Properties

Label 6025.2.a.p.1.4
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(46\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.44838 q^{2} +0.992209 q^{3} +3.99457 q^{4} -2.42931 q^{6} -0.744704 q^{7} -4.88345 q^{8} -2.01552 q^{9} +O(q^{10})\) \(q-2.44838 q^{2} +0.992209 q^{3} +3.99457 q^{4} -2.42931 q^{6} -0.744704 q^{7} -4.88345 q^{8} -2.01552 q^{9} -2.60457 q^{11} +3.96344 q^{12} +4.18428 q^{13} +1.82332 q^{14} +3.96742 q^{16} +0.484012 q^{17} +4.93476 q^{18} +3.30187 q^{19} -0.738902 q^{21} +6.37697 q^{22} -1.44005 q^{23} -4.84541 q^{24} -10.2447 q^{26} -4.97645 q^{27} -2.97477 q^{28} -0.129471 q^{29} +4.43651 q^{31} +0.0531507 q^{32} -2.58428 q^{33} -1.18504 q^{34} -8.05113 q^{36} +4.67172 q^{37} -8.08424 q^{38} +4.15168 q^{39} -9.21272 q^{41} +1.80911 q^{42} -7.65578 q^{43} -10.4041 q^{44} +3.52579 q^{46} -2.28201 q^{47} +3.93651 q^{48} -6.44542 q^{49} +0.480241 q^{51} +16.7144 q^{52} +12.5450 q^{53} +12.1842 q^{54} +3.63673 q^{56} +3.27615 q^{57} +0.316993 q^{58} -7.30045 q^{59} -5.28903 q^{61} -10.8623 q^{62} +1.50097 q^{63} -8.06498 q^{64} +6.32729 q^{66} +5.69391 q^{67} +1.93342 q^{68} -1.42883 q^{69} +2.08218 q^{71} +9.84271 q^{72} +15.5697 q^{73} -11.4381 q^{74} +13.1895 q^{76} +1.93963 q^{77} -10.1649 q^{78} -10.0023 q^{79} +1.10889 q^{81} +22.5562 q^{82} -2.71488 q^{83} -2.95159 q^{84} +18.7442 q^{86} -0.128462 q^{87} +12.7193 q^{88} -9.86499 q^{89} -3.11605 q^{91} -5.75237 q^{92} +4.40195 q^{93} +5.58723 q^{94} +0.0527366 q^{96} +6.26809 q^{97} +15.7808 q^{98} +5.24956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44838 −1.73127 −0.865633 0.500679i \(-0.833084\pi\)
−0.865633 + 0.500679i \(0.833084\pi\)
\(3\) 0.992209 0.572852 0.286426 0.958102i \(-0.407533\pi\)
0.286426 + 0.958102i \(0.407533\pi\)
\(4\) 3.99457 1.99728
\(5\) 0 0
\(6\) −2.42931 −0.991760
\(7\) −0.744704 −0.281472 −0.140736 0.990047i \(-0.544947\pi\)
−0.140736 + 0.990047i \(0.544947\pi\)
\(8\) −4.88345 −1.72656
\(9\) −2.01552 −0.671840
\(10\) 0 0
\(11\) −2.60457 −0.785307 −0.392654 0.919686i \(-0.628443\pi\)
−0.392654 + 0.919686i \(0.628443\pi\)
\(12\) 3.96344 1.14415
\(13\) 4.18428 1.16051 0.580256 0.814434i \(-0.302953\pi\)
0.580256 + 0.814434i \(0.302953\pi\)
\(14\) 1.82332 0.487302
\(15\) 0 0
\(16\) 3.96742 0.991856
\(17\) 0.484012 0.117390 0.0586950 0.998276i \(-0.481306\pi\)
0.0586950 + 0.998276i \(0.481306\pi\)
\(18\) 4.93476 1.16313
\(19\) 3.30187 0.757502 0.378751 0.925499i \(-0.376354\pi\)
0.378751 + 0.925499i \(0.376354\pi\)
\(20\) 0 0
\(21\) −0.738902 −0.161242
\(22\) 6.37697 1.35958
\(23\) −1.44005 −0.300271 −0.150135 0.988665i \(-0.547971\pi\)
−0.150135 + 0.988665i \(0.547971\pi\)
\(24\) −4.84541 −0.989065
\(25\) 0 0
\(26\) −10.2447 −2.00915
\(27\) −4.97645 −0.957717
\(28\) −2.97477 −0.562179
\(29\) −0.129471 −0.0240421 −0.0120210 0.999928i \(-0.503827\pi\)
−0.0120210 + 0.999928i \(0.503827\pi\)
\(30\) 0 0
\(31\) 4.43651 0.796821 0.398410 0.917207i \(-0.369562\pi\)
0.398410 + 0.917207i \(0.369562\pi\)
\(32\) 0.0531507 0.00939580
\(33\) −2.58428 −0.449865
\(34\) −1.18504 −0.203234
\(35\) 0 0
\(36\) −8.05113 −1.34186
\(37\) 4.67172 0.768026 0.384013 0.923328i \(-0.374542\pi\)
0.384013 + 0.923328i \(0.374542\pi\)
\(38\) −8.08424 −1.31144
\(39\) 4.15168 0.664802
\(40\) 0 0
\(41\) −9.21272 −1.43878 −0.719392 0.694604i \(-0.755580\pi\)
−0.719392 + 0.694604i \(0.755580\pi\)
\(42\) 1.80911 0.279152
\(43\) −7.65578 −1.16749 −0.583747 0.811935i \(-0.698414\pi\)
−0.583747 + 0.811935i \(0.698414\pi\)
\(44\) −10.4041 −1.56848
\(45\) 0 0
\(46\) 3.52579 0.519849
\(47\) −2.28201 −0.332865 −0.166433 0.986053i \(-0.553225\pi\)
−0.166433 + 0.986053i \(0.553225\pi\)
\(48\) 3.93651 0.568187
\(49\) −6.44542 −0.920774
\(50\) 0 0
\(51\) 0.480241 0.0672472
\(52\) 16.7144 2.31787
\(53\) 12.5450 1.72319 0.861596 0.507595i \(-0.169465\pi\)
0.861596 + 0.507595i \(0.169465\pi\)
\(54\) 12.1842 1.65806
\(55\) 0 0
\(56\) 3.63673 0.485978
\(57\) 3.27615 0.433936
\(58\) 0.316993 0.0416232
\(59\) −7.30045 −0.950438 −0.475219 0.879868i \(-0.657631\pi\)
−0.475219 + 0.879868i \(0.657631\pi\)
\(60\) 0 0
\(61\) −5.28903 −0.677190 −0.338595 0.940932i \(-0.609952\pi\)
−0.338595 + 0.940932i \(0.609952\pi\)
\(62\) −10.8623 −1.37951
\(63\) 1.50097 0.189104
\(64\) −8.06498 −1.00812
\(65\) 0 0
\(66\) 6.32729 0.778836
\(67\) 5.69391 0.695621 0.347811 0.937565i \(-0.386925\pi\)
0.347811 + 0.937565i \(0.386925\pi\)
\(68\) 1.93342 0.234461
\(69\) −1.42883 −0.172011
\(70\) 0 0
\(71\) 2.08218 0.247109 0.123555 0.992338i \(-0.460571\pi\)
0.123555 + 0.992338i \(0.460571\pi\)
\(72\) 9.84271 1.15997
\(73\) 15.5697 1.82230 0.911149 0.412076i \(-0.135196\pi\)
0.911149 + 0.412076i \(0.135196\pi\)
\(74\) −11.4381 −1.32966
\(75\) 0 0
\(76\) 13.1895 1.51294
\(77\) 1.93963 0.221042
\(78\) −10.1649 −1.15095
\(79\) −10.0023 −1.12534 −0.562671 0.826681i \(-0.690226\pi\)
−0.562671 + 0.826681i \(0.690226\pi\)
\(80\) 0 0
\(81\) 1.10889 0.123210
\(82\) 22.5562 2.49092
\(83\) −2.71488 −0.297997 −0.148999 0.988837i \(-0.547605\pi\)
−0.148999 + 0.988837i \(0.547605\pi\)
\(84\) −2.95159 −0.322045
\(85\) 0 0
\(86\) 18.7442 2.02124
\(87\) −0.128462 −0.0137726
\(88\) 12.7193 1.35588
\(89\) −9.86499 −1.04569 −0.522843 0.852429i \(-0.675129\pi\)
−0.522843 + 0.852429i \(0.675129\pi\)
\(90\) 0 0
\(91\) −3.11605 −0.326651
\(92\) −5.75237 −0.599726
\(93\) 4.40195 0.456461
\(94\) 5.58723 0.576279
\(95\) 0 0
\(96\) 0.0527366 0.00538241
\(97\) 6.26809 0.636428 0.318214 0.948019i \(-0.396917\pi\)
0.318214 + 0.948019i \(0.396917\pi\)
\(98\) 15.7808 1.59410
\(99\) 5.24956 0.527601
\(100\) 0 0
\(101\) 4.57863 0.455591 0.227796 0.973709i \(-0.426848\pi\)
0.227796 + 0.973709i \(0.426848\pi\)
\(102\) −1.17581 −0.116423
\(103\) 5.95554 0.586817 0.293409 0.955987i \(-0.405210\pi\)
0.293409 + 0.955987i \(0.405210\pi\)
\(104\) −20.4338 −2.00369
\(105\) 0 0
\(106\) −30.7150 −2.98330
\(107\) 4.83097 0.467027 0.233514 0.972354i \(-0.424978\pi\)
0.233514 + 0.972354i \(0.424978\pi\)
\(108\) −19.8787 −1.91283
\(109\) 9.62741 0.922138 0.461069 0.887364i \(-0.347466\pi\)
0.461069 + 0.887364i \(0.347466\pi\)
\(110\) 0 0
\(111\) 4.63532 0.439965
\(112\) −2.95456 −0.279179
\(113\) 4.74825 0.446677 0.223339 0.974741i \(-0.428304\pi\)
0.223339 + 0.974741i \(0.428304\pi\)
\(114\) −8.02126 −0.751260
\(115\) 0 0
\(116\) −0.517179 −0.0480188
\(117\) −8.43351 −0.779678
\(118\) 17.8743 1.64546
\(119\) −0.360446 −0.0330420
\(120\) 0 0
\(121\) −4.21622 −0.383293
\(122\) 12.9495 1.17240
\(123\) −9.14094 −0.824211
\(124\) 17.7219 1.59148
\(125\) 0 0
\(126\) −3.67494 −0.327389
\(127\) −2.13691 −0.189620 −0.0948099 0.995495i \(-0.530224\pi\)
−0.0948099 + 0.995495i \(0.530224\pi\)
\(128\) 19.6398 1.73593
\(129\) −7.59613 −0.668802
\(130\) 0 0
\(131\) −15.2770 −1.33476 −0.667378 0.744719i \(-0.732584\pi\)
−0.667378 + 0.744719i \(0.732584\pi\)
\(132\) −10.3231 −0.898507
\(133\) −2.45892 −0.213215
\(134\) −13.9408 −1.20431
\(135\) 0 0
\(136\) −2.36365 −0.202681
\(137\) −15.6904 −1.34052 −0.670259 0.742128i \(-0.733817\pi\)
−0.670259 + 0.742128i \(0.733817\pi\)
\(138\) 3.49832 0.297797
\(139\) 13.8387 1.17378 0.586891 0.809666i \(-0.300352\pi\)
0.586891 + 0.809666i \(0.300352\pi\)
\(140\) 0 0
\(141\) −2.26423 −0.190683
\(142\) −5.09797 −0.427812
\(143\) −10.8983 −0.911358
\(144\) −7.99642 −0.666369
\(145\) 0 0
\(146\) −38.1206 −3.15488
\(147\) −6.39520 −0.527467
\(148\) 18.6615 1.53396
\(149\) −4.70517 −0.385463 −0.192731 0.981252i \(-0.561735\pi\)
−0.192731 + 0.981252i \(0.561735\pi\)
\(150\) 0 0
\(151\) 15.7760 1.28383 0.641914 0.766776i \(-0.278140\pi\)
0.641914 + 0.766776i \(0.278140\pi\)
\(152\) −16.1245 −1.30787
\(153\) −0.975536 −0.0788674
\(154\) −4.74896 −0.382682
\(155\) 0 0
\(156\) 16.5842 1.32780
\(157\) −6.26473 −0.499980 −0.249990 0.968248i \(-0.580427\pi\)
−0.249990 + 0.968248i \(0.580427\pi\)
\(158\) 24.4893 1.94827
\(159\) 12.4473 0.987134
\(160\) 0 0
\(161\) 1.07241 0.0845178
\(162\) −2.71498 −0.213309
\(163\) −22.7092 −1.77872 −0.889362 0.457204i \(-0.848851\pi\)
−0.889362 + 0.457204i \(0.848851\pi\)
\(164\) −36.8008 −2.87366
\(165\) 0 0
\(166\) 6.64707 0.515913
\(167\) −18.4720 −1.42941 −0.714703 0.699428i \(-0.753438\pi\)
−0.714703 + 0.699428i \(0.753438\pi\)
\(168\) 3.60840 0.278394
\(169\) 4.50823 0.346787
\(170\) 0 0
\(171\) −6.65500 −0.508920
\(172\) −30.5815 −2.33182
\(173\) 11.4775 0.872615 0.436307 0.899798i \(-0.356286\pi\)
0.436307 + 0.899798i \(0.356286\pi\)
\(174\) 0.314523 0.0238440
\(175\) 0 0
\(176\) −10.3334 −0.778911
\(177\) −7.24358 −0.544460
\(178\) 24.1532 1.81036
\(179\) −12.4461 −0.930266 −0.465133 0.885241i \(-0.653994\pi\)
−0.465133 + 0.885241i \(0.653994\pi\)
\(180\) 0 0
\(181\) −11.1005 −0.825090 −0.412545 0.910937i \(-0.635360\pi\)
−0.412545 + 0.910937i \(0.635360\pi\)
\(182\) 7.62928 0.565520
\(183\) −5.24782 −0.387930
\(184\) 7.03241 0.518436
\(185\) 0 0
\(186\) −10.7776 −0.790255
\(187\) −1.26064 −0.0921873
\(188\) −9.11564 −0.664826
\(189\) 3.70598 0.269570
\(190\) 0 0
\(191\) 5.17318 0.374318 0.187159 0.982330i \(-0.440072\pi\)
0.187159 + 0.982330i \(0.440072\pi\)
\(192\) −8.00214 −0.577505
\(193\) −14.2338 −1.02457 −0.512285 0.858816i \(-0.671201\pi\)
−0.512285 + 0.858816i \(0.671201\pi\)
\(194\) −15.3467 −1.10183
\(195\) 0 0
\(196\) −25.7466 −1.83905
\(197\) −6.64124 −0.473169 −0.236585 0.971611i \(-0.576028\pi\)
−0.236585 + 0.971611i \(0.576028\pi\)
\(198\) −12.8529 −0.913418
\(199\) 9.13468 0.647541 0.323770 0.946136i \(-0.395050\pi\)
0.323770 + 0.946136i \(0.395050\pi\)
\(200\) 0 0
\(201\) 5.64954 0.398488
\(202\) −11.2102 −0.788750
\(203\) 0.0964172 0.00676716
\(204\) 1.91835 0.134312
\(205\) 0 0
\(206\) −14.5814 −1.01594
\(207\) 2.90245 0.201734
\(208\) 16.6008 1.15106
\(209\) −8.59996 −0.594871
\(210\) 0 0
\(211\) −19.5990 −1.34925 −0.674626 0.738160i \(-0.735695\pi\)
−0.674626 + 0.738160i \(0.735695\pi\)
\(212\) 50.1119 3.44170
\(213\) 2.06596 0.141557
\(214\) −11.8280 −0.808548
\(215\) 0 0
\(216\) 24.3022 1.65356
\(217\) −3.30389 −0.224283
\(218\) −23.5716 −1.59647
\(219\) 15.4484 1.04391
\(220\) 0 0
\(221\) 2.02524 0.136233
\(222\) −11.3490 −0.761697
\(223\) −4.78461 −0.320401 −0.160200 0.987085i \(-0.551214\pi\)
−0.160200 + 0.987085i \(0.551214\pi\)
\(224\) −0.0395815 −0.00264465
\(225\) 0 0
\(226\) −11.6255 −0.773318
\(227\) −21.1630 −1.40464 −0.702319 0.711862i \(-0.747852\pi\)
−0.702319 + 0.711862i \(0.747852\pi\)
\(228\) 13.0868 0.866694
\(229\) 22.4594 1.48416 0.742080 0.670311i \(-0.233839\pi\)
0.742080 + 0.670311i \(0.233839\pi\)
\(230\) 0 0
\(231\) 1.92452 0.126624
\(232\) 0.632263 0.0415101
\(233\) −11.0004 −0.720658 −0.360329 0.932825i \(-0.617336\pi\)
−0.360329 + 0.932825i \(0.617336\pi\)
\(234\) 20.6484 1.34983
\(235\) 0 0
\(236\) −29.1621 −1.89829
\(237\) −9.92434 −0.644655
\(238\) 0.882508 0.0572045
\(239\) −2.21903 −0.143537 −0.0717686 0.997421i \(-0.522864\pi\)
−0.0717686 + 0.997421i \(0.522864\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 10.3229 0.663582
\(243\) 16.0296 1.02830
\(244\) −21.1274 −1.35254
\(245\) 0 0
\(246\) 22.3805 1.42693
\(247\) 13.8160 0.879089
\(248\) −21.6655 −1.37576
\(249\) −2.69373 −0.170708
\(250\) 0 0
\(251\) 11.1504 0.703807 0.351903 0.936036i \(-0.385535\pi\)
0.351903 + 0.936036i \(0.385535\pi\)
\(252\) 5.99571 0.377694
\(253\) 3.75071 0.235805
\(254\) 5.23196 0.328282
\(255\) 0 0
\(256\) −31.9558 −1.99724
\(257\) −8.50879 −0.530763 −0.265382 0.964143i \(-0.585498\pi\)
−0.265382 + 0.964143i \(0.585498\pi\)
\(258\) 18.5982 1.15787
\(259\) −3.47905 −0.216177
\(260\) 0 0
\(261\) 0.260951 0.0161524
\(262\) 37.4039 2.31082
\(263\) 10.5798 0.652377 0.326188 0.945305i \(-0.394236\pi\)
0.326188 + 0.945305i \(0.394236\pi\)
\(264\) 12.6202 0.776720
\(265\) 0 0
\(266\) 6.02037 0.369132
\(267\) −9.78813 −0.599024
\(268\) 22.7447 1.38935
\(269\) 6.26143 0.381766 0.190883 0.981613i \(-0.438865\pi\)
0.190883 + 0.981613i \(0.438865\pi\)
\(270\) 0 0
\(271\) 6.22770 0.378306 0.189153 0.981948i \(-0.439426\pi\)
0.189153 + 0.981948i \(0.439426\pi\)
\(272\) 1.92028 0.116434
\(273\) −3.09178 −0.187123
\(274\) 38.4160 2.32079
\(275\) 0 0
\(276\) −5.70755 −0.343554
\(277\) −0.195324 −0.0117359 −0.00586793 0.999983i \(-0.501868\pi\)
−0.00586793 + 0.999983i \(0.501868\pi\)
\(278\) −33.8824 −2.03213
\(279\) −8.94188 −0.535336
\(280\) 0 0
\(281\) −21.0354 −1.25486 −0.627432 0.778671i \(-0.715894\pi\)
−0.627432 + 0.778671i \(0.715894\pi\)
\(282\) 5.54370 0.330123
\(283\) −12.8269 −0.762478 −0.381239 0.924477i \(-0.624503\pi\)
−0.381239 + 0.924477i \(0.624503\pi\)
\(284\) 8.31740 0.493547
\(285\) 0 0
\(286\) 26.6831 1.57780
\(287\) 6.86075 0.404977
\(288\) −0.107126 −0.00631248
\(289\) −16.7657 −0.986220
\(290\) 0 0
\(291\) 6.21926 0.364579
\(292\) 62.1943 3.63965
\(293\) 25.7912 1.50674 0.753369 0.657598i \(-0.228427\pi\)
0.753369 + 0.657598i \(0.228427\pi\)
\(294\) 15.6579 0.913186
\(295\) 0 0
\(296\) −22.8141 −1.32604
\(297\) 12.9615 0.752102
\(298\) 11.5200 0.667338
\(299\) −6.02557 −0.348468
\(300\) 0 0
\(301\) 5.70129 0.328617
\(302\) −38.6255 −2.22265
\(303\) 4.54296 0.260986
\(304\) 13.0999 0.751332
\(305\) 0 0
\(306\) 2.38848 0.136540
\(307\) −28.5348 −1.62856 −0.814282 0.580469i \(-0.802869\pi\)
−0.814282 + 0.580469i \(0.802869\pi\)
\(308\) 7.74799 0.441483
\(309\) 5.90914 0.336160
\(310\) 0 0
\(311\) 4.04451 0.229343 0.114672 0.993403i \(-0.463418\pi\)
0.114672 + 0.993403i \(0.463418\pi\)
\(312\) −20.2746 −1.14782
\(313\) 10.8140 0.611243 0.305622 0.952153i \(-0.401136\pi\)
0.305622 + 0.952153i \(0.401136\pi\)
\(314\) 15.3384 0.865598
\(315\) 0 0
\(316\) −39.9547 −2.24763
\(317\) −2.62335 −0.147342 −0.0736711 0.997283i \(-0.523472\pi\)
−0.0736711 + 0.997283i \(0.523472\pi\)
\(318\) −30.4757 −1.70899
\(319\) 0.337215 0.0188804
\(320\) 0 0
\(321\) 4.79333 0.267538
\(322\) −2.62567 −0.146323
\(323\) 1.59815 0.0889232
\(324\) 4.42953 0.246085
\(325\) 0 0
\(326\) 55.6008 3.07944
\(327\) 9.55240 0.528249
\(328\) 44.9899 2.48415
\(329\) 1.69942 0.0936922
\(330\) 0 0
\(331\) −10.6123 −0.583307 −0.291653 0.956524i \(-0.594205\pi\)
−0.291653 + 0.956524i \(0.594205\pi\)
\(332\) −10.8448 −0.595185
\(333\) −9.41594 −0.515991
\(334\) 45.2264 2.47468
\(335\) 0 0
\(336\) −2.93154 −0.159928
\(337\) −3.53987 −0.192829 −0.0964146 0.995341i \(-0.530737\pi\)
−0.0964146 + 0.995341i \(0.530737\pi\)
\(338\) −11.0379 −0.600381
\(339\) 4.71125 0.255880
\(340\) 0 0
\(341\) −11.5552 −0.625749
\(342\) 16.2940 0.881076
\(343\) 10.0129 0.540643
\(344\) 37.3866 2.01575
\(345\) 0 0
\(346\) −28.1012 −1.51073
\(347\) 13.6131 0.730791 0.365396 0.930852i \(-0.380934\pi\)
0.365396 + 0.930852i \(0.380934\pi\)
\(348\) −0.513149 −0.0275077
\(349\) 3.51082 0.187930 0.0939649 0.995576i \(-0.470046\pi\)
0.0939649 + 0.995576i \(0.470046\pi\)
\(350\) 0 0
\(351\) −20.8229 −1.11144
\(352\) −0.138435 −0.00737859
\(353\) −10.7398 −0.571621 −0.285810 0.958286i \(-0.592263\pi\)
−0.285810 + 0.958286i \(0.592263\pi\)
\(354\) 17.7350 0.942606
\(355\) 0 0
\(356\) −39.4063 −2.08853
\(357\) −0.357637 −0.0189282
\(358\) 30.4728 1.61054
\(359\) 12.0903 0.638099 0.319050 0.947738i \(-0.396636\pi\)
0.319050 + 0.947738i \(0.396636\pi\)
\(360\) 0 0
\(361\) −8.09763 −0.426191
\(362\) 27.1781 1.42845
\(363\) −4.18337 −0.219570
\(364\) −12.4473 −0.652415
\(365\) 0 0
\(366\) 12.8487 0.671610
\(367\) −2.89274 −0.151000 −0.0754999 0.997146i \(-0.524055\pi\)
−0.0754999 + 0.997146i \(0.524055\pi\)
\(368\) −5.71328 −0.297825
\(369\) 18.5684 0.966634
\(370\) 0 0
\(371\) −9.34233 −0.485030
\(372\) 17.5839 0.911681
\(373\) −37.8889 −1.96181 −0.980907 0.194479i \(-0.937698\pi\)
−0.980907 + 0.194479i \(0.937698\pi\)
\(374\) 3.08653 0.159601
\(375\) 0 0
\(376\) 11.1441 0.574713
\(377\) −0.541741 −0.0279011
\(378\) −9.07365 −0.466698
\(379\) −9.33140 −0.479322 −0.239661 0.970857i \(-0.577036\pi\)
−0.239661 + 0.970857i \(0.577036\pi\)
\(380\) 0 0
\(381\) −2.12026 −0.108624
\(382\) −12.6659 −0.648044
\(383\) −34.9438 −1.78554 −0.892771 0.450510i \(-0.851242\pi\)
−0.892771 + 0.450510i \(0.851242\pi\)
\(384\) 19.4868 0.994433
\(385\) 0 0
\(386\) 34.8497 1.77380
\(387\) 15.4304 0.784370
\(388\) 25.0383 1.27113
\(389\) −22.2652 −1.12889 −0.564445 0.825470i \(-0.690910\pi\)
−0.564445 + 0.825470i \(0.690910\pi\)
\(390\) 0 0
\(391\) −0.697000 −0.0352488
\(392\) 31.4759 1.58977
\(393\) −15.1580 −0.764618
\(394\) 16.2603 0.819182
\(395\) 0 0
\(396\) 20.9697 1.05377
\(397\) −18.6917 −0.938110 −0.469055 0.883169i \(-0.655405\pi\)
−0.469055 + 0.883169i \(0.655405\pi\)
\(398\) −22.3652 −1.12107
\(399\) −2.43976 −0.122141
\(400\) 0 0
\(401\) 30.3420 1.51521 0.757604 0.652715i \(-0.226370\pi\)
0.757604 + 0.652715i \(0.226370\pi\)
\(402\) −13.8322 −0.689889
\(403\) 18.5636 0.924720
\(404\) 18.2897 0.909944
\(405\) 0 0
\(406\) −0.236066 −0.0117158
\(407\) −12.1678 −0.603136
\(408\) −2.34523 −0.116106
\(409\) 16.1799 0.800046 0.400023 0.916505i \(-0.369002\pi\)
0.400023 + 0.916505i \(0.369002\pi\)
\(410\) 0 0
\(411\) −15.5681 −0.767918
\(412\) 23.7898 1.17204
\(413\) 5.43668 0.267521
\(414\) −7.10630 −0.349255
\(415\) 0 0
\(416\) 0.222398 0.0109039
\(417\) 13.7309 0.672404
\(418\) 21.0560 1.02988
\(419\) 14.4615 0.706488 0.353244 0.935531i \(-0.385079\pi\)
0.353244 + 0.935531i \(0.385079\pi\)
\(420\) 0 0
\(421\) 14.6314 0.713093 0.356546 0.934278i \(-0.383954\pi\)
0.356546 + 0.934278i \(0.383954\pi\)
\(422\) 47.9858 2.33591
\(423\) 4.59944 0.223632
\(424\) −61.2631 −2.97520
\(425\) 0 0
\(426\) −5.05825 −0.245073
\(427\) 3.93876 0.190610
\(428\) 19.2976 0.932785
\(429\) −10.8133 −0.522073
\(430\) 0 0
\(431\) 17.3814 0.837233 0.418616 0.908163i \(-0.362515\pi\)
0.418616 + 0.908163i \(0.362515\pi\)
\(432\) −19.7437 −0.949917
\(433\) 22.7286 1.09227 0.546133 0.837698i \(-0.316099\pi\)
0.546133 + 0.837698i \(0.316099\pi\)
\(434\) 8.08917 0.388293
\(435\) 0 0
\(436\) 38.4573 1.84177
\(437\) −4.75486 −0.227456
\(438\) −37.8236 −1.80728
\(439\) −36.3500 −1.73489 −0.867446 0.497531i \(-0.834240\pi\)
−0.867446 + 0.497531i \(0.834240\pi\)
\(440\) 0 0
\(441\) 12.9909 0.618613
\(442\) −4.95856 −0.235855
\(443\) 41.2429 1.95951 0.979755 0.200201i \(-0.0641594\pi\)
0.979755 + 0.200201i \(0.0641594\pi\)
\(444\) 18.5161 0.878735
\(445\) 0 0
\(446\) 11.7145 0.554699
\(447\) −4.66851 −0.220813
\(448\) 6.00602 0.283758
\(449\) 1.81576 0.0856909 0.0428454 0.999082i \(-0.486358\pi\)
0.0428454 + 0.999082i \(0.486358\pi\)
\(450\) 0 0
\(451\) 23.9952 1.12989
\(452\) 18.9672 0.892141
\(453\) 15.6530 0.735444
\(454\) 51.8151 2.43180
\(455\) 0 0
\(456\) −15.9989 −0.749218
\(457\) 9.57207 0.447763 0.223881 0.974616i \(-0.428127\pi\)
0.223881 + 0.974616i \(0.428127\pi\)
\(458\) −54.9892 −2.56948
\(459\) −2.40866 −0.112427
\(460\) 0 0
\(461\) −7.96834 −0.371123 −0.185561 0.982633i \(-0.559410\pi\)
−0.185561 + 0.982633i \(0.559410\pi\)
\(462\) −4.71196 −0.219220
\(463\) 20.5525 0.955157 0.477579 0.878589i \(-0.341515\pi\)
0.477579 + 0.878589i \(0.341515\pi\)
\(464\) −0.513664 −0.0238463
\(465\) 0 0
\(466\) 26.9331 1.24765
\(467\) −15.8957 −0.735567 −0.367783 0.929912i \(-0.619883\pi\)
−0.367783 + 0.929912i \(0.619883\pi\)
\(468\) −33.6882 −1.55724
\(469\) −4.24027 −0.195798
\(470\) 0 0
\(471\) −6.21592 −0.286415
\(472\) 35.6514 1.64099
\(473\) 19.9400 0.916842
\(474\) 24.2985 1.11607
\(475\) 0 0
\(476\) −1.43982 −0.0659942
\(477\) −25.2848 −1.15771
\(478\) 5.43303 0.248501
\(479\) −41.6793 −1.90437 −0.952187 0.305516i \(-0.901171\pi\)
−0.952187 + 0.305516i \(0.901171\pi\)
\(480\) 0 0
\(481\) 19.5478 0.891303
\(482\) −2.44838 −0.111521
\(483\) 1.06406 0.0484162
\(484\) −16.8420 −0.765544
\(485\) 0 0
\(486\) −39.2465 −1.78026
\(487\) −7.56632 −0.342863 −0.171431 0.985196i \(-0.554839\pi\)
−0.171431 + 0.985196i \(0.554839\pi\)
\(488\) 25.8287 1.16921
\(489\) −22.5323 −1.01895
\(490\) 0 0
\(491\) −26.7723 −1.20822 −0.604108 0.796903i \(-0.706470\pi\)
−0.604108 + 0.796903i \(0.706470\pi\)
\(492\) −36.5141 −1.64618
\(493\) −0.0626653 −0.00282230
\(494\) −33.8268 −1.52194
\(495\) 0 0
\(496\) 17.6015 0.790331
\(497\) −1.55061 −0.0695543
\(498\) 6.59528 0.295542
\(499\) −27.0405 −1.21050 −0.605249 0.796036i \(-0.706926\pi\)
−0.605249 + 0.796036i \(0.706926\pi\)
\(500\) 0 0
\(501\) −18.3281 −0.818838
\(502\) −27.3004 −1.21848
\(503\) 0.950190 0.0423669 0.0211834 0.999776i \(-0.493257\pi\)
0.0211834 + 0.999776i \(0.493257\pi\)
\(504\) −7.32990 −0.326500
\(505\) 0 0
\(506\) −9.18315 −0.408241
\(507\) 4.47311 0.198658
\(508\) −8.53601 −0.378724
\(509\) −32.8758 −1.45719 −0.728596 0.684944i \(-0.759827\pi\)
−0.728596 + 0.684944i \(0.759827\pi\)
\(510\) 0 0
\(511\) −11.5948 −0.512926
\(512\) 38.9603 1.72182
\(513\) −16.4316 −0.725473
\(514\) 20.8327 0.918893
\(515\) 0 0
\(516\) −30.3432 −1.33579
\(517\) 5.94365 0.261402
\(518\) 8.51803 0.374261
\(519\) 11.3880 0.499879
\(520\) 0 0
\(521\) −7.96960 −0.349155 −0.174577 0.984643i \(-0.555856\pi\)
−0.174577 + 0.984643i \(0.555856\pi\)
\(522\) −0.638906 −0.0279642
\(523\) −16.8372 −0.736240 −0.368120 0.929778i \(-0.619999\pi\)
−0.368120 + 0.929778i \(0.619999\pi\)
\(524\) −61.0249 −2.66589
\(525\) 0 0
\(526\) −25.9033 −1.12944
\(527\) 2.14732 0.0935389
\(528\) −10.2529 −0.446201
\(529\) −20.9263 −0.909837
\(530\) 0 0
\(531\) 14.7142 0.638543
\(532\) −9.82231 −0.425851
\(533\) −38.5486 −1.66973
\(534\) 23.9651 1.03707
\(535\) 0 0
\(536\) −27.8059 −1.20103
\(537\) −12.3491 −0.532905
\(538\) −15.3304 −0.660939
\(539\) 16.7875 0.723090
\(540\) 0 0
\(541\) 22.9397 0.986254 0.493127 0.869957i \(-0.335854\pi\)
0.493127 + 0.869957i \(0.335854\pi\)
\(542\) −15.2478 −0.654948
\(543\) −11.0140 −0.472655
\(544\) 0.0257256 0.00110297
\(545\) 0 0
\(546\) 7.56984 0.323959
\(547\) 8.56387 0.366164 0.183082 0.983098i \(-0.441393\pi\)
0.183082 + 0.983098i \(0.441393\pi\)
\(548\) −62.6761 −2.67739
\(549\) 10.6601 0.454964
\(550\) 0 0
\(551\) −0.427495 −0.0182119
\(552\) 6.97762 0.296987
\(553\) 7.44873 0.316752
\(554\) 0.478227 0.0203179
\(555\) 0 0
\(556\) 55.2795 2.34437
\(557\) −6.79073 −0.287732 −0.143866 0.989597i \(-0.545954\pi\)
−0.143866 + 0.989597i \(0.545954\pi\)
\(558\) 21.8931 0.926810
\(559\) −32.0339 −1.35489
\(560\) 0 0
\(561\) −1.25082 −0.0528097
\(562\) 51.5025 2.17250
\(563\) −20.2542 −0.853612 −0.426806 0.904343i \(-0.640361\pi\)
−0.426806 + 0.904343i \(0.640361\pi\)
\(564\) −9.04462 −0.380847
\(565\) 0 0
\(566\) 31.4050 1.32005
\(567\) −0.825794 −0.0346801
\(568\) −10.1682 −0.426649
\(569\) −31.2543 −1.31025 −0.655125 0.755521i \(-0.727384\pi\)
−0.655125 + 0.755521i \(0.727384\pi\)
\(570\) 0 0
\(571\) −31.1637 −1.30416 −0.652081 0.758149i \(-0.726104\pi\)
−0.652081 + 0.758149i \(0.726104\pi\)
\(572\) −43.5338 −1.82024
\(573\) 5.13287 0.214429
\(574\) −16.7977 −0.701123
\(575\) 0 0
\(576\) 16.2551 0.677297
\(577\) −30.7522 −1.28023 −0.640114 0.768280i \(-0.721113\pi\)
−0.640114 + 0.768280i \(0.721113\pi\)
\(578\) 41.0489 1.70741
\(579\) −14.1229 −0.586927
\(580\) 0 0
\(581\) 2.02179 0.0838778
\(582\) −15.2271 −0.631184
\(583\) −32.6744 −1.35323
\(584\) −76.0341 −3.14631
\(585\) 0 0
\(586\) −63.1467 −2.60857
\(587\) −17.7844 −0.734042 −0.367021 0.930213i \(-0.619622\pi\)
−0.367021 + 0.930213i \(0.619622\pi\)
\(588\) −25.5460 −1.05350
\(589\) 14.6488 0.603593
\(590\) 0 0
\(591\) −6.58950 −0.271056
\(592\) 18.5347 0.761770
\(593\) 1.96286 0.0806051 0.0403026 0.999188i \(-0.487168\pi\)
0.0403026 + 0.999188i \(0.487168\pi\)
\(594\) −31.7347 −1.30209
\(595\) 0 0
\(596\) −18.7951 −0.769878
\(597\) 9.06352 0.370945
\(598\) 14.7529 0.603291
\(599\) −26.8177 −1.09574 −0.547871 0.836563i \(-0.684562\pi\)
−0.547871 + 0.836563i \(0.684562\pi\)
\(600\) 0 0
\(601\) 31.3885 1.28036 0.640182 0.768223i \(-0.278859\pi\)
0.640182 + 0.768223i \(0.278859\pi\)
\(602\) −13.9589 −0.568923
\(603\) −11.4762 −0.467346
\(604\) 63.0181 2.56417
\(605\) 0 0
\(606\) −11.1229 −0.451837
\(607\) 31.9764 1.29788 0.648941 0.760839i \(-0.275212\pi\)
0.648941 + 0.760839i \(0.275212\pi\)
\(608\) 0.175497 0.00711733
\(609\) 0.0956661 0.00387658
\(610\) 0 0
\(611\) −9.54858 −0.386294
\(612\) −3.89684 −0.157521
\(613\) 19.1393 0.773028 0.386514 0.922283i \(-0.373679\pi\)
0.386514 + 0.922283i \(0.373679\pi\)
\(614\) 69.8639 2.81948
\(615\) 0 0
\(616\) −9.47211 −0.381642
\(617\) −40.5121 −1.63096 −0.815478 0.578788i \(-0.803526\pi\)
−0.815478 + 0.578788i \(0.803526\pi\)
\(618\) −14.4678 −0.581982
\(619\) −8.35556 −0.335838 −0.167919 0.985801i \(-0.553705\pi\)
−0.167919 + 0.985801i \(0.553705\pi\)
\(620\) 0 0
\(621\) 7.16632 0.287575
\(622\) −9.90251 −0.397054
\(623\) 7.34650 0.294331
\(624\) 16.4715 0.659387
\(625\) 0 0
\(626\) −26.4768 −1.05822
\(627\) −8.53295 −0.340773
\(628\) −25.0249 −0.998601
\(629\) 2.26117 0.0901586
\(630\) 0 0
\(631\) 18.3668 0.731169 0.365585 0.930778i \(-0.380869\pi\)
0.365585 + 0.930778i \(0.380869\pi\)
\(632\) 48.8456 1.94297
\(633\) −19.4463 −0.772922
\(634\) 6.42297 0.255089
\(635\) 0 0
\(636\) 49.7215 1.97159
\(637\) −26.9694 −1.06857
\(638\) −0.825630 −0.0326870
\(639\) −4.19668 −0.166018
\(640\) 0 0
\(641\) −21.6917 −0.856772 −0.428386 0.903596i \(-0.640918\pi\)
−0.428386 + 0.903596i \(0.640918\pi\)
\(642\) −11.7359 −0.463179
\(643\) −23.2362 −0.916347 −0.458174 0.888863i \(-0.651496\pi\)
−0.458174 + 0.888863i \(0.651496\pi\)
\(644\) 4.28381 0.168806
\(645\) 0 0
\(646\) −3.91287 −0.153950
\(647\) 24.4246 0.960232 0.480116 0.877205i \(-0.340595\pi\)
0.480116 + 0.877205i \(0.340595\pi\)
\(648\) −5.41521 −0.212729
\(649\) 19.0145 0.746386
\(650\) 0 0
\(651\) −3.27815 −0.128481
\(652\) −90.7135 −3.55261
\(653\) 13.0994 0.512618 0.256309 0.966595i \(-0.417494\pi\)
0.256309 + 0.966595i \(0.417494\pi\)
\(654\) −23.3879 −0.914540
\(655\) 0 0
\(656\) −36.5507 −1.42707
\(657\) −31.3811 −1.22429
\(658\) −4.16083 −0.162206
\(659\) −37.3844 −1.45629 −0.728145 0.685423i \(-0.759617\pi\)
−0.728145 + 0.685423i \(0.759617\pi\)
\(660\) 0 0
\(661\) 30.5258 1.18731 0.593657 0.804718i \(-0.297683\pi\)
0.593657 + 0.804718i \(0.297683\pi\)
\(662\) 25.9830 1.00986
\(663\) 2.00946 0.0780411
\(664\) 13.2580 0.514511
\(665\) 0 0
\(666\) 23.0538 0.893317
\(667\) 0.186444 0.00721913
\(668\) −73.7876 −2.85493
\(669\) −4.74733 −0.183542
\(670\) 0 0
\(671\) 13.7756 0.531802
\(672\) −0.0392732 −0.00151499
\(673\) 18.0019 0.693923 0.346962 0.937879i \(-0.387213\pi\)
0.346962 + 0.937879i \(0.387213\pi\)
\(674\) 8.66696 0.333839
\(675\) 0 0
\(676\) 18.0084 0.692632
\(677\) 1.78554 0.0686239 0.0343119 0.999411i \(-0.489076\pi\)
0.0343119 + 0.999411i \(0.489076\pi\)
\(678\) −11.5349 −0.442997
\(679\) −4.66787 −0.179137
\(680\) 0 0
\(681\) −20.9981 −0.804650
\(682\) 28.2915 1.08334
\(683\) −16.9962 −0.650343 −0.325171 0.945655i \(-0.605422\pi\)
−0.325171 + 0.945655i \(0.605422\pi\)
\(684\) −26.5838 −1.01646
\(685\) 0 0
\(686\) −24.5153 −0.935998
\(687\) 22.2844 0.850205
\(688\) −30.3737 −1.15799
\(689\) 52.4919 1.99978
\(690\) 0 0
\(691\) −9.73250 −0.370242 −0.185121 0.982716i \(-0.559268\pi\)
−0.185121 + 0.982716i \(0.559268\pi\)
\(692\) 45.8475 1.74286
\(693\) −3.90937 −0.148505
\(694\) −33.3301 −1.26519
\(695\) 0 0
\(696\) 0.627338 0.0237792
\(697\) −4.45906 −0.168899
\(698\) −8.59582 −0.325356
\(699\) −10.9147 −0.412831
\(700\) 0 0
\(701\) 31.1728 1.17738 0.588690 0.808359i \(-0.299644\pi\)
0.588690 + 0.808359i \(0.299644\pi\)
\(702\) 50.9823 1.92420
\(703\) 15.4254 0.581781
\(704\) 21.0058 0.791686
\(705\) 0 0
\(706\) 26.2951 0.989627
\(707\) −3.40973 −0.128236
\(708\) −28.9349 −1.08744
\(709\) −47.2147 −1.77318 −0.886592 0.462552i \(-0.846934\pi\)
−0.886592 + 0.462552i \(0.846934\pi\)
\(710\) 0 0
\(711\) 20.1598 0.756050
\(712\) 48.1752 1.80544
\(713\) −6.38879 −0.239262
\(714\) 0.875632 0.0327697
\(715\) 0 0
\(716\) −49.7168 −1.85801
\(717\) −2.20174 −0.0822256
\(718\) −29.6015 −1.10472
\(719\) 10.9829 0.409592 0.204796 0.978805i \(-0.434347\pi\)
0.204796 + 0.978805i \(0.434347\pi\)
\(720\) 0 0
\(721\) −4.43512 −0.165172
\(722\) 19.8261 0.737851
\(723\) 0.992209 0.0369007
\(724\) −44.3415 −1.64794
\(725\) 0 0
\(726\) 10.2425 0.380134
\(727\) 4.07723 0.151216 0.0756080 0.997138i \(-0.475910\pi\)
0.0756080 + 0.997138i \(0.475910\pi\)
\(728\) 15.2171 0.563983
\(729\) 12.5780 0.465853
\(730\) 0 0
\(731\) −3.70549 −0.137052
\(732\) −20.9628 −0.774806
\(733\) −13.3951 −0.494759 −0.247379 0.968919i \(-0.579569\pi\)
−0.247379 + 0.968919i \(0.579569\pi\)
\(734\) 7.08253 0.261421
\(735\) 0 0
\(736\) −0.0765396 −0.00282129
\(737\) −14.8302 −0.546276
\(738\) −45.4626 −1.67350
\(739\) 22.3405 0.821810 0.410905 0.911678i \(-0.365213\pi\)
0.410905 + 0.911678i \(0.365213\pi\)
\(740\) 0 0
\(741\) 13.7083 0.503588
\(742\) 22.8736 0.839716
\(743\) −36.1839 −1.32746 −0.663730 0.747973i \(-0.731027\pi\)
−0.663730 + 0.747973i \(0.731027\pi\)
\(744\) −21.4967 −0.788107
\(745\) 0 0
\(746\) 92.7665 3.39642
\(747\) 5.47191 0.200207
\(748\) −5.03572 −0.184124
\(749\) −3.59764 −0.131455
\(750\) 0 0
\(751\) −10.1216 −0.369341 −0.184671 0.982800i \(-0.559122\pi\)
−0.184671 + 0.982800i \(0.559122\pi\)
\(752\) −9.05370 −0.330155
\(753\) 11.0635 0.403177
\(754\) 1.32639 0.0483042
\(755\) 0 0
\(756\) 14.8038 0.538408
\(757\) 32.6680 1.18734 0.593670 0.804709i \(-0.297679\pi\)
0.593670 + 0.804709i \(0.297679\pi\)
\(758\) 22.8468 0.829834
\(759\) 3.72148 0.135081
\(760\) 0 0
\(761\) 24.2568 0.879309 0.439655 0.898167i \(-0.355101\pi\)
0.439655 + 0.898167i \(0.355101\pi\)
\(762\) 5.19120 0.188057
\(763\) −7.16957 −0.259556
\(764\) 20.6646 0.747619
\(765\) 0 0
\(766\) 85.5556 3.09125
\(767\) −30.5472 −1.10299
\(768\) −31.7069 −1.14412
\(769\) −16.5744 −0.597689 −0.298845 0.954302i \(-0.596601\pi\)
−0.298845 + 0.954302i \(0.596601\pi\)
\(770\) 0 0
\(771\) −8.44249 −0.304049
\(772\) −56.8578 −2.04636
\(773\) −37.9826 −1.36614 −0.683070 0.730353i \(-0.739356\pi\)
−0.683070 + 0.730353i \(0.739356\pi\)
\(774\) −37.7794 −1.35795
\(775\) 0 0
\(776\) −30.6099 −1.09883
\(777\) −3.45194 −0.123838
\(778\) 54.5137 1.95441
\(779\) −30.4192 −1.08988
\(780\) 0 0
\(781\) −5.42318 −0.194057
\(782\) 1.70652 0.0610251
\(783\) 0.644303 0.0230255
\(784\) −25.5717 −0.913275
\(785\) 0 0
\(786\) 37.1125 1.32376
\(787\) 1.38906 0.0495146 0.0247573 0.999693i \(-0.492119\pi\)
0.0247573 + 0.999693i \(0.492119\pi\)
\(788\) −26.5289 −0.945052
\(789\) 10.4973 0.373715
\(790\) 0 0
\(791\) −3.53604 −0.125727
\(792\) −25.6360 −0.910936
\(793\) −22.1308 −0.785887
\(794\) 45.7644 1.62412
\(795\) 0 0
\(796\) 36.4891 1.29332
\(797\) 48.2065 1.70756 0.853781 0.520632i \(-0.174304\pi\)
0.853781 + 0.520632i \(0.174304\pi\)
\(798\) 5.97346 0.211458
\(799\) −1.10452 −0.0390751
\(800\) 0 0
\(801\) 19.8831 0.702534
\(802\) −74.2888 −2.62323
\(803\) −40.5524 −1.43106
\(804\) 22.5675 0.795893
\(805\) 0 0
\(806\) −45.4508 −1.60094
\(807\) 6.21265 0.218695
\(808\) −22.3596 −0.786606
\(809\) 14.6738 0.515902 0.257951 0.966158i \(-0.416953\pi\)
0.257951 + 0.966158i \(0.416953\pi\)
\(810\) 0 0
\(811\) −19.7745 −0.694377 −0.347189 0.937795i \(-0.612864\pi\)
−0.347189 + 0.937795i \(0.612864\pi\)
\(812\) 0.385145 0.0135159
\(813\) 6.17918 0.216713
\(814\) 29.7914 1.04419
\(815\) 0 0
\(816\) 1.90532 0.0666995
\(817\) −25.2784 −0.884379
\(818\) −39.6146 −1.38509
\(819\) 6.28047 0.219457
\(820\) 0 0
\(821\) −28.5257 −0.995554 −0.497777 0.867305i \(-0.665850\pi\)
−0.497777 + 0.867305i \(0.665850\pi\)
\(822\) 38.1167 1.32947
\(823\) 20.1194 0.701320 0.350660 0.936503i \(-0.385957\pi\)
0.350660 + 0.936503i \(0.385957\pi\)
\(824\) −29.0836 −1.01318
\(825\) 0 0
\(826\) −13.3111 −0.463151
\(827\) −25.3763 −0.882421 −0.441211 0.897404i \(-0.645451\pi\)
−0.441211 + 0.897404i \(0.645451\pi\)
\(828\) 11.5940 0.402920
\(829\) 40.5872 1.40965 0.704826 0.709380i \(-0.251025\pi\)
0.704826 + 0.709380i \(0.251025\pi\)
\(830\) 0 0
\(831\) −0.193802 −0.00672291
\(832\) −33.7462 −1.16994
\(833\) −3.11966 −0.108090
\(834\) −33.6184 −1.16411
\(835\) 0 0
\(836\) −34.3531 −1.18813
\(837\) −22.0781 −0.763129
\(838\) −35.4071 −1.22312
\(839\) −16.9800 −0.586216 −0.293108 0.956079i \(-0.594689\pi\)
−0.293108 + 0.956079i \(0.594689\pi\)
\(840\) 0 0
\(841\) −28.9832 −0.999422
\(842\) −35.8233 −1.23455
\(843\) −20.8715 −0.718852
\(844\) −78.2895 −2.69484
\(845\) 0 0
\(846\) −11.2612 −0.387167
\(847\) 3.13984 0.107886
\(848\) 49.7714 1.70916
\(849\) −12.7269 −0.436787
\(850\) 0 0
\(851\) −6.72750 −0.230616
\(852\) 8.25260 0.282729
\(853\) −3.23644 −0.110814 −0.0554069 0.998464i \(-0.517646\pi\)
−0.0554069 + 0.998464i \(0.517646\pi\)
\(854\) −9.64358 −0.329997
\(855\) 0 0
\(856\) −23.5918 −0.806351
\(857\) 1.40877 0.0481228 0.0240614 0.999710i \(-0.492340\pi\)
0.0240614 + 0.999710i \(0.492340\pi\)
\(858\) 26.4752 0.903848
\(859\) 43.3662 1.47963 0.739817 0.672808i \(-0.234912\pi\)
0.739817 + 0.672808i \(0.234912\pi\)
\(860\) 0 0
\(861\) 6.80730 0.231992
\(862\) −42.5563 −1.44947
\(863\) 36.3292 1.23666 0.618329 0.785919i \(-0.287810\pi\)
0.618329 + 0.785919i \(0.287810\pi\)
\(864\) −0.264501 −0.00899852
\(865\) 0 0
\(866\) −55.6482 −1.89100
\(867\) −16.6351 −0.564958
\(868\) −13.1976 −0.447956
\(869\) 26.0516 0.883739
\(870\) 0 0
\(871\) 23.8249 0.807276
\(872\) −47.0150 −1.59213
\(873\) −12.6335 −0.427578
\(874\) 11.6417 0.393786
\(875\) 0 0
\(876\) 61.7097 2.08498
\(877\) −30.8667 −1.04229 −0.521147 0.853467i \(-0.674496\pi\)
−0.521147 + 0.853467i \(0.674496\pi\)
\(878\) 88.9987 3.00356
\(879\) 25.5903 0.863139
\(880\) 0 0
\(881\) −34.9920 −1.17891 −0.589456 0.807801i \(-0.700658\pi\)
−0.589456 + 0.807801i \(0.700658\pi\)
\(882\) −31.8066 −1.07098
\(883\) −44.7518 −1.50602 −0.753008 0.658011i \(-0.771398\pi\)
−0.753008 + 0.658011i \(0.771398\pi\)
\(884\) 8.08996 0.272095
\(885\) 0 0
\(886\) −100.978 −3.39243
\(887\) −21.2497 −0.713495 −0.356747 0.934201i \(-0.616114\pi\)
−0.356747 + 0.934201i \(0.616114\pi\)
\(888\) −22.6364 −0.759627
\(889\) 1.59136 0.0533726
\(890\) 0 0
\(891\) −2.88818 −0.0967576
\(892\) −19.1124 −0.639931
\(893\) −7.53491 −0.252146
\(894\) 11.4303 0.382286
\(895\) 0 0
\(896\) −14.6259 −0.488616
\(897\) −5.97863 −0.199621
\(898\) −4.44566 −0.148354
\(899\) −0.574397 −0.0191572
\(900\) 0 0
\(901\) 6.07194 0.202286
\(902\) −58.7493 −1.95614
\(903\) 5.65687 0.188249
\(904\) −23.1878 −0.771216
\(905\) 0 0
\(906\) −38.3246 −1.27325
\(907\) −7.07983 −0.235082 −0.117541 0.993068i \(-0.537501\pi\)
−0.117541 + 0.993068i \(0.537501\pi\)
\(908\) −84.5370 −2.80546
\(909\) −9.22833 −0.306085
\(910\) 0 0
\(911\) −40.6767 −1.34768 −0.673840 0.738877i \(-0.735356\pi\)
−0.673840 + 0.738877i \(0.735356\pi\)
\(912\) 12.9979 0.430402
\(913\) 7.07110 0.234019
\(914\) −23.4361 −0.775196
\(915\) 0 0
\(916\) 89.7156 2.96429
\(917\) 11.3768 0.375696
\(918\) 5.89731 0.194640
\(919\) −11.3936 −0.375841 −0.187920 0.982184i \(-0.560175\pi\)
−0.187920 + 0.982184i \(0.560175\pi\)
\(920\) 0 0
\(921\) −28.3124 −0.932927
\(922\) 19.5095 0.642512
\(923\) 8.71243 0.286773
\(924\) 7.68763 0.252904
\(925\) 0 0
\(926\) −50.3204 −1.65363
\(927\) −12.0035 −0.394247
\(928\) −0.00688145 −0.000225895 0
\(929\) −38.5646 −1.26526 −0.632631 0.774453i \(-0.718025\pi\)
−0.632631 + 0.774453i \(0.718025\pi\)
\(930\) 0 0
\(931\) −21.2819 −0.697488
\(932\) −43.9417 −1.43936
\(933\) 4.01300 0.131380
\(934\) 38.9188 1.27346
\(935\) 0 0
\(936\) 41.1847 1.34616
\(937\) 35.6493 1.16461 0.582306 0.812970i \(-0.302151\pi\)
0.582306 + 0.812970i \(0.302151\pi\)
\(938\) 10.3818 0.338978
\(939\) 10.7297 0.350152
\(940\) 0 0
\(941\) −0.459712 −0.0149862 −0.00749308 0.999972i \(-0.502385\pi\)
−0.00749308 + 0.999972i \(0.502385\pi\)
\(942\) 15.2189 0.495860
\(943\) 13.2668 0.432025
\(944\) −28.9640 −0.942697
\(945\) 0 0
\(946\) −48.8207 −1.58730
\(947\) −16.4312 −0.533944 −0.266972 0.963704i \(-0.586023\pi\)
−0.266972 + 0.963704i \(0.586023\pi\)
\(948\) −39.6434 −1.28756
\(949\) 65.1482 2.11480
\(950\) 0 0
\(951\) −2.60291 −0.0844053
\(952\) 1.76022 0.0570490
\(953\) 27.4225 0.888302 0.444151 0.895952i \(-0.353505\pi\)
0.444151 + 0.895952i \(0.353505\pi\)
\(954\) 61.9067 2.00430
\(955\) 0 0
\(956\) −8.86406 −0.286684
\(957\) 0.334588 0.0108157
\(958\) 102.047 3.29698
\(959\) 11.6847 0.377318
\(960\) 0 0
\(961\) −11.3174 −0.365076
\(962\) −47.8604 −1.54308
\(963\) −9.73692 −0.313768
\(964\) 3.99457 0.128656
\(965\) 0 0
\(966\) −2.60521 −0.0838213
\(967\) 45.1755 1.45275 0.726373 0.687300i \(-0.241204\pi\)
0.726373 + 0.687300i \(0.241204\pi\)
\(968\) 20.5897 0.661779
\(969\) 1.58569 0.0509398
\(970\) 0 0
\(971\) 50.1290 1.60872 0.804359 0.594144i \(-0.202509\pi\)
0.804359 + 0.594144i \(0.202509\pi\)
\(972\) 64.0312 2.05380
\(973\) −10.3057 −0.330386
\(974\) 18.5252 0.593587
\(975\) 0 0
\(976\) −20.9838 −0.671675
\(977\) 2.05208 0.0656518 0.0328259 0.999461i \(-0.489549\pi\)
0.0328259 + 0.999461i \(0.489549\pi\)
\(978\) 55.1676 1.76407
\(979\) 25.6940 0.821185
\(980\) 0 0
\(981\) −19.4042 −0.619530
\(982\) 65.5487 2.09174
\(983\) −48.6503 −1.55170 −0.775852 0.630915i \(-0.782680\pi\)
−0.775852 + 0.630915i \(0.782680\pi\)
\(984\) 44.6394 1.42305
\(985\) 0 0
\(986\) 0.153428 0.00488616
\(987\) 1.68618 0.0536718
\(988\) 55.1888 1.75579
\(989\) 11.0247 0.350565
\(990\) 0 0
\(991\) 50.2126 1.59506 0.797528 0.603282i \(-0.206141\pi\)
0.797528 + 0.603282i \(0.206141\pi\)
\(992\) 0.235804 0.00748677
\(993\) −10.5297 −0.334149
\(994\) 3.79648 0.120417
\(995\) 0 0
\(996\) −10.7603 −0.340953
\(997\) 21.8288 0.691325 0.345663 0.938359i \(-0.387654\pi\)
0.345663 + 0.938359i \(0.387654\pi\)
\(998\) 66.2053 2.09569
\(999\) −23.2485 −0.735551
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 6025.2.a.p.1.4 46
5.2 odd 4 1205.2.b.c.724.4 46
5.3 odd 4 1205.2.b.c.724.43 yes 46
5.4 even 2 inner 6025.2.a.p.1.43 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.4 46 5.2 odd 4
1205.2.b.c.724.43 yes 46 5.3 odd 4
6025.2.a.p.1.4 46 1.1 even 1 trivial
6025.2.a.p.1.43 46 5.4 even 2 inner