \(0.550582\pi\)
\(182\) 7.23532 0.536318
\(183\) 19.2407 1.42232
\(184\) −51.8656 −3.82358
\(185\) −0.805961 −0.0592554
\(186\) 15.6549 1.14788
\(187\) −3.19631 −0.233737
\(188\) −5.55175 −0.404903
\(189\) −11.5218 −0.838085
\(190\) −0.260135 −0.0188722
\(191\) 13.2374 0.957824 0.478912 0.877863i \(-0.341031\pi\)
0.478912 + 0.877863i \(0.341031\pi\)
\(192\) −22.2143 −1.60318
\(193\) 14.8525 1.06911 0.534554 0.845134i \(-0.320480\pi\)
0.534554 + 0.845134i \(0.320480\pi\)
\(194\) −31.6257 −2.27059
\(195\) 0.241692 0.0173079
\(196\) −14.3428 −1.02448
\(197\) 22.4429 1.59899 0.799494 0.600674i \(-0.205101\pi\)
0.799494 + 0.600674i \(0.205101\pi\)
\(198\) −2.83587 −0.201536
\(199\) −10.4590 −0.741422 −0.370711 0.928748i \(-0.620886\pi\)
−0.370711 + 0.928748i \(0.620886\pi\)
\(200\) 40.6296 2.87295
\(201\) 10.8524 0.765471
\(202\) −37.3781 −2.62992
\(203\) −10.7525 −0.754680
\(204\) −18.6662 −1.30690
\(205\) −0.689183 −0.0481346
\(206\) 22.9606 1.59974
\(207\) −5.31950 −0.369731
\(208\) 15.3756 1.06611
\(209\) 1.01330 0.0700912
\(210\) 0.984046 0.0679056
\(211\) −12.2074 −0.840390 −0.420195 0.907434i \(-0.638038\pi\)
−0.420195 + 0.907434i \(0.638038\pi\)
\(212\) −15.9272 −1.09388
\(213\) −5.42118 −0.371453
\(214\) 20.0252 1.36890
\(215\) −1.14711 −0.0782321
\(216\) −45.9940 −3.12949
\(217\) −8.17406 −0.554891
\(218\) 28.4742 1.92851
\(219\) 18.3442 1.23959
\(220\) 0.796833 0.0537225
\(221\) 3.33883 0.224594
\(222\) 25.5719 1.71627
\(223\) 3.99085 0.267247 0.133624 0.991032i \(-0.457339\pi\)
0.133624 + 0.991032i \(0.457339\pi\)
\(224\) 29.3176 1.95886
\(225\) 4.16710 0.277807
\(226\) −15.4801 −1.02972
\(227\) 23.1676 1.53769 0.768844 0.639437i \(-0.220832\pi\)
0.768844 + 0.639437i \(0.220832\pi\)
\(228\) 5.91758 0.391901
\(229\) −14.5876 −0.963973 −0.481986 0.876179i \(-0.660085\pi\)
−0.481986 + 0.876179i \(0.660085\pi\)
\(230\) 2.08476 0.137465
\(231\) −3.83312 −0.252201
\(232\) −42.9233 −2.81805
\(233\) −22.0413 −1.44398 −0.721988 0.691906i \(-0.756771\pi\)
−0.721988 + 0.691906i \(0.756771\pi\)
\(234\) 2.96232 0.193653
\(235\) 0.135059 0.00881030
\(236\) −43.8219 −2.85256
\(237\) −15.3569 −0.997538
\(238\) 13.5940 0.881167
\(239\) −2.97495 −0.192433 −0.0962167 0.995360i \(-0.530674\pi\)
−0.0962167 + 0.995360i \(0.530674\pi\)
\(240\) 2.09117 0.134985
\(241\) −6.97510 −0.449306 −0.224653 0.974439i \(-0.572125\pi\)
−0.224653 + 0.974439i \(0.572125\pi\)
\(242\) 24.9114 1.60136
\(243\) −8.40655 −0.539280
\(244\) −66.2631 −4.24206
\(245\) 0.348922 0.0222918
\(246\) 21.8667 1.39417
\(247\) −1.05848 −0.0673493
\(248\) −32.6302 −2.07202
\(249\) 3.75125 0.237726
\(250\) −3.27122 −0.206890
\(251\) −13.5245 −0.853658 −0.426829 0.904332i \(-0.640369\pi\)
−0.426829 + 0.904332i \(0.640369\pi\)
\(252\) 8.64730 0.544728
\(253\) −8.12068 −0.510543
\(254\) −5.78040 −0.362695
\(255\) 0.454100 0.0284368
\(256\) 0.166096 0.0103810
\(257\) −7.74036 −0.482830 −0.241415 0.970422i \(-0.577612\pi\)
−0.241415 + 0.970422i \(0.577612\pi\)
\(258\) 36.3959 2.26591
\(259\) −13.3521 −0.829658
\(260\) −0.832363 −0.0516209
\(261\) −4.40235 −0.272498
\(262\) 33.9887 2.09983
\(263\) −5.46077 −0.336726 −0.168363 0.985725i \(-0.553848\pi\)
−0.168363 + 0.985725i \(0.553848\pi\)
\(264\) −15.3015 −0.941743
\(265\) 0.387466 0.0238019
\(266\) −4.30957 −0.264237
\(267\) 5.96917 0.365307
\(268\) −37.3746 −2.28302
\(269\) −5.03875 −0.307218 −0.153609 0.988132i \(-0.549090\pi\)
−0.153609 + 0.988132i \(0.549090\pi\)
\(270\) 1.84875 0.112511
\(271\) 28.3921 1.72470 0.862349 0.506314i \(-0.168992\pi\)
0.862349 + 0.506314i \(0.168992\pi\)
\(272\) 28.8883 1.75161
\(273\) 4.00403 0.242335
\(274\) −5.98340 −0.361470
\(275\) 6.36145 0.383610
\(276\) −47.4242 −2.85460
\(277\) −16.2218 −0.974673 −0.487337 0.873214i \(-0.662032\pi\)
−0.487337 + 0.873214i \(0.662032\pi\)
\(278\) 58.3011 3.49666
\(279\) −3.34666 −0.200359
\(280\) −2.05108 −0.122576
\(281\) −10.6618 −0.636031 −0.318016 0.948085i \(-0.603016\pi\)
−0.318016 + 0.948085i \(0.603016\pi\)
\(282\) −4.28522 −0.255181
\(283\) −11.0767 −0.658443 −0.329222 0.944253i \(-0.606786\pi\)
−0.329222 + 0.944253i \(0.606786\pi\)
\(284\) 18.6700 1.10786
\(285\) −0.143959 −0.00852740
\(286\) 4.52224 0.267406
\(287\) −11.4175 −0.673951
\(288\) 12.0033 0.707302
\(289\) −10.7269 −0.630993
\(290\) 1.72532 0.101314
\(291\) −17.5017 −1.02597
\(292\) −63.1756 −3.69707
\(293\) 16.2931 0.951853 0.475926 0.879485i \(-0.342113\pi\)
0.475926 + 0.879485i \(0.342113\pi\)
\(294\) −11.0707 −0.645659
\(295\) 1.06607 0.0620691
\(296\) −53.3004 −3.09802
\(297\) −7.20136 −0.417865
\(298\) −46.7780 −2.70977
\(299\) 8.48277 0.490571
\(300\) 37.1504 2.14488
\(301\) −19.0037 −1.09536
\(302\) 13.1097 0.754378
\(303\) −20.6851 −1.18833
\(304\) −9.15818 −0.525258
\(305\) 1.61200 0.0923031
\(306\) 5.56570 0.318170
\(307\) −6.26009 −0.357282 −0.178641 0.983914i \(-0.557170\pi\)
−0.178641 + 0.983914i \(0.557170\pi\)
\(308\) 13.2009 0.752189
\(309\) 12.7064 0.722842
\(310\) 1.31158 0.0744929
\(311\) −6.34983 −0.360066 −0.180033 0.983661i \(-0.557620\pi\)
−0.180033 + 0.983661i \(0.557620\pi\)
\(312\) 15.9838 0.904903
\(313\) −12.4130 −0.701624 −0.350812 0.936446i \(-0.614094\pi\)
−0.350812 + 0.936446i \(0.614094\pi\)
\(314\) −37.9840 −2.14356
\(315\) −0.210366 −0.0118528
\(316\) 52.8876 2.97516
\(317\) −12.7675 −0.717095 −0.358548 0.933511i \(-0.616728\pi\)
−0.358548 + 0.933511i \(0.616728\pi\)
\(318\) −12.2937 −0.689396
\(319\) −6.72057 −0.376280
\(320\) −1.86113 −0.104040
\(321\) 11.0820 0.618535
\(322\) 34.5375 1.92470
\(323\) −1.98871 −0.110655
\(324\) −29.3500 −1.63055
\(325\) −6.64510 −0.368604
\(326\) −60.8372 −3.36946
\(327\) 15.7576 0.871398
\(328\) −45.5776 −2.51660
\(329\) 2.23748 0.123356
\(330\) 0.615050 0.0338574
\(331\) 12.9665 0.712705 0.356352 0.934352i \(-0.384020\pi\)
0.356352 + 0.934352i \(0.384020\pi\)
\(332\) −12.9189 −0.709017
\(333\) −5.46666 −0.299571
\(334\) 17.8226 0.975210
\(335\) 0.909225 0.0496763
\(336\) 34.6438 1.88997
\(337\) 30.2355 1.64703 0.823517 0.567292i \(-0.192009\pi\)
0.823517 + 0.567292i \(0.192009\pi\)
\(338\) 29.8332 1.62271
\(339\) −8.56667 −0.465278
\(340\) −1.56387 −0.0848129
\(341\) −5.10897 −0.276666
\(342\) −1.76444 −0.0954101
\(343\) 20.0730 1.08384
\(344\) −75.8614 −4.09017
\(345\) 1.15371 0.0621134
\(346\) −5.16606 −0.277729
\(347\) 7.18036 0.385462 0.192731 0.981252i \(-0.438266\pi\)
0.192731 + 0.981252i \(0.438266\pi\)
\(348\) −39.2477 −2.10390
\(349\) 26.1025 1.39724 0.698618 0.715495i \(-0.253799\pi\)
0.698618 + 0.715495i \(0.253799\pi\)
\(350\) −27.0554 −1.44617
\(351\) 7.52245 0.401519
\(352\) 18.3241 0.976679
\(353\) −3.78779 −0.201604 −0.100802 0.994907i \(-0.532141\pi\)
−0.100802 + 0.994907i \(0.532141\pi\)
\(354\) −33.8247 −1.79776
\(355\) −0.454191 −0.0241060
\(356\) −20.5572 −1.08953
\(357\) 7.52292 0.398155
\(358\) −57.3800 −3.03263
\(359\) 30.1551 1.59152 0.795762 0.605609i \(-0.207070\pi\)
0.795762 + 0.605609i \(0.207070\pi\)
\(360\) −0.839763 −0.0442594
\(361\) −18.3695 −0.966818
\(362\) 11.3183 0.594878
\(363\) 13.7860 0.723575
\(364\) −13.7895 −0.722765
\(365\) 1.53689 0.0804447
\(366\) −51.1464 −2.67346
\(367\) −2.14491 −0.111963 −0.0559817 0.998432i \(-0.517829\pi\)
−0.0559817 + 0.998432i \(0.517829\pi\)
\(368\) 73.3948 3.82597
\(369\) −4.67458 −0.243349
\(370\) 2.14243 0.111380
\(371\) 6.41902 0.333259
\(372\) −29.8360 −1.54693
\(373\) −17.4326 −0.902628 −0.451314 0.892365i \(-0.649045\pi\)
−0.451314 + 0.892365i \(0.649045\pi\)
\(374\) 8.49654 0.439346
\(375\) −1.81030 −0.0934833
\(376\) 8.93185 0.460625
\(377\) 7.02023 0.361560
\(378\) 30.6275 1.57531
\(379\) 14.8171 0.761102 0.380551 0.924760i \(-0.375734\pi\)
0.380551 + 0.924760i \(0.375734\pi\)
\(380\) 0.495780 0.0254330
\(381\) −3.19888 −0.163884
\(382\) −35.1881 −1.80038
\(383\) 32.0701 1.63871 0.819353 0.573289i \(-0.194333\pi\)
0.819353 + 0.573289i \(0.194333\pi\)
\(384\) 16.8055 0.857602
\(385\) −0.321142 −0.0163669
\(386\) −39.4815 −2.00955
\(387\) −7.78059 −0.395509
\(388\) 60.2740 3.05995
\(389\) −30.4168 −1.54219 −0.771097 0.636718i \(-0.780292\pi\)
−0.771097 + 0.636718i \(0.780292\pi\)
\(390\) −0.642474 −0.0325329
\(391\) 15.9377 0.806006
\(392\) 23.0752 1.16547
\(393\) 18.8094 0.948808
\(394\) −59.6584 −3.00554
\(395\) −1.28661 −0.0647366
\(396\) 5.40475 0.271599
\(397\) 30.6312 1.53733 0.768667 0.639650i \(-0.220920\pi\)
0.768667 + 0.639650i \(0.220920\pi\)
\(398\) 27.8026 1.39362
\(399\) −2.38492 −0.119395
\(400\) −57.4948 −2.87474
\(401\) 12.8447 0.641433 0.320717 0.947175i \(-0.396076\pi\)
0.320717 + 0.947175i \(0.396076\pi\)
\(402\) −28.8483 −1.43882
\(403\) 5.33677 0.265843
\(404\) 71.2372 3.54419
\(405\) 0.714007 0.0354793
\(406\) 28.5827 1.41854
\(407\) −8.34534 −0.413663
\(408\) 30.0309 1.48675
\(409\) −35.3205 −1.74648 −0.873242 0.487287i \(-0.837987\pi\)
−0.873242 + 0.487287i \(0.837987\pi\)
\(410\) 1.83201 0.0904764
\(411\) −3.31122 −0.163330
\(412\) −43.7595 −2.15588
\(413\) 17.6612 0.869053
\(414\) 14.1405 0.694966
\(415\) 0.314283 0.0154275
\(416\) −19.1412 −0.938473
\(417\) 32.2638 1.57997
\(418\) −2.69358 −0.131747
\(419\) −13.0390 −0.636995 −0.318498 0.947924i \(-0.603178\pi\)
−0.318498 + 0.947924i \(0.603178\pi\)
\(420\) −1.87545 −0.0915124
\(421\) −15.0702 −0.734478 −0.367239 0.930127i \(-0.619697\pi\)
−0.367239 + 0.930127i \(0.619697\pi\)
\(422\) 32.4500 1.57964
\(423\) 0.916079 0.0445413
\(424\) 25.6242 1.24442
\(425\) −12.4850 −0.605614
\(426\) 14.4108 0.698204
\(427\) 26.7055 1.29237
\(428\) −38.1652 −1.84478
\(429\) 2.50261 0.120827
\(430\) 3.04928 0.147049
\(431\) 35.3658 1.70351 0.851755 0.523940i \(-0.175539\pi\)
0.851755 + 0.523940i \(0.175539\pi\)
\(432\) 65.0859 3.13145
\(433\) −28.5793 −1.37343 −0.686716 0.726926i \(-0.740948\pi\)
−0.686716 + 0.726926i \(0.740948\pi\)
\(434\) 21.7286 1.04300
\(435\) 0.954792 0.0457788
\(436\) −54.2676 −2.59895
\(437\) −5.05259 −0.241698
\(438\) −48.7632 −2.33000
\(439\) 38.1836 1.82240 0.911201 0.411962i \(-0.135156\pi\)
0.911201 + 0.411962i \(0.135156\pi\)
\(440\) −1.28197 −0.0611157
\(441\) 2.36666 0.112698
\(442\) −8.87539 −0.422159
\(443\) 39.1935 1.86214 0.931071 0.364838i \(-0.118876\pi\)
0.931071 + 0.364838i \(0.118876\pi\)
\(444\) −48.7362 −2.31292
\(445\) 0.500102 0.0237071
\(446\) −10.6086 −0.502332
\(447\) −25.8870 −1.22441
\(448\) −30.8327 −1.45671
\(449\) 14.4712 0.682940 0.341470 0.939893i \(-0.389075\pi\)
0.341470 + 0.939893i \(0.389075\pi\)
\(450\) −11.0771 −0.522181
\(451\) −7.13616 −0.336029
\(452\) 29.5027 1.38769
\(453\) 7.25491 0.340865
\(454\) −61.5849 −2.89032
\(455\) 0.335461 0.0157267
\(456\) −9.52041 −0.445834
\(457\) −2.23754 −0.104668 −0.0523338 0.998630i \(-0.516666\pi\)
−0.0523338 + 0.998630i \(0.516666\pi\)
\(458\) 38.7771 1.81194
\(459\) 14.1335 0.659693
\(460\) −3.97324 −0.185253
\(461\) −4.76473 −0.221916 −0.110958 0.993825i \(-0.535392\pi\)
−0.110958 + 0.993825i \(0.535392\pi\)
\(462\) 10.1893 0.474050
\(463\) −20.1966 −0.938617 −0.469309 0.883034i \(-0.655497\pi\)
−0.469309 + 0.883034i \(0.655497\pi\)
\(464\) 60.7406 2.81981
\(465\) 0.725831 0.0336596
\(466\) 58.5910 2.71418
\(467\) 19.5488 0.904611 0.452306 0.891863i \(-0.350602\pi\)
0.452306 + 0.891863i \(0.350602\pi\)
\(468\) −5.64574 −0.260974
\(469\) 15.0628 0.695537
\(470\) −0.359019 −0.0165603
\(471\) −21.0204 −0.968568
\(472\) 70.5022 3.24513
\(473\) −11.8778 −0.546140
\(474\) 40.8222 1.87503
\(475\) 3.95802 0.181606
\(476\) −25.9081 −1.18750
\(477\) 2.62810 0.120332
\(478\) 7.90810 0.361708
\(479\) −0.979237 −0.0447425 −0.0223712 0.999750i \(-0.507122\pi\)
−0.0223712 + 0.999750i \(0.507122\pi\)
\(480\) −2.60331 −0.118824
\(481\) 8.71745 0.397481
\(482\) 18.5414 0.844540
\(483\) 19.1130 0.869674
\(484\) −47.4774 −2.15806
\(485\) −1.46631 −0.0665815
\(486\) 22.3466 1.01366
\(487\) 27.8793 1.26333 0.631666 0.775241i \(-0.282371\pi\)
0.631666 + 0.775241i \(0.282371\pi\)
\(488\) 106.606 4.82584
\(489\) −33.6674 −1.52249
\(490\) −0.927516 −0.0419009
\(491\) −3.72056 −0.167907 −0.0839534 0.996470i \(-0.526755\pi\)
−0.0839534 + 0.996470i \(0.526755\pi\)
\(492\) −41.6747 −1.87884
\(493\) 13.1899 0.594041
\(494\) 2.81368 0.126593
\(495\) −0.131483 −0.00590973
\(496\) 46.1749 2.07331
\(497\) −7.52443 −0.337517
\(498\) −9.97169 −0.446842
\(499\) 39.3383 1.76102 0.880511 0.474025i \(-0.157199\pi\)
0.880511 + 0.474025i \(0.157199\pi\)
\(500\) 6.23447 0.278814
\(501\) 9.86304 0.440648
\(502\) 35.9512 1.60458
\(503\) 35.8281 1.59749 0.798747 0.601667i \(-0.205496\pi\)
0.798747 + 0.601667i \(0.205496\pi\)
\(504\) −13.9121 −0.619693
\(505\) −1.73301 −0.0771181
\(506\) 21.5867 0.959645
\(507\) 16.5097 0.733221
\(508\) 11.0166 0.488783
\(509\) −0.332989 −0.0147595 −0.00737974 0.999973i \(-0.502349\pi\)
−0.00737974 + 0.999973i \(0.502349\pi\)
\(510\) −1.20710 −0.0534514
\(511\) 25.4612 1.12634
\(512\) 22.4065 0.990237
\(513\) −4.48059 −0.197823
\(514\) 20.5757 0.907554
\(515\) 1.06455 0.0469098
\(516\) −69.3653 −3.05364
\(517\) 1.39848 0.0615049
\(518\) 35.4929 1.55947
\(519\) −2.85890 −0.125492
\(520\) 1.33913 0.0587249
\(521\) 15.4969 0.678930 0.339465 0.940619i \(-0.389754\pi\)
0.339465 + 0.940619i \(0.389754\pi\)
\(522\) 11.7025 0.512203
\(523\) −15.5011 −0.677816 −0.338908 0.940820i \(-0.610057\pi\)
−0.338908 + 0.940820i \(0.610057\pi\)
\(524\) −64.7775 −2.82982
\(525\) −14.9725 −0.653452
\(526\) 14.5160 0.632928
\(527\) 10.0269 0.436779
\(528\) 21.6531 0.942331
\(529\) 17.4921 0.760525
\(530\) −1.02998 −0.0447393
\(531\) 7.23093 0.313796
\(532\) 8.21341 0.356097
\(533\) 7.45435 0.322884
\(534\) −15.8674 −0.686651
\(535\) 0.928457 0.0401407
\(536\) 60.1296 2.59720
\(537\) −31.7541 −1.37029
\(538\) 13.3942 0.577463
\(539\) 3.61292 0.155620
\(540\) −3.52344 −0.151625
\(541\) −26.0999 −1.12212 −0.561061 0.827774i \(-0.689607\pi\)
−0.561061 + 0.827774i \(0.689607\pi\)
\(542\) −75.4729 −3.24184
\(543\) 6.26356 0.268795
\(544\) −35.9631 −1.54191
\(545\) 1.32019 0.0565506
\(546\) −10.6437 −0.455506
\(547\) −5.71922 −0.244536 −0.122268 0.992497i \(-0.539017\pi\)
−0.122268 + 0.992497i \(0.539017\pi\)
\(548\) 11.4035 0.487133
\(549\) 10.9339 0.466647
\(550\) −16.9102 −0.721054
\(551\) −4.18146 −0.178136
\(552\) 76.2977 3.24745
\(553\) −21.3149 −0.906401
\(554\) 43.1213 1.83205
\(555\) 1.18562 0.0503269
\(556\) −111.113 −4.71225
\(557\) 33.7544 1.43022 0.715110 0.699012i \(-0.246377\pi\)
0.715110 + 0.699012i \(0.246377\pi\)
\(558\) 8.89619 0.376606
\(559\) 12.4074 0.524776
\(560\) 2.90248 0.122652
\(561\) 4.70199 0.198518
\(562\) 28.3416 1.19552
\(563\) −33.3496 −1.40552 −0.702759 0.711428i \(-0.748049\pi\)
−0.702759 + 0.711428i \(0.748049\pi\)
\(564\) 8.16700 0.343893
\(565\) −0.717723 −0.0301948
\(566\) 29.4445 1.23765
\(567\) 11.8287 0.496759
\(568\) −30.0369 −1.26032
\(569\) 18.5066 0.775838 0.387919 0.921693i \(-0.373194\pi\)
0.387919 + 0.921693i \(0.373194\pi\)
\(570\) 0.382677 0.0160286
\(571\) −22.2615 −0.931615 −0.465808 0.884886i \(-0.654236\pi\)
−0.465808 + 0.884886i \(0.654236\pi\)
\(572\) −8.61872 −0.360367
\(573\) −19.4731 −0.813500
\(574\) 30.3503 1.26680
\(575\) −31.7200 −1.32282
\(576\) −12.6237 −0.525986
\(577\) −32.7314 −1.36263 −0.681313 0.731992i \(-0.738591\pi\)
−0.681313 + 0.731992i \(0.738591\pi\)
\(578\) 28.5146 1.18605
\(579\) −21.8491 −0.908016
\(580\) −3.28820 −0.136535
\(581\) 5.20661 0.216007
\(582\) 46.5236 1.92846
\(583\) 4.01203 0.166161
\(584\) 101.639 4.20585
\(585\) 0.137346 0.00567855
\(586\) −43.3108 −1.78915
\(587\) −13.5519 −0.559346 −0.279673 0.960095i \(-0.590226\pi\)
−0.279673 + 0.960095i \(0.590226\pi\)
\(588\) 21.0992 0.870117
\(589\) −3.17874 −0.130978
\(590\) −2.83387 −0.116668
\(591\) −33.0150 −1.35805
\(592\) 75.4253 3.09996
\(593\) −29.3196 −1.20401 −0.602006 0.798491i \(-0.705632\pi\)
−0.602006 + 0.798491i \(0.705632\pi\)
\(594\) 19.1429 0.785442
\(595\) 0.630276 0.0258388
\(596\) 89.1520 3.65181
\(597\) 15.3860 0.629705
\(598\) −22.5492 −0.922105
\(599\) −33.1465 −1.35433 −0.677165 0.735831i \(-0.736792\pi\)
−0.677165 + 0.735831i \(0.736792\pi\)
\(600\) −59.7689 −2.44006
\(601\) 0.0735303 0.00299936 0.00149968 0.999999i \(-0.499523\pi\)
0.00149968 + 0.999999i \(0.499523\pi\)
\(602\) 50.5164 2.05889
\(603\) 6.16708 0.251143
\(604\) −24.9852 −1.01663
\(605\) 1.15500 0.0469574
\(606\) 54.9858 2.23364
\(607\) 19.8711 0.806542 0.403271 0.915081i \(-0.367873\pi\)
0.403271 + 0.915081i \(0.367873\pi\)
\(608\) 11.4010 0.462373
\(609\) 15.8177 0.640966
\(610\) −4.28509 −0.173498
\(611\) −1.46083 −0.0590989
\(612\) −10.6074 −0.428779
\(613\) 21.7731 0.879409 0.439705 0.898142i \(-0.355083\pi\)
0.439705 + 0.898142i \(0.355083\pi\)
\(614\) 16.6408 0.671567
\(615\) 1.01383 0.0408817
\(616\) −21.2380 −0.855704
\(617\) 18.1435 0.730430 0.365215 0.930923i \(-0.380995\pi\)
0.365215 + 0.930923i \(0.380995\pi\)
\(618\) −33.7766 −1.35869
\(619\) 9.55638 0.384103 0.192052 0.981385i \(-0.438486\pi\)
0.192052 + 0.981385i \(0.438486\pi\)
\(620\) −2.49969 −0.100390
\(621\) 35.9080 1.44094
\(622\) 16.8793 0.676799
\(623\) 8.28502 0.331932
\(624\) −22.6186 −0.905468
\(625\) 24.7724 0.990895
\(626\) 32.9966 1.31881
\(627\) −1.49063 −0.0595299
\(628\) 72.3920 2.88875
\(629\) 16.3786 0.653059
\(630\) 0.559201 0.0222791
\(631\) −5.80640 −0.231149 −0.115575 0.993299i \(-0.536871\pi\)
−0.115575 + 0.993299i \(0.536871\pi\)
\(632\) −85.0873 −3.38459
\(633\) 17.9579 0.713761
\(634\) 33.9390 1.34789
\(635\) −0.268005 −0.0106354
\(636\) 23.4300 0.929059
\(637\) −3.77401 −0.149532
\(638\) 17.8648 0.707276
\(639\) −3.08068 −0.121870
\(640\) 1.40798 0.0556553
\(641\) 21.8923 0.864694 0.432347 0.901707i \(-0.357686\pi\)
0.432347 + 0.901707i \(0.357686\pi\)
\(642\) −29.4585 −1.16263
\(643\) 33.3216 1.31408 0.657038 0.753858i \(-0.271809\pi\)
0.657038 + 0.753858i \(0.271809\pi\)
\(644\) −65.8233 −2.59380
\(645\) 1.68747 0.0664442
\(646\) 5.28644 0.207992
\(647\) −29.5283 −1.16088 −0.580438 0.814305i \(-0.697119\pi\)
−0.580438 + 0.814305i \(0.697119\pi\)
\(648\) 47.2193 1.85495
\(649\) 11.0387 0.433305
\(650\) 17.6642 0.692848
\(651\) 12.0246 0.471281
\(652\) 115.947 4.54083
\(653\) 38.6693 1.51325 0.756624 0.653850i \(-0.226847\pi\)
0.756624 + 0.653850i \(0.226847\pi\)
\(654\) −41.8874 −1.63793
\(655\) 1.57587 0.0615742
\(656\) 64.4967 2.51817
\(657\) 10.4244 0.406695
\(658\) −5.94775 −0.231867
\(659\) −14.2591 −0.555456 −0.277728 0.960660i \(-0.589581\pi\)
−0.277728 + 0.960660i \(0.589581\pi\)
\(660\) −1.17220 −0.0456277
\(661\) −21.4216 −0.833202 −0.416601 0.909089i \(-0.636779\pi\)
−0.416601 + 0.909089i \(0.636779\pi\)
\(662\) −34.4681 −1.33964
\(663\) −4.91164 −0.190752
\(664\) 20.7844 0.806591
\(665\) −0.199811 −0.00774832
\(666\) 14.5317 0.563090
\(667\) 33.5107 1.29754
\(668\) −33.9673 −1.31423
\(669\) −5.87081 −0.226979
\(670\) −2.41693 −0.0933743
\(671\) 16.6916 0.644370
\(672\) −43.1281 −1.66370
\(673\) 5.83221 0.224815 0.112408 0.993662i \(-0.464144\pi\)
0.112408 + 0.993662i \(0.464144\pi\)
\(674\) −80.3730 −3.09585
\(675\) −28.1291 −1.08269
\(676\) −56.8576 −2.18683
\(677\) −2.33503 −0.0897423 −0.0448712 0.998993i \(-0.514288\pi\)
−0.0448712 + 0.998993i \(0.514288\pi\)
\(678\) 22.7722 0.874561
\(679\) −24.2918 −0.932233
\(680\) 2.51601 0.0964847
\(681\) −34.0811 −1.30599
\(682\) 13.5808 0.520037
\(683\) 17.6777 0.676419 0.338209 0.941071i \(-0.390179\pi\)
0.338209 + 0.941071i \(0.390179\pi\)
\(684\) 3.36277 0.128579
\(685\) −0.277416 −0.0105995
\(686\) −53.3588 −2.03725
\(687\) 21.4593 0.818723
\(688\) 107.351 4.09273
\(689\) −4.19092 −0.159661
\(690\) −3.06682 −0.116752
\(691\) 25.8715 0.984200 0.492100 0.870539i \(-0.336229\pi\)
0.492100 + 0.870539i \(0.336229\pi\)
\(692\) 9.84575 0.374279
\(693\) −2.17824 −0.0827444
\(694\) −19.0871 −0.724535
\(695\) 2.70309 0.102534
\(696\) 63.1430 2.39343
\(697\) 14.0055 0.530496
\(698\) −69.3866 −2.62632
\(699\) 32.4243 1.22640
\(700\) 51.5636 1.94892
\(701\) −31.4019 −1.18603 −0.593017 0.805190i \(-0.702063\pi\)
−0.593017 + 0.805190i \(0.702063\pi\)
\(702\) −19.9964 −0.754717
\(703\) −5.19237 −0.195834
\(704\) −19.2712 −0.726309
\(705\) −0.198681 −0.00748277
\(706\) 10.0688 0.378946
\(707\) −28.7102 −1.07976
\(708\) 64.4650 2.42274
\(709\) 4.68375 0.175902 0.0879509 0.996125i \(-0.471968\pi\)
0.0879509 + 0.996125i \(0.471968\pi\)
\(710\) 1.20735 0.0453109
\(711\) −8.72683 −0.327282
\(712\) 33.0731 1.23947
\(713\) 25.4748 0.954038
\(714\) −19.9977 −0.748394
\(715\) 0.209671 0.00784124
\(716\) 109.358 4.08689
\(717\) 4.37635 0.163438
\(718\) −80.1593 −2.99152
\(719\) 40.1197 1.49621 0.748106 0.663580i \(-0.230964\pi\)
0.748106 + 0.663580i \(0.230964\pi\)
\(720\) 1.18835 0.0442871
\(721\) 17.6361 0.656802
\(722\) 48.8305 1.81728
\(723\) 10.2608 0.381605
\(724\) −21.5711 −0.801682
\(725\) −26.2511 −0.974941
\(726\) −36.6463 −1.36007
\(727\) 19.5640 0.725589 0.362794 0.931869i \(-0.381823\pi\)
0.362794 + 0.931869i \(0.381823\pi\)
\(728\) 22.1850 0.822230
\(729\) 29.7465 1.10172
\(730\) −4.08542 −0.151208
\(731\) 23.3114 0.862203
\(732\) 97.4775 3.60287
\(733\) −15.5232 −0.573361 −0.286681 0.958026i \(-0.592552\pi\)
−0.286681 + 0.958026i \(0.592552\pi\)
\(734\) 5.70167 0.210453
\(735\) −0.513288 −0.0189329
\(736\) −91.3694 −3.36792
\(737\) 9.41460 0.346791
\(738\) 12.4261 0.457412
\(739\) −36.0840 −1.32737 −0.663686 0.748012i \(-0.731009\pi\)
−0.663686 + 0.748012i \(0.731009\pi\)
\(740\) −4.08316 −0.150100
\(741\) 1.55709 0.0572012
\(742\) −17.0633 −0.626412
\(743\) 6.71066 0.246190 0.123095 0.992395i \(-0.460718\pi\)
0.123095 + 0.992395i \(0.460718\pi\)
\(744\) 48.0012 1.75981
\(745\) −2.16883 −0.0794598
\(746\) 46.3400 1.69663
\(747\) 2.13171 0.0779953
\(748\) −16.1932 −0.592081
\(749\) 15.3814 0.562025
\(750\) 4.81219 0.175716
\(751\) 46.0707 1.68114 0.840571 0.541701i \(-0.182219\pi\)
0.840571 + 0.541701i \(0.182219\pi\)
\(752\) −12.6394 −0.460913
\(753\) 19.8954 0.725030
\(754\) −18.6614 −0.679608
\(755\) 0.607823 0.0221209
\(756\) −58.3716 −2.12295
\(757\) 2.24877 0.0817329 0.0408664 0.999165i \(-0.486988\pi\)
0.0408664 + 0.999165i \(0.486988\pi\)
\(758\) −39.3872 −1.43061
\(759\) 11.9461 0.433615
\(760\) −0.797628 −0.0289330
\(761\) 31.9562 1.15841 0.579206 0.815181i \(-0.303363\pi\)
0.579206 + 0.815181i \(0.303363\pi\)
\(762\) 8.50337 0.308044
\(763\) 21.8711 0.791786
\(764\) 67.0633 2.42626
\(765\) 0.258050 0.00932983
\(766\) −85.2498 −3.08020
\(767\) −11.5309 −0.416355
\(768\) −0.244338 −0.00881679
\(769\) 2.48880 0.0897486 0.0448743 0.998993i \(-0.485711\pi\)
0.0448743 + 0.998993i \(0.485711\pi\)
\(770\) 0.853670 0.0307641
\(771\) 11.3866 0.410078
\(772\) 75.2459 2.70816
\(773\) −2.76538 −0.0994638 −0.0497319 0.998763i \(-0.515837\pi\)
−0.0497319 + 0.998763i \(0.515837\pi\)
\(774\) 20.6826 0.743421
\(775\) −19.9560 −0.716842
\(776\) −96.9709 −3.48105
\(777\) 19.6418 0.704646
\(778\) 80.8550 2.89879
\(779\) −4.44003 −0.159081
\(780\) 1.22446 0.0438428
\(781\) −4.70293 −0.168284
\(782\) −42.3662 −1.51501
\(783\) 29.7170 1.06200
\(784\) −32.6536 −1.16620
\(785\) −1.76110 −0.0628565
\(786\) −49.9997 −1.78343
\(787\) −21.0935 −0.751900 −0.375950 0.926640i \(-0.622684\pi\)
−0.375950 + 0.926640i \(0.622684\pi\)
\(788\) 113.700 4.05040
\(789\) 8.03316 0.285988
\(790\) 3.42012 0.121682
\(791\) −11.8903 −0.422769
\(792\) −8.69535 −0.308976
\(793\) −17.4358 −0.619163
\(794\) −81.4247 −2.88966
\(795\) −0.569989 −0.0202154
\(796\) −52.9876 −1.87810
\(797\) 33.5808 1.18949 0.594747 0.803913i \(-0.297252\pi\)
0.594747 + 0.803913i \(0.297252\pi\)
\(798\) 6.33967 0.224422
\(799\) −2.74466 −0.0970991
\(800\) 71.5755 2.53058
\(801\) 3.39209 0.119853
\(802\) −34.1442 −1.20567
\(803\) 15.9138 0.561586
\(804\) 54.9806 1.93902
\(805\) 1.60131 0.0564386
\(806\) −14.1864 −0.499694
\(807\) 7.41234 0.260927
\(808\) −114.609 −4.03193
\(809\) −17.8743 −0.628429 −0.314214 0.949352i \(-0.601741\pi\)
−0.314214 + 0.949352i \(0.601741\pi\)
\(810\) −1.89800 −0.0666888
\(811\) 28.5801 1.00358 0.501791 0.864989i \(-0.332674\pi\)
0.501791 + 0.864989i \(0.332674\pi\)
\(812\) −54.4745 −1.91168
\(813\) −41.7667 −1.46482
\(814\) 22.1839 0.777544
\(815\) −2.82068 −0.0988041
\(816\) −42.4966 −1.48768
\(817\) −7.39019 −0.258550
\(818\) 93.8900 3.28279
\(819\) 2.27536 0.0795076
\(820\) −3.49154 −0.121930
\(821\) −47.7934 −1.66800 −0.834000 0.551764i \(-0.813955\pi\)
−0.834000 + 0.551764i \(0.813955\pi\)
\(822\) 8.80198 0.307004
\(823\) −24.8377 −0.865788 −0.432894 0.901445i \(-0.642508\pi\)
−0.432894 + 0.901445i \(0.642508\pi\)
\(824\) 70.4018 2.45256
\(825\) −9.35813 −0.325808
\(826\) −46.9477 −1.63352
\(827\) −4.72241 −0.164214 −0.0821072 0.996624i \(-0.526165\pi\)
−0.0821072 + 0.996624i \(0.526165\pi\)
\(828\) −26.9496 −0.936565
\(829\) 2.58244 0.0896918 0.0448459 0.998994i \(-0.485720\pi\)
0.0448459 + 0.998994i \(0.485720\pi\)
\(830\) −0.835437 −0.0289984
\(831\) 23.8634 0.827811
\(832\) 20.1304 0.697897
\(833\) −7.09075 −0.245680
\(834\) −85.7648 −2.96979
\(835\) 0.826334 0.0285965
\(836\) 5.13357 0.177548
\(837\) 22.5908 0.780853
\(838\) 34.6606 1.19733
\(839\) 27.9234 0.964024 0.482012 0.876165i \(-0.339906\pi\)
0.482012 + 0.876165i \(0.339906\pi\)
\(840\) 3.01728 0.104106
\(841\) −1.26698 −0.0436888
\(842\) 40.0602 1.38056
\(843\) 15.6843 0.540195
\(844\) −61.8450 −2.12879
\(845\) 1.38320 0.0475834
\(846\) −2.43515 −0.0837222
\(847\) 19.1345 0.657468
\(848\) −36.2608 −1.24520
\(849\) 16.2946 0.559230
\(850\) 33.1882 1.13834
\(851\) 41.6123 1.42645
\(852\) −27.4648 −0.940929
\(853\) 51.7741 1.77271 0.886355 0.463006i \(-0.153229\pi\)
0.886355 + 0.463006i \(0.153229\pi\)
\(854\) −70.9895 −2.42921
\(855\) −0.0818072 −0.00279775
\(856\) 61.4014 2.09866
\(857\) 53.7137 1.83482 0.917412 0.397939i \(-0.130275\pi\)
0.917412 + 0.397939i \(0.130275\pi\)
\(858\) −6.65252 −0.227113
\(859\) −1.73783 −0.0592941 −0.0296471 0.999560i \(-0.509438\pi\)
−0.0296471 + 0.999560i \(0.509438\pi\)
\(860\) −5.81148 −0.198170
\(861\) 16.7958 0.572401
\(862\) −94.0105 −3.20201
\(863\) −52.7174 −1.79452 −0.897260 0.441502i \(-0.854446\pi\)
−0.897260 + 0.441502i \(0.854446\pi\)
\(864\) −81.0256 −2.75655
\(865\) −0.239521 −0.00814396
\(866\) 75.9703 2.58158
\(867\) 15.7800 0.535916
\(868\) −41.4114 −1.40560
\(869\) −13.3223 −0.451927
\(870\) −2.53806 −0.0860482
\(871\) −9.83438 −0.333225
\(872\) 87.3075 2.95661
\(873\) −9.94564 −0.336609
\(874\) 13.4310 0.454309
\(875\) −2.51263 −0.0849426
\(876\) 92.9355 3.14000
\(877\) 40.5530 1.36938 0.684689 0.728836i \(-0.259938\pi\)
0.684689 + 0.728836i \(0.259938\pi\)
\(878\) −101.501 −3.42549
\(879\) −23.9682 −0.808429
\(880\) 1.81412 0.0611539
\(881\) −27.5684 −0.928802 −0.464401 0.885625i \(-0.653730\pi\)
−0.464401 + 0.885625i \(0.653730\pi\)
\(882\) −6.29114 −0.211834
\(883\) 25.7517 0.866614 0.433307 0.901246i \(-0.357347\pi\)
0.433307 + 0.901246i \(0.357347\pi\)
\(884\) 16.9152 0.568919
\(885\) −1.56826 −0.0527166
\(886\) −104.186 −3.50018
\(887\) −24.6468 −0.827560 −0.413780 0.910377i \(-0.635792\pi\)
−0.413780 + 0.910377i \(0.635792\pi\)
\(888\) 78.4085 2.63122
\(889\) −4.43994 −0.148911
\(890\) −1.32939 −0.0445612
\(891\) 7.39321 0.247682
\(892\) 20.2185 0.676964
\(893\) 0.870114 0.0291173
\(894\) 68.8136 2.30147
\(895\) −2.66039 −0.0889269
\(896\) 23.3255 0.779250
\(897\) −12.4787 −0.416653
\(898\) −38.4679 −1.28369
\(899\) 21.0826 0.703144
\(900\) 21.1114 0.703713
\(901\) −7.87405 −0.262323
\(902\) 18.9696 0.631618
\(903\) 27.9558 0.930310
\(904\) −47.4650 −1.57866
\(905\) 0.524767 0.0174438
\(906\) −19.2852 −0.640709
\(907\) −44.2748 −1.47012 −0.735060 0.678002i \(-0.762846\pi\)
−0.735060 + 0.678002i \(0.762846\pi\)
\(908\) 117.372 3.89512
\(909\) −11.7547 −0.389877
\(910\) −0.891734 −0.0295607
\(911\) −22.9975 −0.761941 −0.380971 0.924587i \(-0.624410\pi\)
−0.380971 + 0.924587i \(0.624410\pi\)
\(912\) 13.4723 0.446113
\(913\) 3.25425 0.107700
\(914\) 5.94790 0.196739
\(915\) −2.37137 −0.0783950
\(916\) −73.9035 −2.44184
\(917\) 26.1068 0.862123
\(918\) −37.5700 −1.23999
\(919\) 35.6080 1.17460 0.587300 0.809369i \(-0.300191\pi\)
0.587300 + 0.809369i \(0.300191\pi\)
\(920\) 6.39229 0.210747
\(921\) 9.20902 0.303447
\(922\) 12.6658 0.417125
\(923\) 4.91263 0.161701
\(924\) −19.4194 −0.638850
\(925\) −32.5976 −1.07180
\(926\) 53.6874 1.76428
\(927\) 7.22063 0.237157
\(928\) −75.6161 −2.48222
\(929\) −36.3221 −1.19169 −0.595845 0.803099i \(-0.703183\pi\)
−0.595845 + 0.803099i \(0.703183\pi\)
\(930\) −1.92943 −0.0632684
\(931\) 2.24791 0.0736724
\(932\) −111.666 −3.65774
\(933\) 9.34103 0.305812
\(934\) −51.9653 −1.70036
\(935\) 0.393937 0.0128831
\(936\) 9.08306 0.296889
\(937\) −3.50674 −0.114560 −0.0572801 0.998358i \(-0.518243\pi\)
−0.0572801 + 0.998358i \(0.518243\pi\)
\(938\) −40.0405 −1.30737
\(939\) 18.2603 0.595904
\(940\) 0.684238 0.0223174
\(941\) 26.7201 0.871050 0.435525 0.900177i \(-0.356563\pi\)
0.435525 + 0.900177i \(0.356563\pi\)
\(942\) 55.8771 1.82057
\(943\) 35.5830 1.15874
\(944\) −99.7675 −3.24716
\(945\) 1.42003 0.0461934
\(946\) 31.5738 1.02655
\(947\) −18.8544 −0.612687 −0.306344 0.951921i \(-0.599106\pi\)
−0.306344 + 0.951921i \(0.599106\pi\)
\(948\) −77.8012 −2.52686
\(949\) −16.6234 −0.539618
\(950\) −10.5213 −0.341357
\(951\) 18.7819 0.609044
\(952\) 41.6819 1.35092
\(953\) −48.0782 −1.55741 −0.778703 0.627393i \(-0.784122\pi\)
−0.778703 + 0.627393i \(0.784122\pi\)
\(954\) −6.98610 −0.226183
\(955\) −1.63147 −0.0527932
\(956\) −15.0717 −0.487453
\(957\) 9.88642 0.319582
\(958\) 2.60304 0.0841004
\(959\) −4.59586 −0.148408
\(960\) 2.73785 0.0883638
\(961\) −14.9730 −0.483001
\(962\) −23.1730 −0.747128
\(963\) 6.29752 0.202935
\(964\) −35.3373 −1.13814
\(965\) −1.83053 −0.0589270
\(966\) −50.8069 −1.63469
\(967\) 20.2183 0.650176 0.325088 0.945684i \(-0.394606\pi\)
0.325088 + 0.945684i \(0.394606\pi\)
\(968\) 76.3833 2.45505
\(969\) 2.92552 0.0939812
\(970\) 3.89778 0.125150
\(971\) −15.5725 −0.499746 −0.249873 0.968279i \(-0.580389\pi\)
−0.249873 + 0.968279i \(0.580389\pi\)
\(972\) −42.5893 −1.36605
\(973\) 44.7812 1.43562
\(974\) −74.1097 −2.37463
\(975\) 9.77539 0.313063
\(976\) −150.858 −4.82886
\(977\) −19.1176 −0.611626 −0.305813 0.952092i \(-0.598928\pi\)
−0.305813 + 0.952092i \(0.598928\pi\)
\(978\) 89.4957 2.86176
\(979\) 5.17832 0.165500
\(980\) 1.76771 0.0564674
\(981\) 8.95454 0.285896
\(982\) 9.89013 0.315607
\(983\) −16.1669 −0.515644 −0.257822 0.966192i \(-0.583005\pi\)
−0.257822 + 0.966192i \(0.583005\pi\)
\(984\) 67.0477 2.13740
\(985\) −2.76602 −0.0881328
\(986\) −35.0617 −1.11659
\(987\) −3.29149 −0.104769
\(988\) −5.36246 −0.170603
\(989\) 59.2259 1.88327
\(990\) 0.349513 0.0111083
\(991\) −20.5614 −0.653153 −0.326576 0.945171i \(-0.605895\pi\)
−0.326576 + 0.945171i \(0.605895\pi\)
\(992\) −57.4832 −1.82509
\(993\) −19.0746 −0.605315
\(994\) 20.0017 0.634415
\(995\) 1.28905 0.0408656
\(996\) 19.0046 0.602183
\(997\) 4.38677 0.138930 0.0694652 0.997584i \(-0.477871\pi\)
0.0694652 + 0.997584i \(0.477871\pi\)
\(998\) −104.570 −3.31011
\(999\) 36.9014 1.16751
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.1.3 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.3 259 1.1 even 1 trivial