Properties

Label 6017.2.a.f.1.4
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.69280 q^{2} +3.13292 q^{3} +5.25118 q^{4} +0.629801 q^{5} -8.43634 q^{6} -1.84618 q^{7} -8.75479 q^{8} +6.81521 q^{9} +O(q^{10})\) \(q-2.69280 q^{2} +3.13292 q^{3} +5.25118 q^{4} +0.629801 q^{5} -8.43634 q^{6} -1.84618 q^{7} -8.75479 q^{8} +6.81521 q^{9} -1.69593 q^{10} -1.00000 q^{11} +16.4515 q^{12} +0.191424 q^{13} +4.97140 q^{14} +1.97312 q^{15} +13.0725 q^{16} +1.18247 q^{17} -18.3520 q^{18} +4.49167 q^{19} +3.30720 q^{20} -5.78395 q^{21} +2.69280 q^{22} +1.31237 q^{23} -27.4281 q^{24} -4.60335 q^{25} -0.515466 q^{26} +11.9528 q^{27} -9.69464 q^{28} -5.08120 q^{29} -5.31322 q^{30} +0.491248 q^{31} -17.6922 q^{32} -3.13292 q^{33} -3.18416 q^{34} -1.16273 q^{35} +35.7879 q^{36} +8.46907 q^{37} -12.0952 q^{38} +0.599715 q^{39} -5.51378 q^{40} +5.11542 q^{41} +15.5750 q^{42} -3.80104 q^{43} -5.25118 q^{44} +4.29223 q^{45} -3.53395 q^{46} +7.13903 q^{47} +40.9553 q^{48} -3.59161 q^{49} +12.3959 q^{50} +3.70459 q^{51} +1.00520 q^{52} -4.73685 q^{53} -32.1864 q^{54} -0.629801 q^{55} +16.1629 q^{56} +14.0721 q^{57} +13.6827 q^{58} +8.59409 q^{59} +10.3612 q^{60} +9.02264 q^{61} -1.32283 q^{62} -12.5821 q^{63} +21.4965 q^{64} +0.120559 q^{65} +8.43634 q^{66} +5.58299 q^{67} +6.20937 q^{68} +4.11155 q^{69} +3.13100 q^{70} -2.00994 q^{71} -59.6657 q^{72} +0.552084 q^{73} -22.8055 q^{74} -14.4219 q^{75} +23.5866 q^{76} +1.84618 q^{77} -1.61491 q^{78} +9.93583 q^{79} +8.23310 q^{80} +17.0014 q^{81} -13.7748 q^{82} +5.01204 q^{83} -30.3726 q^{84} +0.744721 q^{85} +10.2355 q^{86} -15.9190 q^{87} +8.75479 q^{88} -12.3782 q^{89} -11.5581 q^{90} -0.353403 q^{91} +6.89148 q^{92} +1.53904 q^{93} -19.2240 q^{94} +2.82886 q^{95} -55.4283 q^{96} +16.3610 q^{97} +9.67149 q^{98} -6.81521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69280 −1.90410 −0.952049 0.305945i \(-0.901028\pi\)
−0.952049 + 0.305945i \(0.901028\pi\)
\(3\) 3.13292 1.80879 0.904397 0.426692i \(-0.140321\pi\)
0.904397 + 0.426692i \(0.140321\pi\)
\(4\) 5.25118 2.62559
\(5\) 0.629801 0.281656 0.140828 0.990034i \(-0.455024\pi\)
0.140828 + 0.990034i \(0.455024\pi\)
\(6\) −8.43634 −3.44412
\(7\) −1.84618 −0.697792 −0.348896 0.937162i \(-0.613443\pi\)
−0.348896 + 0.937162i \(0.613443\pi\)
\(8\) −8.75479 −3.09528
\(9\) 6.81521 2.27174
\(10\) −1.69593 −0.536300
\(11\) −1.00000 −0.301511
\(12\) 16.4515 4.74915
\(13\) 0.191424 0.0530913 0.0265457 0.999648i \(-0.491549\pi\)
0.0265457 + 0.999648i \(0.491549\pi\)
\(14\) 4.97140 1.32866
\(15\) 1.97312 0.509457
\(16\) 13.0725 3.26813
\(17\) 1.18247 0.286791 0.143396 0.989665i \(-0.454198\pi\)
0.143396 + 0.989665i \(0.454198\pi\)
\(18\) −18.3520 −4.32561
\(19\) 4.49167 1.03046 0.515230 0.857052i \(-0.327706\pi\)
0.515230 + 0.857052i \(0.327706\pi\)
\(20\) 3.30720 0.739513
\(21\) −5.78395 −1.26216
\(22\) 2.69280 0.574107
\(23\) 1.31237 0.273648 0.136824 0.990595i \(-0.456311\pi\)
0.136824 + 0.990595i \(0.456311\pi\)
\(24\) −27.4281 −5.59873
\(25\) −4.60335 −0.920670
\(26\) −0.515466 −0.101091
\(27\) 11.9528 2.30031
\(28\) −9.69464 −1.83211
\(29\) −5.08120 −0.943555 −0.471778 0.881718i \(-0.656387\pi\)
−0.471778 + 0.881718i \(0.656387\pi\)
\(30\) −5.31322 −0.970057
\(31\) 0.491248 0.0882307 0.0441154 0.999026i \(-0.485953\pi\)
0.0441154 + 0.999026i \(0.485953\pi\)
\(32\) −17.6922 −3.12757
\(33\) −3.13292 −0.545372
\(34\) −3.18416 −0.546079
\(35\) −1.16273 −0.196537
\(36\) 35.7879 5.96465
\(37\) 8.46907 1.39231 0.696153 0.717893i \(-0.254893\pi\)
0.696153 + 0.717893i \(0.254893\pi\)
\(38\) −12.0952 −1.96210
\(39\) 0.599715 0.0960313
\(40\) −5.51378 −0.871804
\(41\) 5.11542 0.798894 0.399447 0.916756i \(-0.369202\pi\)
0.399447 + 0.916756i \(0.369202\pi\)
\(42\) 15.5750 2.40328
\(43\) −3.80104 −0.579653 −0.289827 0.957079i \(-0.593598\pi\)
−0.289827 + 0.957079i \(0.593598\pi\)
\(44\) −5.25118 −0.791645
\(45\) 4.29223 0.639847
\(46\) −3.53395 −0.521052
\(47\) 7.13903 1.04134 0.520668 0.853759i \(-0.325683\pi\)
0.520668 + 0.853759i \(0.325683\pi\)
\(48\) 40.9553 5.91138
\(49\) −3.59161 −0.513087
\(50\) 12.3959 1.75305
\(51\) 3.70459 0.518746
\(52\) 1.00520 0.139396
\(53\) −4.73685 −0.650657 −0.325328 0.945601i \(-0.605475\pi\)
−0.325328 + 0.945601i \(0.605475\pi\)
\(54\) −32.1864 −4.38001
\(55\) −0.629801 −0.0849224
\(56\) 16.1629 2.15986
\(57\) 14.0721 1.86389
\(58\) 13.6827 1.79662
\(59\) 8.59409 1.11886 0.559428 0.828879i \(-0.311021\pi\)
0.559428 + 0.828879i \(0.311021\pi\)
\(60\) 10.3612 1.33763
\(61\) 9.02264 1.15523 0.577616 0.816309i \(-0.303983\pi\)
0.577616 + 0.816309i \(0.303983\pi\)
\(62\) −1.32283 −0.168000
\(63\) −12.5821 −1.58520
\(64\) 21.4965 2.68706
\(65\) 0.120559 0.0149535
\(66\) 8.43634 1.03844
\(67\) 5.58299 0.682071 0.341036 0.940050i \(-0.389222\pi\)
0.341036 + 0.940050i \(0.389222\pi\)
\(68\) 6.20937 0.752996
\(69\) 4.11155 0.494972
\(70\) 3.13100 0.374226
\(71\) −2.00994 −0.238536 −0.119268 0.992862i \(-0.538055\pi\)
−0.119268 + 0.992862i \(0.538055\pi\)
\(72\) −59.6657 −7.03167
\(73\) 0.552084 0.0646165 0.0323082 0.999478i \(-0.489714\pi\)
0.0323082 + 0.999478i \(0.489714\pi\)
\(74\) −22.8055 −2.65109
\(75\) −14.4219 −1.66530
\(76\) 23.5866 2.70557
\(77\) 1.84618 0.210392
\(78\) −1.61491 −0.182853
\(79\) 9.93583 1.11787 0.558934 0.829212i \(-0.311210\pi\)
0.558934 + 0.829212i \(0.311210\pi\)
\(80\) 8.23310 0.920489
\(81\) 17.0014 1.88905
\(82\) −13.7748 −1.52117
\(83\) 5.01204 0.550143 0.275072 0.961424i \(-0.411298\pi\)
0.275072 + 0.961424i \(0.411298\pi\)
\(84\) −30.3726 −3.31392
\(85\) 0.744721 0.0807764
\(86\) 10.2355 1.10372
\(87\) −15.9190 −1.70670
\(88\) 8.75479 0.933263
\(89\) −12.3782 −1.31208 −0.656041 0.754725i \(-0.727770\pi\)
−0.656041 + 0.754725i \(0.727770\pi\)
\(90\) −11.5581 −1.21833
\(91\) −0.353403 −0.0370467
\(92\) 6.89148 0.718486
\(93\) 1.53904 0.159591
\(94\) −19.2240 −1.98280
\(95\) 2.82886 0.290235
\(96\) −55.4283 −5.65712
\(97\) 16.3610 1.66121 0.830605 0.556862i \(-0.187995\pi\)
0.830605 + 0.556862i \(0.187995\pi\)
\(98\) 9.67149 0.976968
\(99\) −6.81521 −0.684954
\(100\) −24.1730 −2.41730
\(101\) −4.37156 −0.434986 −0.217493 0.976062i \(-0.569788\pi\)
−0.217493 + 0.976062i \(0.569788\pi\)
\(102\) −9.97572 −0.987744
\(103\) 2.59714 0.255903 0.127952 0.991780i \(-0.459160\pi\)
0.127952 + 0.991780i \(0.459160\pi\)
\(104\) −1.67587 −0.164333
\(105\) −3.64274 −0.355495
\(106\) 12.7554 1.23891
\(107\) −5.72177 −0.553144 −0.276572 0.960993i \(-0.589198\pi\)
−0.276572 + 0.960993i \(0.589198\pi\)
\(108\) 62.7661 6.03967
\(109\) −4.66401 −0.446731 −0.223366 0.974735i \(-0.571704\pi\)
−0.223366 + 0.974735i \(0.571704\pi\)
\(110\) 1.69593 0.161701
\(111\) 26.5330 2.51840
\(112\) −24.1343 −2.28048
\(113\) 2.60502 0.245060 0.122530 0.992465i \(-0.460899\pi\)
0.122530 + 0.992465i \(0.460899\pi\)
\(114\) −37.8933 −3.54903
\(115\) 0.826531 0.0770744
\(116\) −26.6823 −2.47739
\(117\) 1.30459 0.120609
\(118\) −23.1422 −2.13041
\(119\) −2.18306 −0.200120
\(120\) −17.2742 −1.57691
\(121\) 1.00000 0.0909091
\(122\) −24.2962 −2.19967
\(123\) 16.0262 1.44503
\(124\) 2.57963 0.231658
\(125\) −6.04820 −0.540968
\(126\) 33.8812 3.01837
\(127\) 4.17969 0.370888 0.185444 0.982655i \(-0.440628\pi\)
0.185444 + 0.982655i \(0.440628\pi\)
\(128\) −22.5014 −1.98886
\(129\) −11.9084 −1.04847
\(130\) −0.324641 −0.0284729
\(131\) −21.2442 −1.85612 −0.928058 0.372436i \(-0.878523\pi\)
−0.928058 + 0.372436i \(0.878523\pi\)
\(132\) −16.4515 −1.43192
\(133\) −8.29245 −0.719046
\(134\) −15.0339 −1.29873
\(135\) 7.52786 0.647895
\(136\) −10.3523 −0.887700
\(137\) −0.557590 −0.0476381 −0.0238190 0.999716i \(-0.507583\pi\)
−0.0238190 + 0.999716i \(0.507583\pi\)
\(138\) −11.0716 −0.942476
\(139\) −4.84213 −0.410704 −0.205352 0.978688i \(-0.565834\pi\)
−0.205352 + 0.978688i \(0.565834\pi\)
\(140\) −6.10570 −0.516026
\(141\) 22.3660 1.88356
\(142\) 5.41237 0.454196
\(143\) −0.191424 −0.0160076
\(144\) 89.0921 7.42434
\(145\) −3.20015 −0.265758
\(146\) −1.48665 −0.123036
\(147\) −11.2522 −0.928069
\(148\) 44.4726 3.65563
\(149\) 4.00725 0.328287 0.164144 0.986436i \(-0.447514\pi\)
0.164144 + 0.986436i \(0.447514\pi\)
\(150\) 38.8354 3.17090
\(151\) 13.2341 1.07698 0.538488 0.842633i \(-0.318996\pi\)
0.538488 + 0.842633i \(0.318996\pi\)
\(152\) −39.3236 −3.18957
\(153\) 8.05878 0.651514
\(154\) −4.97140 −0.400607
\(155\) 0.309389 0.0248507
\(156\) 3.14921 0.252139
\(157\) 15.3895 1.22822 0.614108 0.789222i \(-0.289516\pi\)
0.614108 + 0.789222i \(0.289516\pi\)
\(158\) −26.7552 −2.12853
\(159\) −14.8402 −1.17690
\(160\) −11.1426 −0.880897
\(161\) −2.42287 −0.190949
\(162\) −45.7815 −3.59693
\(163\) −6.43264 −0.503843 −0.251922 0.967748i \(-0.581063\pi\)
−0.251922 + 0.967748i \(0.581063\pi\)
\(164\) 26.8620 2.09757
\(165\) −1.97312 −0.153607
\(166\) −13.4964 −1.04753
\(167\) 8.10569 0.627237 0.313619 0.949549i \(-0.398459\pi\)
0.313619 + 0.949549i \(0.398459\pi\)
\(168\) 50.6372 3.90675
\(169\) −12.9634 −0.997181
\(170\) −2.00539 −0.153806
\(171\) 30.6117 2.34093
\(172\) −19.9600 −1.52193
\(173\) 8.83103 0.671410 0.335705 0.941967i \(-0.391025\pi\)
0.335705 + 0.941967i \(0.391025\pi\)
\(174\) 42.8667 3.24972
\(175\) 8.49863 0.642436
\(176\) −13.0725 −0.985380
\(177\) 26.9246 2.02378
\(178\) 33.3319 2.49833
\(179\) 0.173536 0.0129707 0.00648534 0.999979i \(-0.497936\pi\)
0.00648534 + 0.999979i \(0.497936\pi\)
\(180\) 22.5393 1.67998
\(181\) 20.1633 1.49873 0.749364 0.662159i \(-0.230359\pi\)
0.749364 + 0.662159i \(0.230359\pi\)
\(182\) 0.951644 0.0705405
\(183\) 28.2672 2.08958
\(184\) −11.4895 −0.847017
\(185\) 5.33383 0.392151
\(186\) −4.14433 −0.303877
\(187\) −1.18247 −0.0864708
\(188\) 37.4884 2.73412
\(189\) −22.0670 −1.60514
\(190\) −7.61756 −0.552636
\(191\) −1.16185 −0.0840684 −0.0420342 0.999116i \(-0.513384\pi\)
−0.0420342 + 0.999116i \(0.513384\pi\)
\(192\) 67.3468 4.86034
\(193\) 20.3694 1.46622 0.733112 0.680108i \(-0.238067\pi\)
0.733112 + 0.680108i \(0.238067\pi\)
\(194\) −44.0570 −3.16311
\(195\) 0.377701 0.0270478
\(196\) −18.8602 −1.34716
\(197\) 12.6379 0.900412 0.450206 0.892925i \(-0.351351\pi\)
0.450206 + 0.892925i \(0.351351\pi\)
\(198\) 18.3520 1.30422
\(199\) 6.16727 0.437186 0.218593 0.975816i \(-0.429853\pi\)
0.218593 + 0.975816i \(0.429853\pi\)
\(200\) 40.3013 2.84974
\(201\) 17.4911 1.23373
\(202\) 11.7717 0.828257
\(203\) 9.38082 0.658405
\(204\) 19.4535 1.36202
\(205\) 3.22170 0.225013
\(206\) −6.99357 −0.487265
\(207\) 8.94406 0.621655
\(208\) 2.50239 0.173510
\(209\) −4.49167 −0.310695
\(210\) 9.80917 0.676897
\(211\) 6.86196 0.472397 0.236198 0.971705i \(-0.424098\pi\)
0.236198 + 0.971705i \(0.424098\pi\)
\(212\) −24.8741 −1.70836
\(213\) −6.29698 −0.431462
\(214\) 15.4076 1.05324
\(215\) −2.39390 −0.163263
\(216\) −104.644 −7.12011
\(217\) −0.906933 −0.0615666
\(218\) 12.5593 0.850620
\(219\) 1.72964 0.116878
\(220\) −3.30720 −0.222971
\(221\) 0.226353 0.0152261
\(222\) −71.4480 −4.79527
\(223\) −6.10884 −0.409078 −0.204539 0.978858i \(-0.565570\pi\)
−0.204539 + 0.978858i \(0.565570\pi\)
\(224\) 32.6630 2.18239
\(225\) −31.3728 −2.09152
\(226\) −7.01481 −0.466618
\(227\) −14.6953 −0.975360 −0.487680 0.873022i \(-0.662157\pi\)
−0.487680 + 0.873022i \(0.662157\pi\)
\(228\) 73.8949 4.89381
\(229\) 13.2217 0.873712 0.436856 0.899532i \(-0.356092\pi\)
0.436856 + 0.899532i \(0.356092\pi\)
\(230\) −2.22568 −0.146757
\(231\) 5.78395 0.380556
\(232\) 44.4848 2.92057
\(233\) −5.52740 −0.362112 −0.181056 0.983473i \(-0.557952\pi\)
−0.181056 + 0.983473i \(0.557952\pi\)
\(234\) −3.51300 −0.229652
\(235\) 4.49617 0.293298
\(236\) 45.1291 2.93766
\(237\) 31.1282 2.02199
\(238\) 5.87854 0.381049
\(239\) 11.9781 0.774802 0.387401 0.921911i \(-0.373373\pi\)
0.387401 + 0.921911i \(0.373373\pi\)
\(240\) 25.7937 1.66497
\(241\) 26.0583 1.67857 0.839283 0.543695i \(-0.182975\pi\)
0.839283 + 0.543695i \(0.182975\pi\)
\(242\) −2.69280 −0.173100
\(243\) 17.4059 1.11659
\(244\) 47.3795 3.03316
\(245\) −2.26200 −0.144514
\(246\) −43.1554 −2.75149
\(247\) 0.859812 0.0547085
\(248\) −4.30077 −0.273099
\(249\) 15.7024 0.995096
\(250\) 16.2866 1.03006
\(251\) −28.1862 −1.77909 −0.889547 0.456843i \(-0.848980\pi\)
−0.889547 + 0.456843i \(0.848980\pi\)
\(252\) −66.0710 −4.16208
\(253\) −1.31237 −0.0825078
\(254\) −11.2551 −0.706207
\(255\) 2.33316 0.146108
\(256\) 17.5988 1.09992
\(257\) 23.6865 1.47752 0.738762 0.673966i \(-0.235411\pi\)
0.738762 + 0.673966i \(0.235411\pi\)
\(258\) 32.0669 1.99640
\(259\) −15.6355 −0.971540
\(260\) 0.633076 0.0392617
\(261\) −34.6294 −2.14351
\(262\) 57.2065 3.53423
\(263\) −12.7626 −0.786976 −0.393488 0.919330i \(-0.628732\pi\)
−0.393488 + 0.919330i \(0.628732\pi\)
\(264\) 27.4281 1.68808
\(265\) −2.98328 −0.183261
\(266\) 22.3299 1.36913
\(267\) −38.7798 −2.37329
\(268\) 29.3173 1.79084
\(269\) 3.45652 0.210748 0.105374 0.994433i \(-0.466396\pi\)
0.105374 + 0.994433i \(0.466396\pi\)
\(270\) −20.2710 −1.23366
\(271\) 1.03655 0.0629659 0.0314829 0.999504i \(-0.489977\pi\)
0.0314829 + 0.999504i \(0.489977\pi\)
\(272\) 15.4579 0.937272
\(273\) −1.10718 −0.0670098
\(274\) 1.50148 0.0907076
\(275\) 4.60335 0.277592
\(276\) 21.5905 1.29959
\(277\) −23.5298 −1.41377 −0.706883 0.707331i \(-0.749899\pi\)
−0.706883 + 0.707331i \(0.749899\pi\)
\(278\) 13.0389 0.782021
\(279\) 3.34796 0.200437
\(280\) 10.1794 0.608338
\(281\) 13.1537 0.784682 0.392341 0.919820i \(-0.371665\pi\)
0.392341 + 0.919820i \(0.371665\pi\)
\(282\) −60.2273 −3.58649
\(283\) −8.60573 −0.511558 −0.255779 0.966735i \(-0.582332\pi\)
−0.255779 + 0.966735i \(0.582332\pi\)
\(284\) −10.5546 −0.626298
\(285\) 8.86260 0.524975
\(286\) 0.515466 0.0304801
\(287\) −9.44400 −0.557462
\(288\) −120.576 −7.10500
\(289\) −15.6018 −0.917751
\(290\) 8.61736 0.506029
\(291\) 51.2578 3.00479
\(292\) 2.89909 0.169656
\(293\) 30.8647 1.80313 0.901567 0.432640i \(-0.142418\pi\)
0.901567 + 0.432640i \(0.142418\pi\)
\(294\) 30.3000 1.76713
\(295\) 5.41257 0.315132
\(296\) −74.1449 −4.30959
\(297\) −11.9528 −0.693569
\(298\) −10.7907 −0.625091
\(299\) 0.251218 0.0145283
\(300\) −75.7322 −4.37240
\(301\) 7.01742 0.404477
\(302\) −35.6368 −2.05067
\(303\) −13.6958 −0.786801
\(304\) 58.7176 3.36768
\(305\) 5.68247 0.325377
\(306\) −21.7007 −1.24055
\(307\) 7.07258 0.403654 0.201827 0.979421i \(-0.435312\pi\)
0.201827 + 0.979421i \(0.435312\pi\)
\(308\) 9.69464 0.552403
\(309\) 8.13663 0.462876
\(310\) −0.833122 −0.0473181
\(311\) −17.1562 −0.972840 −0.486420 0.873725i \(-0.661698\pi\)
−0.486420 + 0.873725i \(0.661698\pi\)
\(312\) −5.25038 −0.297244
\(313\) 13.4028 0.757573 0.378786 0.925484i \(-0.376341\pi\)
0.378786 + 0.925484i \(0.376341\pi\)
\(314\) −41.4409 −2.33864
\(315\) −7.92424 −0.446480
\(316\) 52.1748 2.93506
\(317\) −0.865757 −0.0486258 −0.0243129 0.999704i \(-0.507740\pi\)
−0.0243129 + 0.999704i \(0.507740\pi\)
\(318\) 39.9617 2.24094
\(319\) 5.08120 0.284493
\(320\) 13.5385 0.756825
\(321\) −17.9259 −1.00052
\(322\) 6.52431 0.363586
\(323\) 5.31127 0.295527
\(324\) 89.2776 4.95987
\(325\) −0.881189 −0.0488796
\(326\) 17.3218 0.959368
\(327\) −14.6120 −0.808044
\(328\) −44.7844 −2.47280
\(329\) −13.1800 −0.726635
\(330\) 5.31322 0.292483
\(331\) −25.9705 −1.42747 −0.713733 0.700418i \(-0.752997\pi\)
−0.713733 + 0.700418i \(0.752997\pi\)
\(332\) 26.3192 1.44445
\(333\) 57.7185 3.16295
\(334\) −21.8270 −1.19432
\(335\) 3.51618 0.192109
\(336\) −75.6109 −4.12491
\(337\) −3.40896 −0.185698 −0.0928488 0.995680i \(-0.529597\pi\)
−0.0928488 + 0.995680i \(0.529597\pi\)
\(338\) 34.9077 1.89873
\(339\) 8.16134 0.443263
\(340\) 3.91067 0.212086
\(341\) −0.491248 −0.0266026
\(342\) −82.4312 −4.45737
\(343\) 19.5540 1.05582
\(344\) 33.2773 1.79419
\(345\) 2.58946 0.139412
\(346\) −23.7802 −1.27843
\(347\) 25.5302 1.37053 0.685266 0.728293i \(-0.259686\pi\)
0.685266 + 0.728293i \(0.259686\pi\)
\(348\) −83.5936 −4.48109
\(349\) 4.24664 0.227317 0.113659 0.993520i \(-0.463743\pi\)
0.113659 + 0.993520i \(0.463743\pi\)
\(350\) −22.8851 −1.22326
\(351\) 2.28804 0.122126
\(352\) 17.6922 0.942997
\(353\) −28.1613 −1.49888 −0.749438 0.662074i \(-0.769676\pi\)
−0.749438 + 0.662074i \(0.769676\pi\)
\(354\) −72.5027 −3.85347
\(355\) −1.26586 −0.0671850
\(356\) −64.9999 −3.44499
\(357\) −6.83935 −0.361977
\(358\) −0.467298 −0.0246975
\(359\) −31.8326 −1.68006 −0.840030 0.542540i \(-0.817463\pi\)
−0.840030 + 0.542540i \(0.817463\pi\)
\(360\) −37.5775 −1.98051
\(361\) 1.17511 0.0618482
\(362\) −54.2958 −2.85372
\(363\) 3.13292 0.164436
\(364\) −1.85578 −0.0972694
\(365\) 0.347703 0.0181996
\(366\) −76.1181 −3.97876
\(367\) 3.04435 0.158914 0.0794569 0.996838i \(-0.474681\pi\)
0.0794569 + 0.996838i \(0.474681\pi\)
\(368\) 17.1560 0.894317
\(369\) 34.8626 1.81488
\(370\) −14.3630 −0.746694
\(371\) 8.74509 0.454023
\(372\) 8.08179 0.419021
\(373\) −1.33581 −0.0691658 −0.0345829 0.999402i \(-0.511010\pi\)
−0.0345829 + 0.999402i \(0.511010\pi\)
\(374\) 3.18416 0.164649
\(375\) −18.9486 −0.978499
\(376\) −62.5007 −3.22323
\(377\) −0.972661 −0.0500946
\(378\) 59.4220 3.05634
\(379\) 20.4880 1.05240 0.526198 0.850362i \(-0.323617\pi\)
0.526198 + 0.850362i \(0.323617\pi\)
\(380\) 14.8549 0.762038
\(381\) 13.0947 0.670860
\(382\) 3.12863 0.160074
\(383\) −2.75043 −0.140540 −0.0702702 0.997528i \(-0.522386\pi\)
−0.0702702 + 0.997528i \(0.522386\pi\)
\(384\) −70.4950 −3.59743
\(385\) 1.16273 0.0592581
\(386\) −54.8508 −2.79183
\(387\) −25.9049 −1.31682
\(388\) 85.9147 4.36166
\(389\) 31.3500 1.58951 0.794755 0.606930i \(-0.207599\pi\)
0.794755 + 0.606930i \(0.207599\pi\)
\(390\) −1.01707 −0.0515016
\(391\) 1.55184 0.0784797
\(392\) 31.4438 1.58815
\(393\) −66.5565 −3.35733
\(394\) −34.0313 −1.71447
\(395\) 6.25760 0.314854
\(396\) −35.7879 −1.79841
\(397\) −4.84846 −0.243337 −0.121669 0.992571i \(-0.538825\pi\)
−0.121669 + 0.992571i \(0.538825\pi\)
\(398\) −16.6072 −0.832446
\(399\) −25.9796 −1.30061
\(400\) −60.1775 −3.00887
\(401\) 17.3865 0.868242 0.434121 0.900854i \(-0.357059\pi\)
0.434121 + 0.900854i \(0.357059\pi\)
\(402\) −47.1000 −2.34914
\(403\) 0.0940364 0.00468429
\(404\) −22.9558 −1.14210
\(405\) 10.7075 0.532061
\(406\) −25.2607 −1.25367
\(407\) −8.46907 −0.419796
\(408\) −32.4329 −1.60567
\(409\) −21.2591 −1.05119 −0.525596 0.850734i \(-0.676158\pi\)
−0.525596 + 0.850734i \(0.676158\pi\)
\(410\) −8.67539 −0.428447
\(411\) −1.74689 −0.0861675
\(412\) 13.6380 0.671897
\(413\) −15.8663 −0.780728
\(414\) −24.0846 −1.18369
\(415\) 3.15659 0.154951
\(416\) −3.38670 −0.166047
\(417\) −15.1700 −0.742879
\(418\) 12.0952 0.591595
\(419\) 18.6206 0.909678 0.454839 0.890574i \(-0.349697\pi\)
0.454839 + 0.890574i \(0.349697\pi\)
\(420\) −19.1287 −0.933384
\(421\) −18.3024 −0.892006 −0.446003 0.895031i \(-0.647153\pi\)
−0.446003 + 0.895031i \(0.647153\pi\)
\(422\) −18.4779 −0.899490
\(423\) 48.6540 2.36564
\(424\) 41.4701 2.01397
\(425\) −5.44333 −0.264040
\(426\) 16.9565 0.821547
\(427\) −16.6574 −0.806110
\(428\) −30.0460 −1.45233
\(429\) −0.599715 −0.0289545
\(430\) 6.44630 0.310868
\(431\) 4.55660 0.219484 0.109742 0.993960i \(-0.464998\pi\)
0.109742 + 0.993960i \(0.464998\pi\)
\(432\) 156.253 7.51772
\(433\) 12.0666 0.579886 0.289943 0.957044i \(-0.406364\pi\)
0.289943 + 0.957044i \(0.406364\pi\)
\(434\) 2.44219 0.117229
\(435\) −10.0258 −0.480701
\(436\) −24.4916 −1.17293
\(437\) 5.89472 0.281983
\(438\) −4.65757 −0.222547
\(439\) 3.91608 0.186904 0.0934520 0.995624i \(-0.470210\pi\)
0.0934520 + 0.995624i \(0.470210\pi\)
\(440\) 5.51378 0.262859
\(441\) −24.4776 −1.16560
\(442\) −0.609523 −0.0289920
\(443\) 9.52765 0.452672 0.226336 0.974049i \(-0.427325\pi\)
0.226336 + 0.974049i \(0.427325\pi\)
\(444\) 139.329 6.61228
\(445\) −7.79578 −0.369555
\(446\) 16.4499 0.778925
\(447\) 12.5544 0.593804
\(448\) −39.6864 −1.87501
\(449\) 22.5450 1.06397 0.531983 0.846755i \(-0.321447\pi\)
0.531983 + 0.846755i \(0.321447\pi\)
\(450\) 84.4807 3.98246
\(451\) −5.11542 −0.240876
\(452\) 13.6794 0.643427
\(453\) 41.4614 1.94803
\(454\) 39.5715 1.85718
\(455\) −0.222574 −0.0104344
\(456\) −123.198 −5.76927
\(457\) 17.0814 0.799034 0.399517 0.916726i \(-0.369178\pi\)
0.399517 + 0.916726i \(0.369178\pi\)
\(458\) −35.6033 −1.66363
\(459\) 14.1338 0.659708
\(460\) 4.34026 0.202366
\(461\) −27.9013 −1.29949 −0.649746 0.760151i \(-0.725125\pi\)
−0.649746 + 0.760151i \(0.725125\pi\)
\(462\) −15.5750 −0.724616
\(463\) −8.07133 −0.375106 −0.187553 0.982254i \(-0.560056\pi\)
−0.187553 + 0.982254i \(0.560056\pi\)
\(464\) −66.4242 −3.08367
\(465\) 0.969290 0.0449498
\(466\) 14.8842 0.689497
\(467\) −41.9705 −1.94217 −0.971083 0.238743i \(-0.923265\pi\)
−0.971083 + 0.238743i \(0.923265\pi\)
\(468\) 6.85064 0.316671
\(469\) −10.3072 −0.475943
\(470\) −12.1073 −0.558468
\(471\) 48.2141 2.22159
\(472\) −75.2394 −3.46318
\(473\) 3.80104 0.174772
\(474\) −83.8220 −3.85007
\(475\) −20.6767 −0.948714
\(476\) −11.4636 −0.525434
\(477\) −32.2826 −1.47812
\(478\) −32.2548 −1.47530
\(479\) 34.6024 1.58102 0.790512 0.612446i \(-0.209814\pi\)
0.790512 + 0.612446i \(0.209814\pi\)
\(480\) −34.9088 −1.59336
\(481\) 1.62118 0.0739194
\(482\) −70.1699 −3.19615
\(483\) −7.59067 −0.345387
\(484\) 5.25118 0.238690
\(485\) 10.3042 0.467889
\(486\) −46.8707 −2.12610
\(487\) 9.80073 0.444114 0.222057 0.975034i \(-0.428723\pi\)
0.222057 + 0.975034i \(0.428723\pi\)
\(488\) −78.9913 −3.57577
\(489\) −20.1530 −0.911349
\(490\) 6.09112 0.275169
\(491\) −16.9619 −0.765479 −0.382740 0.923856i \(-0.625019\pi\)
−0.382740 + 0.923856i \(0.625019\pi\)
\(492\) 84.1565 3.79407
\(493\) −6.00837 −0.270603
\(494\) −2.31530 −0.104170
\(495\) −4.29223 −0.192921
\(496\) 6.42186 0.288350
\(497\) 3.71071 0.166448
\(498\) −42.2833 −1.89476
\(499\) −6.46814 −0.289554 −0.144777 0.989464i \(-0.546246\pi\)
−0.144777 + 0.989464i \(0.546246\pi\)
\(500\) −31.7602 −1.42036
\(501\) 25.3945 1.13454
\(502\) 75.8997 3.38757
\(503\) 18.6676 0.832346 0.416173 0.909286i \(-0.363371\pi\)
0.416173 + 0.909286i \(0.363371\pi\)
\(504\) 110.154 4.90664
\(505\) −2.75321 −0.122516
\(506\) 3.53395 0.157103
\(507\) −40.6132 −1.80370
\(508\) 21.9483 0.973800
\(509\) −43.7542 −1.93937 −0.969686 0.244355i \(-0.921424\pi\)
−0.969686 + 0.244355i \(0.921424\pi\)
\(510\) −6.28272 −0.278204
\(511\) −1.01925 −0.0450888
\(512\) −2.38723 −0.105502
\(513\) 53.6878 2.37038
\(514\) −63.7831 −2.81335
\(515\) 1.63568 0.0720766
\(516\) −62.5330 −2.75286
\(517\) −7.13903 −0.313974
\(518\) 42.1032 1.84991
\(519\) 27.6669 1.21444
\(520\) −1.05547 −0.0462853
\(521\) −14.8152 −0.649064 −0.324532 0.945875i \(-0.605207\pi\)
−0.324532 + 0.945875i \(0.605207\pi\)
\(522\) 93.2502 4.08145
\(523\) 23.0712 1.00883 0.504417 0.863460i \(-0.331708\pi\)
0.504417 + 0.863460i \(0.331708\pi\)
\(524\) −111.557 −4.87340
\(525\) 26.6255 1.16203
\(526\) 34.3671 1.49848
\(527\) 0.580886 0.0253038
\(528\) −40.9553 −1.78235
\(529\) −21.2777 −0.925117
\(530\) 8.03337 0.348947
\(531\) 58.5705 2.54174
\(532\) −43.5451 −1.88792
\(533\) 0.979211 0.0424144
\(534\) 104.426 4.51897
\(535\) −3.60358 −0.155796
\(536\) −48.8779 −2.11120
\(537\) 0.543675 0.0234613
\(538\) −9.30772 −0.401284
\(539\) 3.59161 0.154702
\(540\) 39.5302 1.70111
\(541\) −24.2591 −1.04298 −0.521491 0.853257i \(-0.674624\pi\)
−0.521491 + 0.853257i \(0.674624\pi\)
\(542\) −2.79122 −0.119893
\(543\) 63.1701 2.71089
\(544\) −20.9205 −0.896958
\(545\) −2.93740 −0.125824
\(546\) 2.98143 0.127593
\(547\) 1.00000 0.0427569
\(548\) −2.92800 −0.125078
\(549\) 61.4912 2.62438
\(550\) −12.3959 −0.528563
\(551\) −22.8231 −0.972296
\(552\) −35.9957 −1.53208
\(553\) −18.3434 −0.780039
\(554\) 63.3610 2.69195
\(555\) 16.7105 0.709321
\(556\) −25.4269 −1.07834
\(557\) −9.57659 −0.405773 −0.202887 0.979202i \(-0.565032\pi\)
−0.202887 + 0.979202i \(0.565032\pi\)
\(558\) −9.01538 −0.381652
\(559\) −0.727609 −0.0307746
\(560\) −15.1998 −0.642309
\(561\) −3.70459 −0.156408
\(562\) −35.4202 −1.49411
\(563\) −19.6264 −0.827156 −0.413578 0.910469i \(-0.635721\pi\)
−0.413578 + 0.910469i \(0.635721\pi\)
\(564\) 117.448 4.94546
\(565\) 1.64065 0.0690225
\(566\) 23.1735 0.974056
\(567\) −31.3878 −1.31816
\(568\) 17.5966 0.738336
\(569\) −26.1269 −1.09530 −0.547648 0.836709i \(-0.684477\pi\)
−0.547648 + 0.836709i \(0.684477\pi\)
\(570\) −23.8652 −0.999605
\(571\) 19.8091 0.828986 0.414493 0.910053i \(-0.363959\pi\)
0.414493 + 0.910053i \(0.363959\pi\)
\(572\) −1.00520 −0.0420295
\(573\) −3.63998 −0.152062
\(574\) 25.4308 1.06146
\(575\) −6.04129 −0.251939
\(576\) 146.503 6.10429
\(577\) 3.03944 0.126534 0.0632669 0.997997i \(-0.479848\pi\)
0.0632669 + 0.997997i \(0.479848\pi\)
\(578\) 42.0125 1.74749
\(579\) 63.8158 2.65210
\(580\) −16.8045 −0.697771
\(581\) −9.25315 −0.383885
\(582\) −138.027 −5.72141
\(583\) 4.73685 0.196180
\(584\) −4.83337 −0.200006
\(585\) 0.821633 0.0339703
\(586\) −83.1124 −3.43334
\(587\) −27.1861 −1.12209 −0.561044 0.827786i \(-0.689600\pi\)
−0.561044 + 0.827786i \(0.689600\pi\)
\(588\) −59.0875 −2.43673
\(589\) 2.20652 0.0909182
\(590\) −14.5750 −0.600042
\(591\) 39.5935 1.62866
\(592\) 110.712 4.55025
\(593\) −30.6121 −1.25709 −0.628545 0.777773i \(-0.716349\pi\)
−0.628545 + 0.777773i \(0.716349\pi\)
\(594\) 32.1864 1.32062
\(595\) −1.37489 −0.0563651
\(596\) 21.0428 0.861948
\(597\) 19.3216 0.790780
\(598\) −0.676480 −0.0276633
\(599\) −3.52901 −0.144191 −0.0720957 0.997398i \(-0.522969\pi\)
−0.0720957 + 0.997398i \(0.522969\pi\)
\(600\) 126.261 5.15458
\(601\) 8.61605 0.351456 0.175728 0.984439i \(-0.443772\pi\)
0.175728 + 0.984439i \(0.443772\pi\)
\(602\) −18.8965 −0.770164
\(603\) 38.0493 1.54949
\(604\) 69.4946 2.82770
\(605\) 0.629801 0.0256051
\(606\) 36.8800 1.49815
\(607\) 21.0059 0.852604 0.426302 0.904581i \(-0.359816\pi\)
0.426302 + 0.904581i \(0.359816\pi\)
\(608\) −79.4675 −3.22283
\(609\) 29.3894 1.19092
\(610\) −15.3018 −0.619551
\(611\) 1.36658 0.0552859
\(612\) 42.3181 1.71061
\(613\) 18.6886 0.754827 0.377413 0.926045i \(-0.376814\pi\)
0.377413 + 0.926045i \(0.376814\pi\)
\(614\) −19.0451 −0.768596
\(615\) 10.0933 0.407002
\(616\) −16.1629 −0.651223
\(617\) −35.6183 −1.43394 −0.716969 0.697106i \(-0.754471\pi\)
−0.716969 + 0.697106i \(0.754471\pi\)
\(618\) −21.9103 −0.881362
\(619\) 6.41327 0.257771 0.128886 0.991659i \(-0.458860\pi\)
0.128886 + 0.991659i \(0.458860\pi\)
\(620\) 1.62466 0.0652477
\(621\) 15.6864 0.629474
\(622\) 46.1983 1.85238
\(623\) 22.8523 0.915559
\(624\) 7.83980 0.313843
\(625\) 19.2076 0.768303
\(626\) −36.0912 −1.44249
\(627\) −14.0721 −0.561984
\(628\) 80.8130 3.22479
\(629\) 10.0144 0.399301
\(630\) 21.3384 0.850142
\(631\) −34.6751 −1.38039 −0.690196 0.723622i \(-0.742476\pi\)
−0.690196 + 0.723622i \(0.742476\pi\)
\(632\) −86.9861 −3.46012
\(633\) 21.4980 0.854469
\(634\) 2.33131 0.0925882
\(635\) 2.63238 0.104463
\(636\) −77.9285 −3.09007
\(637\) −0.687518 −0.0272405
\(638\) −13.6827 −0.541702
\(639\) −13.6982 −0.541891
\(640\) −14.1714 −0.560173
\(641\) −34.0768 −1.34595 −0.672977 0.739663i \(-0.734985\pi\)
−0.672977 + 0.739663i \(0.734985\pi\)
\(642\) 48.2708 1.90510
\(643\) 40.8654 1.61157 0.805787 0.592205i \(-0.201742\pi\)
0.805787 + 0.592205i \(0.201742\pi\)
\(644\) −12.7229 −0.501354
\(645\) −7.49991 −0.295309
\(646\) −14.3022 −0.562712
\(647\) 25.8378 1.01579 0.507895 0.861419i \(-0.330424\pi\)
0.507895 + 0.861419i \(0.330424\pi\)
\(648\) −148.844 −5.84714
\(649\) −8.59409 −0.337348
\(650\) 2.37287 0.0930716
\(651\) −2.84135 −0.111361
\(652\) −33.7790 −1.32289
\(653\) 17.7986 0.696514 0.348257 0.937399i \(-0.386774\pi\)
0.348257 + 0.937399i \(0.386774\pi\)
\(654\) 39.3472 1.53860
\(655\) −13.3796 −0.522786
\(656\) 66.8715 2.61089
\(657\) 3.76256 0.146792
\(658\) 35.4910 1.38358
\(659\) −24.6302 −0.959455 −0.479728 0.877417i \(-0.659265\pi\)
−0.479728 + 0.877417i \(0.659265\pi\)
\(660\) −10.3612 −0.403309
\(661\) −41.0429 −1.59639 −0.798193 0.602402i \(-0.794210\pi\)
−0.798193 + 0.602402i \(0.794210\pi\)
\(662\) 69.9333 2.71804
\(663\) 0.709145 0.0275409
\(664\) −43.8794 −1.70285
\(665\) −5.22259 −0.202524
\(666\) −155.424 −6.02257
\(667\) −6.66840 −0.258202
\(668\) 42.5644 1.64687
\(669\) −19.1385 −0.739938
\(670\) −9.46837 −0.365795
\(671\) −9.02264 −0.348315
\(672\) 102.331 3.94749
\(673\) −31.4793 −1.21344 −0.606720 0.794916i \(-0.707515\pi\)
−0.606720 + 0.794916i \(0.707515\pi\)
\(674\) 9.17964 0.353587
\(675\) −55.0227 −2.11783
\(676\) −68.0729 −2.61819
\(677\) 47.1117 1.81065 0.905324 0.424721i \(-0.139628\pi\)
0.905324 + 0.424721i \(0.139628\pi\)
\(678\) −21.9769 −0.844016
\(679\) −30.2054 −1.15918
\(680\) −6.51988 −0.250026
\(681\) −46.0392 −1.76423
\(682\) 1.32283 0.0506539
\(683\) 8.62145 0.329890 0.164945 0.986303i \(-0.447255\pi\)
0.164945 + 0.986303i \(0.447255\pi\)
\(684\) 160.747 6.14633
\(685\) −0.351171 −0.0134175
\(686\) −52.6552 −2.01038
\(687\) 41.4224 1.58036
\(688\) −49.6893 −1.89439
\(689\) −0.906745 −0.0345442
\(690\) −6.97290 −0.265454
\(691\) 0.866372 0.0329583 0.0164792 0.999864i \(-0.494754\pi\)
0.0164792 + 0.999864i \(0.494754\pi\)
\(692\) 46.3733 1.76285
\(693\) 12.5821 0.477955
\(694\) −68.7477 −2.60963
\(695\) −3.04958 −0.115677
\(696\) 139.368 5.28271
\(697\) 6.04883 0.229116
\(698\) −11.4354 −0.432835
\(699\) −17.3169 −0.654986
\(700\) 44.6278 1.68677
\(701\) 21.4631 0.810651 0.405325 0.914172i \(-0.367158\pi\)
0.405325 + 0.914172i \(0.367158\pi\)
\(702\) −6.16123 −0.232541
\(703\) 38.0403 1.43472
\(704\) −21.4965 −0.810179
\(705\) 14.0862 0.530516
\(706\) 75.8329 2.85401
\(707\) 8.07070 0.303530
\(708\) 141.386 5.31362
\(709\) −3.55916 −0.133667 −0.0668334 0.997764i \(-0.521290\pi\)
−0.0668334 + 0.997764i \(0.521290\pi\)
\(710\) 3.40872 0.127927
\(711\) 67.7147 2.53950
\(712\) 108.368 4.06127
\(713\) 0.644698 0.0241441
\(714\) 18.4170 0.689239
\(715\) −0.120559 −0.00450864
\(716\) 0.911268 0.0340557
\(717\) 37.5266 1.40146
\(718\) 85.7189 3.19900
\(719\) 39.7147 1.48111 0.740553 0.671998i \(-0.234564\pi\)
0.740553 + 0.671998i \(0.234564\pi\)
\(720\) 56.1103 2.09111
\(721\) −4.79479 −0.178567
\(722\) −3.16435 −0.117765
\(723\) 81.6388 3.03618
\(724\) 105.881 3.93504
\(725\) 23.3905 0.868703
\(726\) −8.43634 −0.313102
\(727\) 31.3894 1.16417 0.582085 0.813128i \(-0.302237\pi\)
0.582085 + 0.813128i \(0.302237\pi\)
\(728\) 3.09397 0.114670
\(729\) 3.52714 0.130635
\(730\) −0.936295 −0.0346538
\(731\) −4.49462 −0.166240
\(732\) 148.436 5.48637
\(733\) 27.6658 1.02186 0.510929 0.859623i \(-0.329301\pi\)
0.510929 + 0.859623i \(0.329301\pi\)
\(734\) −8.19784 −0.302588
\(735\) −7.08667 −0.261396
\(736\) −23.2187 −0.855851
\(737\) −5.58299 −0.205652
\(738\) −93.8782 −3.45570
\(739\) −11.7156 −0.430967 −0.215483 0.976508i \(-0.569133\pi\)
−0.215483 + 0.976508i \(0.569133\pi\)
\(740\) 28.0089 1.02963
\(741\) 2.69372 0.0989564
\(742\) −23.5488 −0.864504
\(743\) 26.8519 0.985102 0.492551 0.870284i \(-0.336065\pi\)
0.492551 + 0.870284i \(0.336065\pi\)
\(744\) −13.4740 −0.493980
\(745\) 2.52377 0.0924639
\(746\) 3.59708 0.131699
\(747\) 34.1581 1.24978
\(748\) −6.20937 −0.227037
\(749\) 10.5634 0.385979
\(750\) 51.0247 1.86316
\(751\) −15.3552 −0.560317 −0.280159 0.959954i \(-0.590387\pi\)
−0.280159 + 0.959954i \(0.590387\pi\)
\(752\) 93.3253 3.40322
\(753\) −88.3051 −3.21802
\(754\) 2.61918 0.0953850
\(755\) 8.33485 0.303336
\(756\) −115.878 −4.21443
\(757\) 26.1359 0.949926 0.474963 0.880006i \(-0.342461\pi\)
0.474963 + 0.880006i \(0.342461\pi\)
\(758\) −55.1701 −2.00387
\(759\) −4.11155 −0.149240
\(760\) −24.7661 −0.898360
\(761\) 18.5541 0.672584 0.336292 0.941758i \(-0.390827\pi\)
0.336292 + 0.941758i \(0.390827\pi\)
\(762\) −35.2613 −1.27738
\(763\) 8.61061 0.311725
\(764\) −6.10107 −0.220729
\(765\) 5.07543 0.183503
\(766\) 7.40636 0.267603
\(767\) 1.64511 0.0594015
\(768\) 55.1355 1.98953
\(769\) −51.7237 −1.86520 −0.932602 0.360906i \(-0.882467\pi\)
−0.932602 + 0.360906i \(0.882467\pi\)
\(770\) −3.13100 −0.112833
\(771\) 74.2081 2.67254
\(772\) 106.964 3.84970
\(773\) 28.5848 1.02812 0.514061 0.857753i \(-0.328140\pi\)
0.514061 + 0.857753i \(0.328140\pi\)
\(774\) 69.7567 2.50735
\(775\) −2.26139 −0.0812314
\(776\) −143.237 −5.14192
\(777\) −48.9847 −1.75732
\(778\) −84.4194 −3.02658
\(779\) 22.9768 0.823229
\(780\) 1.98338 0.0710163
\(781\) 2.00994 0.0719213
\(782\) −4.17879 −0.149433
\(783\) −60.7343 −2.17047
\(784\) −46.9515 −1.67684
\(785\) 9.69233 0.345934
\(786\) 179.223 6.39269
\(787\) 17.6096 0.627715 0.313858 0.949470i \(-0.398379\pi\)
0.313858 + 0.949470i \(0.398379\pi\)
\(788\) 66.3638 2.36411
\(789\) −39.9842 −1.42348
\(790\) −16.8505 −0.599513
\(791\) −4.80935 −0.171001
\(792\) 59.6657 2.12013
\(793\) 1.72715 0.0613328
\(794\) 13.0560 0.463338
\(795\) −9.34637 −0.331482
\(796\) 32.3855 1.14787
\(797\) −50.9061 −1.80319 −0.901594 0.432584i \(-0.857602\pi\)
−0.901594 + 0.432584i \(0.857602\pi\)
\(798\) 69.9579 2.47648
\(799\) 8.44170 0.298646
\(800\) 81.4433 2.87946
\(801\) −84.3597 −2.98070
\(802\) −46.8185 −1.65322
\(803\) −0.552084 −0.0194826
\(804\) 91.8489 3.23926
\(805\) −1.52593 −0.0537819
\(806\) −0.253221 −0.00891934
\(807\) 10.8290 0.381199
\(808\) 38.2721 1.34641
\(809\) −21.9458 −0.771572 −0.385786 0.922588i \(-0.626070\pi\)
−0.385786 + 0.922588i \(0.626070\pi\)
\(810\) −28.8332 −1.01310
\(811\) −6.28402 −0.220662 −0.110331 0.993895i \(-0.535191\pi\)
−0.110331 + 0.993895i \(0.535191\pi\)
\(812\) 49.2604 1.72870
\(813\) 3.24743 0.113892
\(814\) 22.8055 0.799333
\(815\) −4.05129 −0.141910
\(816\) 48.4284 1.69533
\(817\) −17.0730 −0.597310
\(818\) 57.2464 2.00157
\(819\) −2.40851 −0.0841603
\(820\) 16.9177 0.590792
\(821\) 12.6725 0.442274 0.221137 0.975243i \(-0.429023\pi\)
0.221137 + 0.975243i \(0.429023\pi\)
\(822\) 4.70402 0.164071
\(823\) −9.89246 −0.344830 −0.172415 0.985024i \(-0.555157\pi\)
−0.172415 + 0.985024i \(0.555157\pi\)
\(824\) −22.7374 −0.792094
\(825\) 14.4219 0.502108
\(826\) 42.7247 1.48658
\(827\) −17.8162 −0.619531 −0.309765 0.950813i \(-0.600251\pi\)
−0.309765 + 0.950813i \(0.600251\pi\)
\(828\) 46.9669 1.63221
\(829\) 2.87695 0.0999205 0.0499603 0.998751i \(-0.484091\pi\)
0.0499603 + 0.998751i \(0.484091\pi\)
\(830\) −8.50008 −0.295042
\(831\) −73.7169 −2.55721
\(832\) 4.11493 0.142660
\(833\) −4.24697 −0.147149
\(834\) 40.8499 1.41452
\(835\) 5.10497 0.176665
\(836\) −23.5866 −0.815759
\(837\) 5.87176 0.202958
\(838\) −50.1417 −1.73212
\(839\) −2.09076 −0.0721810 −0.0360905 0.999349i \(-0.511490\pi\)
−0.0360905 + 0.999349i \(0.511490\pi\)
\(840\) 31.8914 1.10036
\(841\) −3.18140 −0.109704
\(842\) 49.2848 1.69847
\(843\) 41.2094 1.41933
\(844\) 36.0334 1.24032
\(845\) −8.16434 −0.280862
\(846\) −131.016 −4.50441
\(847\) −1.84618 −0.0634356
\(848\) −61.9227 −2.12643
\(849\) −26.9611 −0.925303
\(850\) 14.6578 0.502758
\(851\) 11.1145 0.381001
\(852\) −33.0666 −1.13284
\(853\) 4.72068 0.161633 0.0808165 0.996729i \(-0.474247\pi\)
0.0808165 + 0.996729i \(0.474247\pi\)
\(854\) 44.8552 1.53491
\(855\) 19.2793 0.659337
\(856\) 50.0928 1.71214
\(857\) 19.5735 0.668618 0.334309 0.942463i \(-0.391497\pi\)
0.334309 + 0.942463i \(0.391497\pi\)
\(858\) 1.61491 0.0551323
\(859\) −5.56044 −0.189720 −0.0948599 0.995491i \(-0.530240\pi\)
−0.0948599 + 0.995491i \(0.530240\pi\)
\(860\) −12.5708 −0.428661
\(861\) −29.5873 −1.00833
\(862\) −12.2700 −0.417919
\(863\) −40.4696 −1.37760 −0.688800 0.724951i \(-0.741862\pi\)
−0.688800 + 0.724951i \(0.741862\pi\)
\(864\) −211.470 −7.19437
\(865\) 5.56179 0.189107
\(866\) −32.4931 −1.10416
\(867\) −48.8791 −1.66002
\(868\) −4.76247 −0.161649
\(869\) −9.93583 −0.337050
\(870\) 26.9975 0.915302
\(871\) 1.06872 0.0362121
\(872\) 40.8324 1.38276
\(873\) 111.504 3.77383
\(874\) −15.8733 −0.536923
\(875\) 11.1661 0.377483
\(876\) 9.08263 0.306874
\(877\) −15.3534 −0.518447 −0.259224 0.965817i \(-0.583467\pi\)
−0.259224 + 0.965817i \(0.583467\pi\)
\(878\) −10.5452 −0.355884
\(879\) 96.6966 3.26150
\(880\) −8.23310 −0.277538
\(881\) 21.2911 0.717317 0.358658 0.933469i \(-0.383234\pi\)
0.358658 + 0.933469i \(0.383234\pi\)
\(882\) 65.9132 2.21941
\(883\) 33.1831 1.11670 0.558349 0.829606i \(-0.311435\pi\)
0.558349 + 0.829606i \(0.311435\pi\)
\(884\) 1.18862 0.0399776
\(885\) 16.9572 0.570009
\(886\) −25.6561 −0.861932
\(887\) −6.49011 −0.217917 −0.108958 0.994046i \(-0.534752\pi\)
−0.108958 + 0.994046i \(0.534752\pi\)
\(888\) −232.290 −7.79515
\(889\) −7.71648 −0.258802
\(890\) 20.9925 0.703670
\(891\) −17.0014 −0.569569
\(892\) −32.0786 −1.07407
\(893\) 32.0662 1.07305
\(894\) −33.8066 −1.13066
\(895\) 0.109293 0.00365327
\(896\) 41.5416 1.38781
\(897\) 0.787047 0.0262787
\(898\) −60.7093 −2.02590
\(899\) −2.49613 −0.0832506
\(900\) −164.744 −5.49147
\(901\) −5.60119 −0.186603
\(902\) 13.7748 0.458651
\(903\) 21.9850 0.731616
\(904\) −22.8064 −0.758530
\(905\) 12.6989 0.422125
\(906\) −111.647 −3.70923
\(907\) −4.64755 −0.154319 −0.0771597 0.997019i \(-0.524585\pi\)
−0.0771597 + 0.997019i \(0.524585\pi\)
\(908\) −77.1676 −2.56090
\(909\) −29.7931 −0.988174
\(910\) 0.599346 0.0198681
\(911\) −7.11176 −0.235623 −0.117812 0.993036i \(-0.537588\pi\)
−0.117812 + 0.993036i \(0.537588\pi\)
\(912\) 183.958 6.09144
\(913\) −5.01204 −0.165874
\(914\) −45.9968 −1.52144
\(915\) 17.8028 0.588541
\(916\) 69.4293 2.29401
\(917\) 39.2207 1.29518
\(918\) −38.0595 −1.25615
\(919\) −2.51517 −0.0829679 −0.0414839 0.999139i \(-0.513209\pi\)
−0.0414839 + 0.999139i \(0.513209\pi\)
\(920\) −7.23610 −0.238567
\(921\) 22.1579 0.730126
\(922\) 75.1327 2.47436
\(923\) −0.384750 −0.0126642
\(924\) 30.3726 0.999184
\(925\) −38.9861 −1.28186
\(926\) 21.7345 0.714239
\(927\) 17.7000 0.581345
\(928\) 89.8975 2.95103
\(929\) 15.4091 0.505557 0.252778 0.967524i \(-0.418656\pi\)
0.252778 + 0.967524i \(0.418656\pi\)
\(930\) −2.61011 −0.0855888
\(931\) −16.1323 −0.528716
\(932\) −29.0254 −0.950758
\(933\) −53.7491 −1.75967
\(934\) 113.018 3.69807
\(935\) −0.744721 −0.0243550
\(936\) −11.4214 −0.373321
\(937\) −20.0775 −0.655904 −0.327952 0.944694i \(-0.606358\pi\)
−0.327952 + 0.944694i \(0.606358\pi\)
\(938\) 27.7553 0.906243
\(939\) 41.9900 1.37029
\(940\) 23.6102 0.770080
\(941\) −41.0960 −1.33969 −0.669845 0.742501i \(-0.733639\pi\)
−0.669845 + 0.742501i \(0.733639\pi\)
\(942\) −129.831 −4.23012
\(943\) 6.71331 0.218615
\(944\) 112.347 3.65657
\(945\) −13.8978 −0.452096
\(946\) −10.2355 −0.332783
\(947\) −12.8115 −0.416318 −0.208159 0.978095i \(-0.566747\pi\)
−0.208159 + 0.978095i \(0.566747\pi\)
\(948\) 163.460 5.30893
\(949\) 0.105682 0.00343058
\(950\) 55.6784 1.80644
\(951\) −2.71235 −0.0879540
\(952\) 19.1122 0.619430
\(953\) −34.7415 −1.12539 −0.562694 0.826666i \(-0.690235\pi\)
−0.562694 + 0.826666i \(0.690235\pi\)
\(954\) 86.9307 2.81449
\(955\) −0.731733 −0.0236783
\(956\) 62.8994 2.03431
\(957\) 15.9190 0.514589
\(958\) −93.1775 −3.01043
\(959\) 1.02941 0.0332415
\(960\) 42.4151 1.36894
\(961\) −30.7587 −0.992215
\(962\) −4.36552 −0.140750
\(963\) −38.9950 −1.25660
\(964\) 136.837 4.40723
\(965\) 12.8287 0.412970
\(966\) 20.4402 0.657651
\(967\) −11.3562 −0.365190 −0.182595 0.983188i \(-0.558450\pi\)
−0.182595 + 0.983188i \(0.558450\pi\)
\(968\) −8.75479 −0.281389
\(969\) 16.6398 0.534547
\(970\) −27.7471 −0.890907
\(971\) −36.2369 −1.16290 −0.581449 0.813583i \(-0.697514\pi\)
−0.581449 + 0.813583i \(0.697514\pi\)
\(972\) 91.4017 2.93171
\(973\) 8.93946 0.286586
\(974\) −26.3914 −0.845636
\(975\) −2.76070 −0.0884131
\(976\) 117.949 3.77545
\(977\) 15.7635 0.504320 0.252160 0.967686i \(-0.418859\pi\)
0.252160 + 0.967686i \(0.418859\pi\)
\(978\) 54.2680 1.73530
\(979\) 12.3782 0.395607
\(980\) −11.8782 −0.379434
\(981\) −31.7862 −1.01485
\(982\) 45.6750 1.45755
\(983\) −16.6483 −0.530999 −0.265500 0.964111i \(-0.585537\pi\)
−0.265500 + 0.964111i \(0.585537\pi\)
\(984\) −140.306 −4.47279
\(985\) 7.95935 0.253606
\(986\) 16.1793 0.515255
\(987\) −41.2918 −1.31433
\(988\) 4.51503 0.143642
\(989\) −4.98836 −0.158621
\(990\) 11.5581 0.367341
\(991\) 53.4523 1.69797 0.848984 0.528418i \(-0.177215\pi\)
0.848984 + 0.528418i \(0.177215\pi\)
\(992\) −8.69125 −0.275947
\(993\) −81.3635 −2.58199
\(994\) −9.99222 −0.316934
\(995\) 3.88416 0.123136
\(996\) 82.4559 2.61271
\(997\) 5.49056 0.173888 0.0869438 0.996213i \(-0.472290\pi\)
0.0869438 + 0.996213i \(0.472290\pi\)
\(998\) 17.4174 0.551339
\(999\) 101.229 3.20274
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 6017.2.a.f.1.4 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.4 121 1.1 even 1 trivial