Properties

Label 6037.2.a.b.1.6
Level $6037$
Weight $2$
Character 6037.1
Self dual yes
Analytic conductor $48.206$
Analytic rank $0$
Dimension $259$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.6
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61164 q^{2} +1.28286 q^{3} +4.82065 q^{4} -1.11903 q^{5} -3.35038 q^{6} -4.20141 q^{7} -7.36653 q^{8} -1.35426 q^{9} +O(q^{10})\) \(q-2.61164 q^{2} +1.28286 q^{3} +4.82065 q^{4} -1.11903 q^{5} -3.35038 q^{6} -4.20141 q^{7} -7.36653 q^{8} -1.35426 q^{9} +2.92250 q^{10} +2.82959 q^{11} +6.18425 q^{12} +1.00728 q^{13} +10.9726 q^{14} -1.43556 q^{15} +9.59739 q^{16} +1.46991 q^{17} +3.53683 q^{18} -2.86394 q^{19} -5.39446 q^{20} -5.38984 q^{21} -7.38986 q^{22} -3.53074 q^{23} -9.45026 q^{24} -3.74777 q^{25} -2.63066 q^{26} -5.58592 q^{27} -20.2535 q^{28} -8.86395 q^{29} +3.74917 q^{30} -6.85343 q^{31} -10.3319 q^{32} +3.62998 q^{33} -3.83887 q^{34} +4.70150 q^{35} -6.52841 q^{36} -0.211479 q^{37} +7.47957 q^{38} +1.29221 q^{39} +8.24336 q^{40} -7.52978 q^{41} +14.0763 q^{42} +11.1911 q^{43} +13.6405 q^{44} +1.51546 q^{45} +9.22102 q^{46} -1.60481 q^{47} +12.3122 q^{48} +10.6518 q^{49} +9.78782 q^{50} +1.88569 q^{51} +4.85577 q^{52} -3.94279 q^{53} +14.5884 q^{54} -3.16640 q^{55} +30.9498 q^{56} -3.67404 q^{57} +23.1494 q^{58} +10.0715 q^{59} -6.92036 q^{60} -4.38955 q^{61} +17.8987 q^{62} +5.68979 q^{63} +7.78830 q^{64} -1.12718 q^{65} -9.48020 q^{66} +3.36813 q^{67} +7.08592 q^{68} -4.52946 q^{69} -12.2786 q^{70} +1.50833 q^{71} +9.97618 q^{72} +6.72037 q^{73} +0.552308 q^{74} -4.80788 q^{75} -13.8060 q^{76} -11.8883 q^{77} -3.37478 q^{78} -3.72519 q^{79} -10.7398 q^{80} -3.10321 q^{81} +19.6651 q^{82} +1.48778 q^{83} -25.9825 q^{84} -1.64487 q^{85} -29.2272 q^{86} -11.3713 q^{87} -20.8442 q^{88} +1.53772 q^{89} -3.95782 q^{90} -4.23201 q^{91} -17.0205 q^{92} -8.79203 q^{93} +4.19118 q^{94} +3.20483 q^{95} -13.2544 q^{96} +1.89782 q^{97} -27.8187 q^{98} -3.83200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61164 −1.84671 −0.923353 0.383951i \(-0.874563\pi\)
−0.923353 + 0.383951i \(0.874563\pi\)
\(3\) 1.28286 0.740662 0.370331 0.928900i \(-0.379244\pi\)
0.370331 + 0.928900i \(0.379244\pi\)
\(4\) 4.82065 2.41033
\(5\) −1.11903 −0.500445 −0.250223 0.968188i \(-0.580504\pi\)
−0.250223 + 0.968188i \(0.580504\pi\)
\(6\) −3.35038 −1.36779
\(7\) −4.20141 −1.58798 −0.793992 0.607929i \(-0.792001\pi\)
−0.793992 + 0.607929i \(0.792001\pi\)
\(8\) −7.36653 −2.60446
\(9\) −1.35426 −0.451419
\(10\) 2.92250 0.924176
\(11\) 2.82959 0.853153 0.426577 0.904451i \(-0.359719\pi\)
0.426577 + 0.904451i \(0.359719\pi\)
\(12\) 6.18425 1.78524
\(13\) 1.00728 0.279370 0.139685 0.990196i \(-0.455391\pi\)
0.139685 + 0.990196i \(0.455391\pi\)
\(14\) 10.9726 2.93254
\(15\) −1.43556 −0.370661
\(16\) 9.59739 2.39935
\(17\) 1.46991 0.356505 0.178253 0.983985i \(-0.442956\pi\)
0.178253 + 0.983985i \(0.442956\pi\)
\(18\) 3.53683 0.833639
\(19\) −2.86394 −0.657032 −0.328516 0.944498i \(-0.606549\pi\)
−0.328516 + 0.944498i \(0.606549\pi\)
\(20\) −5.39446 −1.20624
\(21\) −5.38984 −1.17616
\(22\) −7.38986 −1.57552
\(23\) −3.53074 −0.736210 −0.368105 0.929784i \(-0.619993\pi\)
−0.368105 + 0.929784i \(0.619993\pi\)
\(24\) −9.45026 −1.92903
\(25\) −3.74777 −0.749554
\(26\) −2.63066 −0.515915
\(27\) −5.58592 −1.07501
\(28\) −20.2535 −3.82756
\(29\) −8.86395 −1.64600 −0.822998 0.568045i \(-0.807700\pi\)
−0.822998 + 0.568045i \(0.807700\pi\)
\(30\) 3.74917 0.684502
\(31\) −6.85343 −1.23091 −0.615457 0.788171i \(-0.711028\pi\)
−0.615457 + 0.788171i \(0.711028\pi\)
\(32\) −10.3319 −1.82643
\(33\) 3.62998 0.631899
\(34\) −3.83887 −0.658361
\(35\) 4.70150 0.794699
\(36\) −6.52841 −1.08807
\(37\) −0.211479 −0.0347670 −0.0173835 0.999849i \(-0.505534\pi\)
−0.0173835 + 0.999849i \(0.505534\pi\)
\(38\) 7.47957 1.21335
\(39\) 1.29221 0.206919
\(40\) 8.24336 1.30339
\(41\) −7.52978 −1.17595 −0.587977 0.808878i \(-0.700075\pi\)
−0.587977 + 0.808878i \(0.700075\pi\)
\(42\) 14.0763 2.17202
\(43\) 11.1911 1.70663 0.853316 0.521394i \(-0.174588\pi\)
0.853316 + 0.521394i \(0.174588\pi\)
\(44\) 13.6405 2.05638
\(45\) 1.51546 0.225911
\(46\) 9.22102 1.35957
\(47\) −1.60481 −0.234085 −0.117043 0.993127i \(-0.537341\pi\)
−0.117043 + 0.993127i \(0.537341\pi\)
\(48\) 12.3122 1.77711
\(49\) 10.6518 1.52169
\(50\) 9.78782 1.38421
\(51\) 1.88569 0.264050
\(52\) 4.85577 0.673374
\(53\) −3.94279 −0.541584 −0.270792 0.962638i \(-0.587286\pi\)
−0.270792 + 0.962638i \(0.587286\pi\)
\(54\) 14.5884 1.98523
\(55\) −3.16640 −0.426957
\(56\) 30.9498 4.13584
\(57\) −3.67404 −0.486639
\(58\) 23.1494 3.03967
\(59\) 10.0715 1.31120 0.655599 0.755110i \(-0.272416\pi\)
0.655599 + 0.755110i \(0.272416\pi\)
\(60\) −6.92036 −0.893414
\(61\) −4.38955 −0.562024 −0.281012 0.959704i \(-0.590670\pi\)
−0.281012 + 0.959704i \(0.590670\pi\)
\(62\) 17.8987 2.27314
\(63\) 5.68979 0.716846
\(64\) 7.78830 0.973537
\(65\) −1.12718 −0.139810
\(66\) −9.48020 −1.16693
\(67\) 3.36813 0.411483 0.205742 0.978606i \(-0.434039\pi\)
0.205742 + 0.978606i \(0.434039\pi\)
\(68\) 7.08592 0.859294
\(69\) −4.52946 −0.545283
\(70\) −12.2786 −1.46758
\(71\) 1.50833 0.179005 0.0895027 0.995987i \(-0.471472\pi\)
0.0895027 + 0.995987i \(0.471472\pi\)
\(72\) 9.97618 1.17570
\(73\) 6.72037 0.786559 0.393280 0.919419i \(-0.371340\pi\)
0.393280 + 0.919419i \(0.371340\pi\)
\(74\) 0.552308 0.0642045
\(75\) −4.80788 −0.555167
\(76\) −13.8060 −1.58366
\(77\) −11.8883 −1.35479
\(78\) −3.37478 −0.382119
\(79\) −3.72519 −0.419116 −0.209558 0.977796i \(-0.567203\pi\)
−0.209558 + 0.977796i \(0.567203\pi\)
\(80\) −10.7398 −1.20074
\(81\) −3.10321 −0.344801
\(82\) 19.6651 2.17164
\(83\) 1.48778 0.163305 0.0816526 0.996661i \(-0.473980\pi\)
0.0816526 + 0.996661i \(0.473980\pi\)
\(84\) −25.9825 −2.83493
\(85\) −1.64487 −0.178411
\(86\) −29.2272 −3.15165
\(87\) −11.3713 −1.21913
\(88\) −20.8442 −2.22200
\(89\) 1.53772 0.162998 0.0814991 0.996673i \(-0.474029\pi\)
0.0814991 + 0.996673i \(0.474029\pi\)
\(90\) −3.95782 −0.417191
\(91\) −4.23201 −0.443635
\(92\) −17.0205 −1.77451
\(93\) −8.79203 −0.911691
\(94\) 4.19118 0.432287
\(95\) 3.20483 0.328809
\(96\) −13.2544 −1.35277
\(97\) 1.89782 0.192694 0.0963470 0.995348i \(-0.469284\pi\)
0.0963470 + 0.995348i \(0.469284\pi\)
\(98\) −27.8187 −2.81012
\(99\) −3.83200 −0.385130
\(100\) −18.0667 −1.80667
\(101\) 15.2431 1.51675 0.758373 0.651820i \(-0.225994\pi\)
0.758373 + 0.651820i \(0.225994\pi\)
\(102\) −4.92475 −0.487623
\(103\) −18.8386 −1.85622 −0.928109 0.372309i \(-0.878566\pi\)
−0.928109 + 0.372309i \(0.878566\pi\)
\(104\) −7.42019 −0.727609
\(105\) 6.03139 0.588603
\(106\) 10.2971 1.00015
\(107\) −6.64813 −0.642699 −0.321349 0.946961i \(-0.604136\pi\)
−0.321349 + 0.946961i \(0.604136\pi\)
\(108\) −26.9278 −2.59113
\(109\) 6.57837 0.630093 0.315047 0.949076i \(-0.397980\pi\)
0.315047 + 0.949076i \(0.397980\pi\)
\(110\) 8.26948 0.788464
\(111\) −0.271300 −0.0257506
\(112\) −40.3226 −3.81012
\(113\) 15.7650 1.48304 0.741522 0.670928i \(-0.234104\pi\)
0.741522 + 0.670928i \(0.234104\pi\)
\(114\) 9.59527 0.898679
\(115\) 3.95101 0.368433
\(116\) −42.7301 −3.96739
\(117\) −1.36412 −0.126113
\(118\) −26.3031 −2.42140
\(119\) −6.17569 −0.566124
\(120\) 10.5751 0.965372
\(121\) −2.99342 −0.272129
\(122\) 11.4639 1.03789
\(123\) −9.65969 −0.870985
\(124\) −33.0380 −2.96690
\(125\) 9.78902 0.875556
\(126\) −14.8597 −1.32381
\(127\) 2.41873 0.214628 0.107314 0.994225i \(-0.465775\pi\)
0.107314 + 0.994225i \(0.465775\pi\)
\(128\) 0.323503 0.0285939
\(129\) 14.3567 1.26404
\(130\) 2.94379 0.258187
\(131\) −7.04690 −0.615690 −0.307845 0.951436i \(-0.599608\pi\)
−0.307845 + 0.951436i \(0.599608\pi\)
\(132\) 17.4989 1.52308
\(133\) 12.0326 1.04336
\(134\) −8.79635 −0.759889
\(135\) 6.25082 0.537985
\(136\) −10.8281 −0.928504
\(137\) −0.657384 −0.0561641 −0.0280821 0.999606i \(-0.508940\pi\)
−0.0280821 + 0.999606i \(0.508940\pi\)
\(138\) 11.8293 1.00698
\(139\) −9.85669 −0.836033 −0.418017 0.908439i \(-0.637275\pi\)
−0.418017 + 0.908439i \(0.637275\pi\)
\(140\) 22.6643 1.91548
\(141\) −2.05875 −0.173378
\(142\) −3.93920 −0.330571
\(143\) 2.85020 0.238346
\(144\) −12.9973 −1.08311
\(145\) 9.91903 0.823731
\(146\) −17.5512 −1.45254
\(147\) 13.6649 1.12706
\(148\) −1.01947 −0.0837998
\(149\) 11.4641 0.939176 0.469588 0.882886i \(-0.344402\pi\)
0.469588 + 0.882886i \(0.344402\pi\)
\(150\) 12.5565 1.02523
\(151\) 6.56656 0.534379 0.267190 0.963644i \(-0.413905\pi\)
0.267190 + 0.963644i \(0.413905\pi\)
\(152\) 21.0973 1.71121
\(153\) −1.99064 −0.160933
\(154\) 31.0478 2.50191
\(155\) 7.66920 0.616005
\(156\) 6.22929 0.498743
\(157\) −6.42856 −0.513055 −0.256527 0.966537i \(-0.582578\pi\)
−0.256527 + 0.966537i \(0.582578\pi\)
\(158\) 9.72884 0.773985
\(159\) −5.05807 −0.401131
\(160\) 11.5617 0.914030
\(161\) 14.8341 1.16909
\(162\) 8.10446 0.636747
\(163\) −10.0848 −0.789902 −0.394951 0.918702i \(-0.629238\pi\)
−0.394951 + 0.918702i \(0.629238\pi\)
\(164\) −36.2985 −2.83443
\(165\) −4.06206 −0.316231
\(166\) −3.88555 −0.301577
\(167\) 0.938901 0.0726543 0.0363272 0.999340i \(-0.488434\pi\)
0.0363272 + 0.999340i \(0.488434\pi\)
\(168\) 39.7044 3.06326
\(169\) −11.9854 −0.921952
\(170\) 4.29581 0.329474
\(171\) 3.87851 0.296597
\(172\) 53.9486 4.11354
\(173\) −13.4312 −1.02115 −0.510577 0.859832i \(-0.670568\pi\)
−0.510577 + 0.859832i \(0.670568\pi\)
\(174\) 29.6976 2.25137
\(175\) 15.7459 1.19028
\(176\) 27.1567 2.04701
\(177\) 12.9204 0.971154
\(178\) −4.01597 −0.301010
\(179\) 24.9757 1.86677 0.933385 0.358878i \(-0.116840\pi\)
0.933385 + 0.358878i \(0.116840\pi\)
\(180\) 7.30549 0.544519
\(181\) −16.7609 −1.24583 −0.622915 0.782290i \(-0.714052\pi\)
−0.622915 + 0.782290i \(0.714052\pi\)
\(182\) 11.0525 0.819265
\(183\) −5.63119 −0.416270
\(184\) 26.0093 1.91743
\(185\) 0.236652 0.0173990
\(186\) 22.9616 1.68363
\(187\) 4.15924 0.304154
\(188\) −7.73622 −0.564222
\(189\) 23.4687 1.70710
\(190\) −8.36986 −0.607213
\(191\) 2.48542 0.179839 0.0899193 0.995949i \(-0.471339\pi\)
0.0899193 + 0.995949i \(0.471339\pi\)
\(192\) 9.99133 0.721062
\(193\) −0.139371 −0.0100322 −0.00501609 0.999987i \(-0.501597\pi\)
−0.00501609 + 0.999987i \(0.501597\pi\)
\(194\) −4.95641 −0.355849
\(195\) −1.44602 −0.103552
\(196\) 51.3488 3.66777
\(197\) −3.99492 −0.284627 −0.142313 0.989822i \(-0.545454\pi\)
−0.142313 + 0.989822i \(0.545454\pi\)
\(198\) 10.0078 0.711222
\(199\) −25.1577 −1.78339 −0.891693 0.452641i \(-0.850482\pi\)
−0.891693 + 0.452641i \(0.850482\pi\)
\(200\) 27.6081 1.95218
\(201\) 4.32086 0.304770
\(202\) −39.8095 −2.80099
\(203\) 37.2411 2.61381
\(204\) 9.09028 0.636447
\(205\) 8.42605 0.588501
\(206\) 49.1995 3.42789
\(207\) 4.78154 0.332340
\(208\) 9.66730 0.670307
\(209\) −8.10377 −0.560549
\(210\) −15.7518 −1.08698
\(211\) −24.6337 −1.69586 −0.847928 0.530112i \(-0.822150\pi\)
−0.847928 + 0.530112i \(0.822150\pi\)
\(212\) −19.0068 −1.30539
\(213\) 1.93498 0.132583
\(214\) 17.3625 1.18688
\(215\) −12.5232 −0.854077
\(216\) 41.1489 2.79982
\(217\) 28.7941 1.95467
\(218\) −17.1803 −1.16360
\(219\) 8.62132 0.582575
\(220\) −15.2641 −1.02911
\(221\) 1.48062 0.0995970
\(222\) 0.708536 0.0475538
\(223\) −8.80877 −0.589879 −0.294940 0.955516i \(-0.595300\pi\)
−0.294940 + 0.955516i \(0.595300\pi\)
\(224\) 43.4084 2.90034
\(225\) 5.07545 0.338363
\(226\) −41.1724 −2.73875
\(227\) −7.88235 −0.523170 −0.261585 0.965180i \(-0.584245\pi\)
−0.261585 + 0.965180i \(0.584245\pi\)
\(228\) −17.7113 −1.17296
\(229\) 25.1134 1.65954 0.829769 0.558106i \(-0.188472\pi\)
0.829769 + 0.558106i \(0.188472\pi\)
\(230\) −10.3186 −0.680388
\(231\) −15.2510 −1.00344
\(232\) 65.2965 4.28693
\(233\) 10.2776 0.673309 0.336654 0.941628i \(-0.390705\pi\)
0.336654 + 0.941628i \(0.390705\pi\)
\(234\) 3.56260 0.232894
\(235\) 1.79583 0.117147
\(236\) 48.5512 3.16041
\(237\) −4.77891 −0.310423
\(238\) 16.1287 1.04547
\(239\) −10.4434 −0.675525 −0.337763 0.941231i \(-0.609670\pi\)
−0.337763 + 0.941231i \(0.609670\pi\)
\(240\) −13.7777 −0.889345
\(241\) −5.73788 −0.369609 −0.184805 0.982775i \(-0.559165\pi\)
−0.184805 + 0.982775i \(0.559165\pi\)
\(242\) 7.81773 0.502543
\(243\) 12.7768 0.819630
\(244\) −21.1605 −1.35466
\(245\) −11.9197 −0.761523
\(246\) 25.2276 1.60845
\(247\) −2.88480 −0.183555
\(248\) 50.4860 3.20586
\(249\) 1.90862 0.120954
\(250\) −25.5654 −1.61690
\(251\) −15.0816 −0.951940 −0.475970 0.879461i \(-0.657903\pi\)
−0.475970 + 0.879461i \(0.657903\pi\)
\(252\) 27.4285 1.72783
\(253\) −9.99055 −0.628101
\(254\) −6.31686 −0.396355
\(255\) −2.11015 −0.132143
\(256\) −16.4215 −1.02634
\(257\) −11.3195 −0.706094 −0.353047 0.935606i \(-0.614854\pi\)
−0.353047 + 0.935606i \(0.614854\pi\)
\(258\) −37.4945 −2.33431
\(259\) 0.888511 0.0552094
\(260\) −5.43375 −0.336987
\(261\) 12.0041 0.743034
\(262\) 18.4039 1.13700
\(263\) 30.9532 1.90865 0.954327 0.298764i \(-0.0965743\pi\)
0.954327 + 0.298764i \(0.0965743\pi\)
\(264\) −26.7403 −1.64575
\(265\) 4.41210 0.271033
\(266\) −31.4247 −1.92677
\(267\) 1.97269 0.120727
\(268\) 16.2366 0.991809
\(269\) 0.638812 0.0389490 0.0194745 0.999810i \(-0.493801\pi\)
0.0194745 + 0.999810i \(0.493801\pi\)
\(270\) −16.3249 −0.993500
\(271\) 16.3560 0.993554 0.496777 0.867878i \(-0.334517\pi\)
0.496777 + 0.867878i \(0.334517\pi\)
\(272\) 14.1073 0.855380
\(273\) −5.42910 −0.328584
\(274\) 1.71685 0.103719
\(275\) −10.6047 −0.639485
\(276\) −21.8350 −1.31431
\(277\) −9.64324 −0.579406 −0.289703 0.957117i \(-0.593557\pi\)
−0.289703 + 0.957117i \(0.593557\pi\)
\(278\) 25.7421 1.54391
\(279\) 9.28132 0.555658
\(280\) −34.6337 −2.06976
\(281\) 18.2904 1.09111 0.545557 0.838074i \(-0.316318\pi\)
0.545557 + 0.838074i \(0.316318\pi\)
\(282\) 5.37671 0.320179
\(283\) 27.8422 1.65505 0.827524 0.561431i \(-0.189749\pi\)
0.827524 + 0.561431i \(0.189749\pi\)
\(284\) 7.27112 0.431462
\(285\) 4.11136 0.243536
\(286\) −7.44369 −0.440155
\(287\) 31.6357 1.86740
\(288\) 13.9920 0.824487
\(289\) −14.8394 −0.872904
\(290\) −25.9049 −1.52119
\(291\) 2.43464 0.142721
\(292\) 32.3966 1.89586
\(293\) −7.24125 −0.423038 −0.211519 0.977374i \(-0.567841\pi\)
−0.211519 + 0.977374i \(0.567841\pi\)
\(294\) −35.6877 −2.08135
\(295\) −11.2703 −0.656183
\(296\) 1.55787 0.0905493
\(297\) −15.8059 −0.917150
\(298\) −29.9401 −1.73438
\(299\) −3.55646 −0.205675
\(300\) −23.1771 −1.33813
\(301\) −47.0185 −2.71010
\(302\) −17.1495 −0.986842
\(303\) 19.5549 1.12340
\(304\) −27.4863 −1.57645
\(305\) 4.91203 0.281262
\(306\) 5.19882 0.297197
\(307\) 32.2779 1.84219 0.921097 0.389333i \(-0.127294\pi\)
0.921097 + 0.389333i \(0.127294\pi\)
\(308\) −57.3092 −3.26549
\(309\) −24.1673 −1.37483
\(310\) −20.0292 −1.13758
\(311\) 14.1352 0.801535 0.400768 0.916180i \(-0.368744\pi\)
0.400768 + 0.916180i \(0.368744\pi\)
\(312\) −9.51909 −0.538913
\(313\) 30.3998 1.71830 0.859148 0.511727i \(-0.170994\pi\)
0.859148 + 0.511727i \(0.170994\pi\)
\(314\) 16.7891 0.947462
\(315\) −6.36705 −0.358742
\(316\) −17.9578 −1.01021
\(317\) 21.3456 1.19889 0.599443 0.800417i \(-0.295389\pi\)
0.599443 + 0.800417i \(0.295389\pi\)
\(318\) 13.2098 0.740771
\(319\) −25.0814 −1.40429
\(320\) −8.71534 −0.487202
\(321\) −8.52864 −0.476023
\(322\) −38.7413 −2.15897
\(323\) −4.20973 −0.234235
\(324\) −14.9595 −0.831083
\(325\) −3.77507 −0.209403
\(326\) 26.3378 1.45872
\(327\) 8.43915 0.466686
\(328\) 55.4683 3.06273
\(329\) 6.74245 0.371723
\(330\) 10.6086 0.583986
\(331\) −7.22501 −0.397122 −0.198561 0.980088i \(-0.563627\pi\)
−0.198561 + 0.980088i \(0.563627\pi\)
\(332\) 7.17208 0.393619
\(333\) 0.286398 0.0156945
\(334\) −2.45207 −0.134171
\(335\) −3.76904 −0.205925
\(336\) −51.7284 −2.82201
\(337\) −22.4614 −1.22355 −0.611774 0.791032i \(-0.709544\pi\)
−0.611774 + 0.791032i \(0.709544\pi\)
\(338\) 31.3015 1.70258
\(339\) 20.2243 1.09844
\(340\) −7.92936 −0.430030
\(341\) −19.3924 −1.05016
\(342\) −10.1293 −0.547728
\(343\) −15.3428 −0.828435
\(344\) −82.4398 −4.44486
\(345\) 5.06861 0.272885
\(346\) 35.0774 1.88577
\(347\) 14.7021 0.789249 0.394624 0.918843i \(-0.370875\pi\)
0.394624 + 0.918843i \(0.370875\pi\)
\(348\) −54.8169 −2.93849
\(349\) −2.83163 −0.151574 −0.0757868 0.997124i \(-0.524147\pi\)
−0.0757868 + 0.997124i \(0.524147\pi\)
\(350\) −41.1226 −2.19810
\(351\) −5.62661 −0.300326
\(352\) −29.2349 −1.55823
\(353\) 4.40691 0.234556 0.117278 0.993099i \(-0.462583\pi\)
0.117278 + 0.993099i \(0.462583\pi\)
\(354\) −33.7433 −1.79344
\(355\) −1.68786 −0.0895825
\(356\) 7.41282 0.392879
\(357\) −7.92257 −0.419307
\(358\) −65.2274 −3.44738
\(359\) 34.1871 1.80433 0.902164 0.431394i \(-0.141978\pi\)
0.902164 + 0.431394i \(0.141978\pi\)
\(360\) −11.1636 −0.588376
\(361\) −10.7979 −0.568309
\(362\) 43.7735 2.30068
\(363\) −3.84015 −0.201556
\(364\) −20.4011 −1.06931
\(365\) −7.52029 −0.393630
\(366\) 14.7066 0.768728
\(367\) −8.41005 −0.439001 −0.219500 0.975612i \(-0.570443\pi\)
−0.219500 + 0.975612i \(0.570443\pi\)
\(368\) −33.8859 −1.76643
\(369\) 10.1973 0.530848
\(370\) −0.618049 −0.0321308
\(371\) 16.5653 0.860026
\(372\) −42.3833 −2.19747
\(373\) 32.2263 1.66861 0.834306 0.551301i \(-0.185868\pi\)
0.834306 + 0.551301i \(0.185868\pi\)
\(374\) −10.8624 −0.561683
\(375\) 12.5580 0.648492
\(376\) 11.8219 0.609666
\(377\) −8.92852 −0.459842
\(378\) −61.2919 −3.15251
\(379\) −4.86791 −0.250048 −0.125024 0.992154i \(-0.539901\pi\)
−0.125024 + 0.992154i \(0.539901\pi\)
\(380\) 15.4494 0.792536
\(381\) 3.10291 0.158967
\(382\) −6.49101 −0.332109
\(383\) −36.9345 −1.88727 −0.943633 0.330994i \(-0.892616\pi\)
−0.943633 + 0.330994i \(0.892616\pi\)
\(384\) 0.415010 0.0211784
\(385\) 13.3033 0.678000
\(386\) 0.363988 0.0185265
\(387\) −15.1557 −0.770407
\(388\) 9.14871 0.464456
\(389\) 6.60571 0.334923 0.167461 0.985879i \(-0.446443\pi\)
0.167461 + 0.985879i \(0.446443\pi\)
\(390\) 3.77648 0.191230
\(391\) −5.18987 −0.262463
\(392\) −78.4670 −3.96318
\(393\) −9.04022 −0.456019
\(394\) 10.4333 0.525622
\(395\) 4.16859 0.209745
\(396\) −18.4727 −0.928289
\(397\) 5.10326 0.256125 0.128063 0.991766i \(-0.459124\pi\)
0.128063 + 0.991766i \(0.459124\pi\)
\(398\) 65.7029 3.29339
\(399\) 15.4362 0.772774
\(400\) −35.9688 −1.79844
\(401\) 32.4967 1.62281 0.811403 0.584487i \(-0.198704\pi\)
0.811403 + 0.584487i \(0.198704\pi\)
\(402\) −11.2845 −0.562821
\(403\) −6.90336 −0.343881
\(404\) 73.4818 3.65586
\(405\) 3.47258 0.172554
\(406\) −97.2603 −4.82695
\(407\) −0.598400 −0.0296616
\(408\) −13.8910 −0.687708
\(409\) −38.6499 −1.91111 −0.955557 0.294806i \(-0.904745\pi\)
−0.955557 + 0.294806i \(0.904745\pi\)
\(410\) −22.0058 −1.08679
\(411\) −0.843335 −0.0415986
\(412\) −90.8141 −4.47409
\(413\) −42.3145 −2.08216
\(414\) −12.4876 −0.613734
\(415\) −1.66487 −0.0817253
\(416\) −10.4071 −0.510251
\(417\) −12.6448 −0.619218
\(418\) 21.1641 1.03517
\(419\) 37.0314 1.80910 0.904550 0.426367i \(-0.140207\pi\)
0.904550 + 0.426367i \(0.140207\pi\)
\(420\) 29.0752 1.41873
\(421\) −22.1194 −1.07803 −0.539016 0.842295i \(-0.681204\pi\)
−0.539016 + 0.842295i \(0.681204\pi\)
\(422\) 64.3344 3.13175
\(423\) 2.17332 0.105671
\(424\) 29.0447 1.41053
\(425\) −5.50888 −0.267220
\(426\) −5.05347 −0.244841
\(427\) 18.4423 0.892484
\(428\) −32.0483 −1.54911
\(429\) 3.65642 0.176534
\(430\) 32.7061 1.57723
\(431\) −2.65193 −0.127739 −0.0638695 0.997958i \(-0.520344\pi\)
−0.0638695 + 0.997958i \(0.520344\pi\)
\(432\) −53.6103 −2.57933
\(433\) 31.9800 1.53686 0.768429 0.639935i \(-0.221039\pi\)
0.768429 + 0.639935i \(0.221039\pi\)
\(434\) −75.1997 −3.60970
\(435\) 12.7248 0.610106
\(436\) 31.7120 1.51873
\(437\) 10.1118 0.483714
\(438\) −22.5158 −1.07584
\(439\) −14.4634 −0.690300 −0.345150 0.938548i \(-0.612172\pi\)
−0.345150 + 0.938548i \(0.612172\pi\)
\(440\) 23.3253 1.11199
\(441\) −14.4253 −0.686920
\(442\) −3.86683 −0.183927
\(443\) 38.2162 1.81571 0.907854 0.419287i \(-0.137720\pi\)
0.907854 + 0.419287i \(0.137720\pi\)
\(444\) −1.30784 −0.0620674
\(445\) −1.72076 −0.0815717
\(446\) 23.0053 1.08933
\(447\) 14.7069 0.695612
\(448\) −32.7218 −1.54596
\(449\) 16.4348 0.775606 0.387803 0.921742i \(-0.373234\pi\)
0.387803 + 0.921742i \(0.373234\pi\)
\(450\) −13.2552 −0.624858
\(451\) −21.3062 −1.00327
\(452\) 75.9975 3.57462
\(453\) 8.42401 0.395795
\(454\) 20.5858 0.966141
\(455\) 4.73575 0.222015
\(456\) 27.0649 1.26743
\(457\) 14.6850 0.686935 0.343468 0.939164i \(-0.388398\pi\)
0.343468 + 0.939164i \(0.388398\pi\)
\(458\) −65.5871 −3.06468
\(459\) −8.21080 −0.383247
\(460\) 19.0464 0.888044
\(461\) 15.3975 0.717131 0.358565 0.933505i \(-0.383266\pi\)
0.358565 + 0.933505i \(0.383266\pi\)
\(462\) 39.8302 1.85307
\(463\) 27.0492 1.25708 0.628540 0.777777i \(-0.283653\pi\)
0.628540 + 0.777777i \(0.283653\pi\)
\(464\) −85.0708 −3.94931
\(465\) 9.83854 0.456252
\(466\) −26.8414 −1.24340
\(467\) −6.17382 −0.285690 −0.142845 0.989745i \(-0.545625\pi\)
−0.142845 + 0.989745i \(0.545625\pi\)
\(468\) −6.57596 −0.303974
\(469\) −14.1509 −0.653428
\(470\) −4.69005 −0.216336
\(471\) −8.24697 −0.380000
\(472\) −74.1919 −3.41496
\(473\) 31.6663 1.45602
\(474\) 12.4808 0.573261
\(475\) 10.7334 0.492481
\(476\) −29.7709 −1.36454
\(477\) 5.33956 0.244481
\(478\) 27.2743 1.24750
\(479\) 15.1701 0.693139 0.346570 0.938024i \(-0.387346\pi\)
0.346570 + 0.938024i \(0.387346\pi\)
\(480\) 14.8320 0.676987
\(481\) −0.213020 −0.00971287
\(482\) 14.9853 0.682560
\(483\) 19.0301 0.865901
\(484\) −14.4302 −0.655920
\(485\) −2.12371 −0.0964329
\(486\) −33.3683 −1.51362
\(487\) −0.567945 −0.0257360 −0.0128680 0.999917i \(-0.504096\pi\)
−0.0128680 + 0.999917i \(0.504096\pi\)
\(488\) 32.3357 1.46377
\(489\) −12.9374 −0.585051
\(490\) 31.1300 1.40631
\(491\) 9.34795 0.421867 0.210934 0.977500i \(-0.432350\pi\)
0.210934 + 0.977500i \(0.432350\pi\)
\(492\) −46.5660 −2.09936
\(493\) −13.0292 −0.586806
\(494\) 7.53405 0.338973
\(495\) 4.28812 0.192737
\(496\) −65.7751 −2.95339
\(497\) −6.33710 −0.284258
\(498\) −4.98463 −0.223367
\(499\) −8.37644 −0.374981 −0.187490 0.982266i \(-0.560035\pi\)
−0.187490 + 0.982266i \(0.560035\pi\)
\(500\) 47.1895 2.11038
\(501\) 1.20448 0.0538123
\(502\) 39.3876 1.75795
\(503\) 0.0103533 0.000461631 0 0.000230816 1.00000i \(-0.499927\pi\)
0.000230816 1.00000i \(0.499927\pi\)
\(504\) −41.9140 −1.86700
\(505\) −17.0575 −0.759049
\(506\) 26.0917 1.15992
\(507\) −15.3756 −0.682855
\(508\) 11.6599 0.517323
\(509\) −28.5771 −1.26666 −0.633328 0.773883i \(-0.718312\pi\)
−0.633328 + 0.773883i \(0.718312\pi\)
\(510\) 5.51094 0.244029
\(511\) −28.2350 −1.24904
\(512\) 42.2399 1.86676
\(513\) 15.9977 0.706317
\(514\) 29.5626 1.30395
\(515\) 21.0809 0.928936
\(516\) 69.2088 3.04675
\(517\) −4.54095 −0.199711
\(518\) −2.32047 −0.101956
\(519\) −17.2304 −0.756330
\(520\) 8.30341 0.364129
\(521\) −5.41399 −0.237191 −0.118596 0.992943i \(-0.537839\pi\)
−0.118596 + 0.992943i \(0.537839\pi\)
\(522\) −31.3503 −1.37217
\(523\) 26.9182 1.17705 0.588526 0.808479i \(-0.299709\pi\)
0.588526 + 0.808479i \(0.299709\pi\)
\(524\) −33.9707 −1.48401
\(525\) 20.1999 0.881595
\(526\) −80.8385 −3.52472
\(527\) −10.0739 −0.438827
\(528\) 34.8383 1.51614
\(529\) −10.5339 −0.457994
\(530\) −11.5228 −0.500519
\(531\) −13.6394 −0.591900
\(532\) 58.0048 2.51483
\(533\) −7.58463 −0.328527
\(534\) −5.15195 −0.222947
\(535\) 7.43945 0.321636
\(536\) −24.8114 −1.07169
\(537\) 32.0404 1.38265
\(538\) −1.66834 −0.0719274
\(539\) 30.1403 1.29824
\(540\) 30.1330 1.29672
\(541\) −30.3367 −1.30428 −0.652138 0.758100i \(-0.726128\pi\)
−0.652138 + 0.758100i \(0.726128\pi\)
\(542\) −42.7158 −1.83480
\(543\) −21.5020 −0.922739
\(544\) −15.1869 −0.651133
\(545\) −7.36139 −0.315327
\(546\) 14.1788 0.606798
\(547\) −0.317784 −0.0135875 −0.00679374 0.999977i \(-0.502163\pi\)
−0.00679374 + 0.999977i \(0.502163\pi\)
\(548\) −3.16902 −0.135374
\(549\) 5.94458 0.253708
\(550\) 27.6955 1.18094
\(551\) 25.3858 1.08147
\(552\) 33.3664 1.42017
\(553\) 15.6510 0.665549
\(554\) 25.1847 1.06999
\(555\) 0.303592 0.0128868
\(556\) −47.5157 −2.01511
\(557\) 20.1990 0.855859 0.427929 0.903812i \(-0.359243\pi\)
0.427929 + 0.903812i \(0.359243\pi\)
\(558\) −24.2395 −1.02614
\(559\) 11.2727 0.476783
\(560\) 45.1222 1.90676
\(561\) 5.33574 0.225275
\(562\) −47.7679 −2.01497
\(563\) 26.6162 1.12174 0.560870 0.827904i \(-0.310467\pi\)
0.560870 + 0.827904i \(0.310467\pi\)
\(564\) −9.92453 −0.417898
\(565\) −17.6415 −0.742183
\(566\) −72.7138 −3.05639
\(567\) 13.0379 0.547538
\(568\) −11.1111 −0.466213
\(569\) 15.3123 0.641924 0.320962 0.947092i \(-0.395994\pi\)
0.320962 + 0.947092i \(0.395994\pi\)
\(570\) −10.7374 −0.449740
\(571\) 14.4782 0.605892 0.302946 0.953008i \(-0.402030\pi\)
0.302946 + 0.953008i \(0.402030\pi\)
\(572\) 13.7398 0.574491
\(573\) 3.18846 0.133200
\(574\) −82.6209 −3.44853
\(575\) 13.2324 0.551830
\(576\) −10.5474 −0.439474
\(577\) 40.6537 1.69244 0.846218 0.532836i \(-0.178874\pi\)
0.846218 + 0.532836i \(0.178874\pi\)
\(578\) 38.7551 1.61200
\(579\) −0.178795 −0.00743045
\(580\) 47.8162 1.98546
\(581\) −6.25078 −0.259326
\(582\) −6.35840 −0.263564
\(583\) −11.1565 −0.462054
\(584\) −49.5057 −2.04856
\(585\) 1.52649 0.0631128
\(586\) 18.9115 0.781228
\(587\) 2.43061 0.100322 0.0501611 0.998741i \(-0.484027\pi\)
0.0501611 + 0.998741i \(0.484027\pi\)
\(588\) 65.8735 2.71658
\(589\) 19.6278 0.808750
\(590\) 29.4340 1.21178
\(591\) −5.12495 −0.210812
\(592\) −2.02965 −0.0834181
\(593\) 23.2360 0.954188 0.477094 0.878852i \(-0.341690\pi\)
0.477094 + 0.878852i \(0.341690\pi\)
\(594\) 41.2792 1.69371
\(595\) 6.91078 0.283314
\(596\) 55.2645 2.26372
\(597\) −32.2740 −1.32089
\(598\) 9.28819 0.379822
\(599\) 17.2938 0.706605 0.353302 0.935509i \(-0.385059\pi\)
0.353302 + 0.935509i \(0.385059\pi\)
\(600\) 35.4174 1.44591
\(601\) −14.5658 −0.594151 −0.297076 0.954854i \(-0.596011\pi\)
−0.297076 + 0.954854i \(0.596011\pi\)
\(602\) 122.795 5.00477
\(603\) −4.56132 −0.185751
\(604\) 31.6551 1.28803
\(605\) 3.34973 0.136186
\(606\) −51.0702 −2.07459
\(607\) 37.2638 1.51249 0.756246 0.654288i \(-0.227031\pi\)
0.756246 + 0.654288i \(0.227031\pi\)
\(608\) 29.5898 1.20002
\(609\) 47.7753 1.93595
\(610\) −12.8285 −0.519409
\(611\) −1.61650 −0.0653965
\(612\) −9.59617 −0.387902
\(613\) 21.9268 0.885614 0.442807 0.896617i \(-0.353983\pi\)
0.442807 + 0.896617i \(0.353983\pi\)
\(614\) −84.2981 −3.40199
\(615\) 10.8095 0.435880
\(616\) 87.5752 3.52850
\(617\) −26.1001 −1.05075 −0.525374 0.850871i \(-0.676075\pi\)
−0.525374 + 0.850871i \(0.676075\pi\)
\(618\) 63.1163 2.53891
\(619\) −2.43384 −0.0978243 −0.0489121 0.998803i \(-0.515575\pi\)
−0.0489121 + 0.998803i \(0.515575\pi\)
\(620\) 36.9706 1.48477
\(621\) 19.7225 0.791435
\(622\) −36.9161 −1.48020
\(623\) −6.46059 −0.258838
\(624\) 12.4018 0.496471
\(625\) 7.78465 0.311386
\(626\) −79.3932 −3.17319
\(627\) −10.3960 −0.415178
\(628\) −30.9898 −1.23663
\(629\) −0.310856 −0.0123946
\(630\) 16.6284 0.662492
\(631\) 2.18041 0.0868006 0.0434003 0.999058i \(-0.486181\pi\)
0.0434003 + 0.999058i \(0.486181\pi\)
\(632\) 27.4417 1.09157
\(633\) −31.6017 −1.25606
\(634\) −55.7469 −2.21399
\(635\) −2.70664 −0.107410
\(636\) −24.3832 −0.966856
\(637\) 10.7294 0.425115
\(638\) 65.5034 2.59331
\(639\) −2.04266 −0.0808066
\(640\) −0.362009 −0.0143097
\(641\) −36.1860 −1.42926 −0.714631 0.699502i \(-0.753405\pi\)
−0.714631 + 0.699502i \(0.753405\pi\)
\(642\) 22.2737 0.879074
\(643\) −13.1340 −0.517954 −0.258977 0.965884i \(-0.583385\pi\)
−0.258977 + 0.965884i \(0.583385\pi\)
\(644\) 71.5100 2.81789
\(645\) −16.0656 −0.632582
\(646\) 10.9943 0.432564
\(647\) 24.8577 0.977256 0.488628 0.872492i \(-0.337497\pi\)
0.488628 + 0.872492i \(0.337497\pi\)
\(648\) 22.8599 0.898021
\(649\) 28.4982 1.11865
\(650\) 9.85912 0.386707
\(651\) 36.9389 1.44775
\(652\) −48.6153 −1.90392
\(653\) −17.5499 −0.686780 −0.343390 0.939193i \(-0.611575\pi\)
−0.343390 + 0.939193i \(0.611575\pi\)
\(654\) −22.0400 −0.861833
\(655\) 7.88569 0.308119
\(656\) −72.2662 −2.82152
\(657\) −9.10111 −0.355068
\(658\) −17.6088 −0.686464
\(659\) −31.3329 −1.22056 −0.610279 0.792187i \(-0.708943\pi\)
−0.610279 + 0.792187i \(0.708943\pi\)
\(660\) −19.5818 −0.762219
\(661\) 16.3526 0.636041 0.318021 0.948084i \(-0.396982\pi\)
0.318021 + 0.948084i \(0.396982\pi\)
\(662\) 18.8691 0.733369
\(663\) 1.89943 0.0737678
\(664\) −10.9598 −0.425322
\(665\) −13.4648 −0.522143
\(666\) −0.747967 −0.0289831
\(667\) 31.2963 1.21180
\(668\) 4.52611 0.175121
\(669\) −11.3005 −0.436901
\(670\) 9.84338 0.380283
\(671\) −12.4206 −0.479493
\(672\) 55.6871 2.14818
\(673\) 31.7777 1.22494 0.612470 0.790494i \(-0.290176\pi\)
0.612470 + 0.790494i \(0.290176\pi\)
\(674\) 58.6610 2.25954
\(675\) 20.9348 0.805780
\(676\) −57.7774 −2.22221
\(677\) −5.83035 −0.224079 −0.112039 0.993704i \(-0.535738\pi\)
−0.112039 + 0.993704i \(0.535738\pi\)
\(678\) −52.8187 −2.02849
\(679\) −7.97350 −0.305995
\(680\) 12.1170 0.464666
\(681\) −10.1120 −0.387492
\(682\) 50.6460 1.93933
\(683\) 10.2312 0.391486 0.195743 0.980655i \(-0.437288\pi\)
0.195743 + 0.980655i \(0.437288\pi\)
\(684\) 18.6970 0.714896
\(685\) 0.735632 0.0281071
\(686\) 40.0699 1.52988
\(687\) 32.2171 1.22916
\(688\) 107.406 4.09481
\(689\) −3.97151 −0.151302
\(690\) −13.2374 −0.503938
\(691\) −40.8206 −1.55289 −0.776444 0.630186i \(-0.782979\pi\)
−0.776444 + 0.630186i \(0.782979\pi\)
\(692\) −64.7471 −2.46132
\(693\) 16.0998 0.611580
\(694\) −38.3965 −1.45751
\(695\) 11.0299 0.418389
\(696\) 83.7666 3.17517
\(697\) −11.0681 −0.419234
\(698\) 7.39519 0.279912
\(699\) 13.1848 0.498694
\(700\) 75.9056 2.86896
\(701\) −41.3896 −1.56326 −0.781631 0.623741i \(-0.785612\pi\)
−0.781631 + 0.623741i \(0.785612\pi\)
\(702\) 14.6947 0.554615
\(703\) 0.605664 0.0228430
\(704\) 22.0377 0.830577
\(705\) 2.30380 0.0867663
\(706\) −11.5093 −0.433157
\(707\) −64.0426 −2.40857
\(708\) 62.2846 2.34080
\(709\) −0.863009 −0.0324110 −0.0162055 0.999869i \(-0.505159\pi\)
−0.0162055 + 0.999869i \(0.505159\pi\)
\(710\) 4.40809 0.165433
\(711\) 5.04486 0.189197
\(712\) −11.3277 −0.424522
\(713\) 24.1977 0.906211
\(714\) 20.6909 0.774337
\(715\) −3.18946 −0.119279
\(716\) 120.399 4.49952
\(717\) −13.3974 −0.500336
\(718\) −89.2844 −3.33206
\(719\) −7.00009 −0.261059 −0.130530 0.991444i \(-0.541668\pi\)
−0.130530 + 0.991444i \(0.541668\pi\)
\(720\) 14.5444 0.542039
\(721\) 79.1484 2.94764
\(722\) 28.2001 1.04950
\(723\) −7.36092 −0.273756
\(724\) −80.7986 −3.00286
\(725\) 33.2201 1.23376
\(726\) 10.0291 0.372214
\(727\) 6.73167 0.249664 0.124832 0.992178i \(-0.460161\pi\)
0.124832 + 0.992178i \(0.460161\pi\)
\(728\) 31.1752 1.15543
\(729\) 25.7005 0.951870
\(730\) 19.6403 0.726919
\(731\) 16.4500 0.608424
\(732\) −27.1460 −1.00335
\(733\) 20.4679 0.755999 0.377999 0.925806i \(-0.376612\pi\)
0.377999 + 0.925806i \(0.376612\pi\)
\(734\) 21.9640 0.810706
\(735\) −15.2914 −0.564031
\(736\) 36.4791 1.34464
\(737\) 9.53044 0.351058
\(738\) −26.6316 −0.980322
\(739\) 45.8462 1.68648 0.843240 0.537538i \(-0.180645\pi\)
0.843240 + 0.537538i \(0.180645\pi\)
\(740\) 1.14082 0.0419372
\(741\) −3.70081 −0.135953
\(742\) −43.2625 −1.58822
\(743\) −14.0817 −0.516608 −0.258304 0.966064i \(-0.583164\pi\)
−0.258304 + 0.966064i \(0.583164\pi\)
\(744\) 64.7667 2.37446
\(745\) −12.8287 −0.470006
\(746\) −84.1633 −3.08144
\(747\) −2.01484 −0.0737191
\(748\) 20.0503 0.733110
\(749\) 27.9315 1.02059
\(750\) −32.7969 −1.19757
\(751\) −35.8379 −1.30774 −0.653872 0.756606i \(-0.726856\pi\)
−0.653872 + 0.756606i \(0.726856\pi\)
\(752\) −15.4020 −0.561652
\(753\) −19.3476 −0.705066
\(754\) 23.3181 0.849194
\(755\) −7.34818 −0.267428
\(756\) 113.135 4.11467
\(757\) 9.88664 0.359336 0.179668 0.983727i \(-0.442498\pi\)
0.179668 + 0.983727i \(0.442498\pi\)
\(758\) 12.7132 0.461765
\(759\) −12.8165 −0.465210
\(760\) −23.6085 −0.856369
\(761\) −2.13679 −0.0774586 −0.0387293 0.999250i \(-0.512331\pi\)
−0.0387293 + 0.999250i \(0.512331\pi\)
\(762\) −8.10367 −0.293565
\(763\) −27.6384 −1.00058
\(764\) 11.9813 0.433470
\(765\) 2.22758 0.0805384
\(766\) 96.4596 3.48523
\(767\) 10.1449 0.366310
\(768\) −21.0665 −0.760173
\(769\) 8.46265 0.305171 0.152586 0.988290i \(-0.451240\pi\)
0.152586 + 0.988290i \(0.451240\pi\)
\(770\) −34.7435 −1.25207
\(771\) −14.5214 −0.522977
\(772\) −0.671861 −0.0241808
\(773\) −42.4446 −1.52663 −0.763313 0.646028i \(-0.776429\pi\)
−0.763313 + 0.646028i \(0.776429\pi\)
\(774\) 39.5812 1.42272
\(775\) 25.6851 0.922636
\(776\) −13.9803 −0.501864
\(777\) 1.13984 0.0408915
\(778\) −17.2517 −0.618504
\(779\) 21.5648 0.772640
\(780\) −6.97077 −0.249593
\(781\) 4.26795 0.152719
\(782\) 13.5541 0.484692
\(783\) 49.5134 1.76946
\(784\) 102.230 3.65106
\(785\) 7.19375 0.256756
\(786\) 23.6098 0.842133
\(787\) −8.01789 −0.285807 −0.142903 0.989737i \(-0.545644\pi\)
−0.142903 + 0.989737i \(0.545644\pi\)
\(788\) −19.2581 −0.686043
\(789\) 39.7087 1.41367
\(790\) −10.8869 −0.387337
\(791\) −66.2351 −2.35505
\(792\) 28.2285 1.00306
\(793\) −4.42152 −0.157013
\(794\) −13.3279 −0.472988
\(795\) 5.66013 0.200744
\(796\) −121.277 −4.29854
\(797\) −21.9098 −0.776085 −0.388043 0.921641i \(-0.626849\pi\)
−0.388043 + 0.921641i \(0.626849\pi\)
\(798\) −40.3137 −1.42709
\(799\) −2.35892 −0.0834526
\(800\) 38.7215 1.36901
\(801\) −2.08247 −0.0735805
\(802\) −84.8696 −2.99685
\(803\) 19.0159 0.671056
\(804\) 20.8294 0.734595
\(805\) −16.5998 −0.585066
\(806\) 18.0291 0.635047
\(807\) 0.819509 0.0288481
\(808\) −112.289 −3.95031
\(809\) 10.5787 0.371927 0.185963 0.982557i \(-0.440459\pi\)
0.185963 + 0.982557i \(0.440459\pi\)
\(810\) −9.06914 −0.318657
\(811\) 0.528482 0.0185575 0.00927876 0.999957i \(-0.497046\pi\)
0.00927876 + 0.999957i \(0.497046\pi\)
\(812\) 179.526 6.30014
\(813\) 20.9825 0.735888
\(814\) 1.56280 0.0547763
\(815\) 11.2852 0.395303
\(816\) 18.0977 0.633548
\(817\) −32.0507 −1.12131
\(818\) 100.940 3.52927
\(819\) 5.73124 0.200266
\(820\) 40.6191 1.41848
\(821\) 18.0156 0.628748 0.314374 0.949299i \(-0.398205\pi\)
0.314374 + 0.949299i \(0.398205\pi\)
\(822\) 2.20248 0.0768205
\(823\) −21.5585 −0.751481 −0.375740 0.926725i \(-0.622612\pi\)
−0.375740 + 0.926725i \(0.622612\pi\)
\(824\) 138.775 4.83444
\(825\) −13.6043 −0.473642
\(826\) 110.510 3.84514
\(827\) 19.2633 0.669850 0.334925 0.942245i \(-0.391289\pi\)
0.334925 + 0.942245i \(0.391289\pi\)
\(828\) 23.0501 0.801047
\(829\) −23.7503 −0.824883 −0.412442 0.910984i \(-0.635324\pi\)
−0.412442 + 0.910984i \(0.635324\pi\)
\(830\) 4.34804 0.150923
\(831\) −12.3710 −0.429144
\(832\) 7.84503 0.271978
\(833\) 15.6572 0.542491
\(834\) 33.0236 1.14351
\(835\) −1.05066 −0.0363595
\(836\) −39.0655 −1.35111
\(837\) 38.2828 1.32325
\(838\) −96.7125 −3.34088
\(839\) −13.3464 −0.460770 −0.230385 0.973100i \(-0.573999\pi\)
−0.230385 + 0.973100i \(0.573999\pi\)
\(840\) −44.4304 −1.53299
\(841\) 49.5697 1.70930
\(842\) 57.7678 1.99081
\(843\) 23.4641 0.808147
\(844\) −118.751 −4.08757
\(845\) 13.4120 0.461387
\(846\) −5.67594 −0.195143
\(847\) 12.5766 0.432136
\(848\) −37.8405 −1.29945
\(849\) 35.7178 1.22583
\(850\) 14.3872 0.493477
\(851\) 0.746679 0.0255958
\(852\) 9.32787 0.319567
\(853\) 16.6009 0.568402 0.284201 0.958765i \(-0.408272\pi\)
0.284201 + 0.958765i \(0.408272\pi\)
\(854\) −48.1646 −1.64816
\(855\) −4.34017 −0.148431
\(856\) 48.9736 1.67388
\(857\) −53.4256 −1.82498 −0.912492 0.409094i \(-0.865845\pi\)
−0.912492 + 0.409094i \(0.865845\pi\)
\(858\) −9.54925 −0.326006
\(859\) 1.37622 0.0469559 0.0234780 0.999724i \(-0.492526\pi\)
0.0234780 + 0.999724i \(0.492526\pi\)
\(860\) −60.3701 −2.05860
\(861\) 40.5843 1.38311
\(862\) 6.92589 0.235897
\(863\) 41.7353 1.42069 0.710343 0.703855i \(-0.248540\pi\)
0.710343 + 0.703855i \(0.248540\pi\)
\(864\) 57.7130 1.96344
\(865\) 15.0299 0.511032
\(866\) −83.5201 −2.83813
\(867\) −19.0369 −0.646527
\(868\) 138.806 4.71139
\(869\) −10.5407 −0.357570
\(870\) −33.2325 −1.12669
\(871\) 3.39267 0.114956
\(872\) −48.4597 −1.64105
\(873\) −2.57013 −0.0869858
\(874\) −26.4084 −0.893278
\(875\) −41.1277 −1.39037
\(876\) 41.5604 1.40420
\(877\) 53.1848 1.79592 0.897962 0.440074i \(-0.145048\pi\)
0.897962 + 0.440074i \(0.145048\pi\)
\(878\) 37.7731 1.27478
\(879\) −9.28955 −0.313329
\(880\) −30.3891 −1.02442
\(881\) 37.8932 1.27665 0.638327 0.769765i \(-0.279627\pi\)
0.638327 + 0.769765i \(0.279627\pi\)
\(882\) 37.6737 1.26854
\(883\) −44.3424 −1.49224 −0.746120 0.665811i \(-0.768086\pi\)
−0.746120 + 0.665811i \(0.768086\pi\)
\(884\) 7.13754 0.240061
\(885\) −14.4583 −0.486010
\(886\) −99.8070 −3.35308
\(887\) −41.0432 −1.37810 −0.689049 0.724715i \(-0.741971\pi\)
−0.689049 + 0.724715i \(0.741971\pi\)
\(888\) 1.99853 0.0670664
\(889\) −10.1621 −0.340825
\(890\) 4.49399 0.150639
\(891\) −8.78081 −0.294168
\(892\) −42.4640 −1.42180
\(893\) 4.59607 0.153802
\(894\) −38.4091 −1.28459
\(895\) −27.9485 −0.934216
\(896\) −1.35917 −0.0454066
\(897\) −4.56246 −0.152336
\(898\) −42.9217 −1.43232
\(899\) 60.7485 2.02608
\(900\) 24.4670 0.815566
\(901\) −5.79554 −0.193078
\(902\) 55.6441 1.85274
\(903\) −60.3184 −2.00727
\(904\) −116.133 −3.86253
\(905\) 18.7560 0.623470
\(906\) −22.0005 −0.730917
\(907\) −34.8391 −1.15681 −0.578407 0.815748i \(-0.696325\pi\)
−0.578407 + 0.815748i \(0.696325\pi\)
\(908\) −37.9981 −1.26101
\(909\) −20.6431 −0.684689
\(910\) −12.3681 −0.409997
\(911\) −1.27351 −0.0421932 −0.0210966 0.999777i \(-0.506716\pi\)
−0.0210966 + 0.999777i \(0.506716\pi\)
\(912\) −35.2612 −1.16762
\(913\) 4.20981 0.139324
\(914\) −38.3519 −1.26857
\(915\) 6.30148 0.208320
\(916\) 121.063 4.00003
\(917\) 29.6069 0.977706
\(918\) 21.4436 0.707746
\(919\) −2.63002 −0.0867565 −0.0433782 0.999059i \(-0.513812\pi\)
−0.0433782 + 0.999059i \(0.513812\pi\)
\(920\) −29.1052 −0.959569
\(921\) 41.4081 1.36444
\(922\) −40.2126 −1.32433
\(923\) 1.51931 0.0500088
\(924\) −73.5199 −2.41863
\(925\) 0.792577 0.0260598
\(926\) −70.6426 −2.32146
\(927\) 25.5123 0.837933
\(928\) 91.5812 3.00630
\(929\) 3.62522 0.118940 0.0594698 0.998230i \(-0.481059\pi\)
0.0594698 + 0.998230i \(0.481059\pi\)
\(930\) −25.6947 −0.842563
\(931\) −30.5062 −0.999799
\(932\) 49.5448 1.62289
\(933\) 18.1336 0.593667
\(934\) 16.1238 0.527586
\(935\) −4.65431 −0.152212
\(936\) 10.0488 0.328457
\(937\) 28.1103 0.918325 0.459162 0.888352i \(-0.348150\pi\)
0.459162 + 0.888352i \(0.348150\pi\)
\(938\) 36.9570 1.20669
\(939\) 38.9988 1.27268
\(940\) 8.65706 0.282362
\(941\) −13.5804 −0.442707 −0.221354 0.975194i \(-0.571047\pi\)
−0.221354 + 0.975194i \(0.571047\pi\)
\(942\) 21.5381 0.701749
\(943\) 26.5857 0.865750
\(944\) 96.6601 3.14602
\(945\) −26.2622 −0.854310
\(946\) −82.7010 −2.68884
\(947\) −12.1484 −0.394769 −0.197385 0.980326i \(-0.563245\pi\)
−0.197385 + 0.980326i \(0.563245\pi\)
\(948\) −23.0375 −0.748222
\(949\) 6.76932 0.219741
\(950\) −28.0317 −0.909469
\(951\) 27.3835 0.887970
\(952\) 45.4934 1.47445
\(953\) 31.1937 1.01046 0.505231 0.862984i \(-0.331407\pi\)
0.505231 + 0.862984i \(0.331407\pi\)
\(954\) −13.9450 −0.451486
\(955\) −2.78126 −0.0899994
\(956\) −50.3439 −1.62824
\(957\) −32.1760 −1.04010
\(958\) −39.6188 −1.28002
\(959\) 2.76194 0.0891876
\(960\) −11.1806 −0.360852
\(961\) 15.9696 0.515147
\(962\) 0.556331 0.0179368
\(963\) 9.00328 0.290127
\(964\) −27.6603 −0.890879
\(965\) 0.155961 0.00502055
\(966\) −49.6998 −1.59906
\(967\) −16.7440 −0.538452 −0.269226 0.963077i \(-0.586768\pi\)
−0.269226 + 0.963077i \(0.586768\pi\)
\(968\) 22.0511 0.708749
\(969\) −5.40051 −0.173489
\(970\) 5.54637 0.178083
\(971\) −40.6364 −1.30408 −0.652041 0.758183i \(-0.726087\pi\)
−0.652041 + 0.758183i \(0.726087\pi\)
\(972\) 61.5924 1.97558
\(973\) 41.4120 1.32761
\(974\) 1.48327 0.0475269
\(975\) −4.84291 −0.155097
\(976\) −42.1282 −1.34849
\(977\) 52.4846 1.67913 0.839565 0.543259i \(-0.182810\pi\)
0.839565 + 0.543259i \(0.182810\pi\)
\(978\) 33.7879 1.08042
\(979\) 4.35112 0.139062
\(980\) −57.4608 −1.83552
\(981\) −8.90881 −0.284436
\(982\) −24.4135 −0.779065
\(983\) 51.1398 1.63111 0.815553 0.578683i \(-0.196433\pi\)
0.815553 + 0.578683i \(0.196433\pi\)
\(984\) 71.1583 2.26845
\(985\) 4.47044 0.142440
\(986\) 34.0276 1.08366
\(987\) 8.64965 0.275322
\(988\) −13.9066 −0.442428
\(989\) −39.5130 −1.25644
\(990\) −11.1990 −0.355928
\(991\) −24.2281 −0.769631 −0.384815 0.922994i \(-0.625735\pi\)
−0.384815 + 0.922994i \(0.625735\pi\)
\(992\) 70.8087 2.24818
\(993\) −9.26871 −0.294134
\(994\) 16.5502 0.524941
\(995\) 28.1523 0.892487
\(996\) 9.20080 0.291539
\(997\) 18.2197 0.577025 0.288512 0.957476i \(-0.406839\pi\)
0.288512 + 0.957476i \(0.406839\pi\)
\(998\) 21.8762 0.692480
\(999\) 1.18131 0.0373749
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.1.6 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.6 259 1.1 even 1 trivial