Properties

Label 2671.2.a.a.1.13
Level $2671$
Weight $2$
Character 2671.1
Self dual yes
Analytic conductor $21.328$
Analytic rank $1$
Dimension $100$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2671 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2671.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.3280423799\)
Analytic rank: \(1\)
Dimension: \(100\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 2671.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.34805 q^{2} -1.17352 q^{3} +3.51335 q^{4} +0.325575 q^{5} +2.75549 q^{6} -3.11218 q^{7} -3.55342 q^{8} -1.62284 q^{9} +O(q^{10})\) \(q-2.34805 q^{2} -1.17352 q^{3} +3.51335 q^{4} +0.325575 q^{5} +2.75549 q^{6} -3.11218 q^{7} -3.55342 q^{8} -1.62284 q^{9} -0.764466 q^{10} +0.901782 q^{11} -4.12299 q^{12} +0.278911 q^{13} +7.30756 q^{14} -0.382069 q^{15} +1.31691 q^{16} +4.78193 q^{17} +3.81052 q^{18} -6.54262 q^{19} +1.14386 q^{20} +3.65222 q^{21} -2.11743 q^{22} +0.624344 q^{23} +4.17002 q^{24} -4.89400 q^{25} -0.654898 q^{26} +5.42501 q^{27} -10.9342 q^{28} +4.53032 q^{29} +0.897119 q^{30} +10.5723 q^{31} +4.01465 q^{32} -1.05826 q^{33} -11.2282 q^{34} -1.01325 q^{35} -5.70161 q^{36} +2.02104 q^{37} +15.3624 q^{38} -0.327309 q^{39} -1.15690 q^{40} -5.23071 q^{41} -8.57560 q^{42} +7.56540 q^{43} +3.16827 q^{44} -0.528357 q^{45} -1.46599 q^{46} -10.7040 q^{47} -1.54543 q^{48} +2.68568 q^{49} +11.4914 q^{50} -5.61170 q^{51} +0.979913 q^{52} +1.60569 q^{53} -12.7382 q^{54} +0.293597 q^{55} +11.0589 q^{56} +7.67792 q^{57} -10.6374 q^{58} +8.21823 q^{59} -1.34234 q^{60} -12.1066 q^{61} -24.8243 q^{62} +5.05058 q^{63} -12.0604 q^{64} +0.0908065 q^{65} +2.48486 q^{66} +11.3945 q^{67} +16.8006 q^{68} -0.732683 q^{69} +2.37916 q^{70} -3.12791 q^{71} +5.76664 q^{72} -2.36889 q^{73} -4.74550 q^{74} +5.74322 q^{75} -22.9865 q^{76} -2.80651 q^{77} +0.768539 q^{78} +13.5492 q^{79} +0.428754 q^{80} -1.49785 q^{81} +12.2820 q^{82} -12.4417 q^{83} +12.8315 q^{84} +1.55687 q^{85} -17.7640 q^{86} -5.31644 q^{87} -3.20441 q^{88} -4.77624 q^{89} +1.24061 q^{90} -0.868023 q^{91} +2.19354 q^{92} -12.4068 q^{93} +25.1335 q^{94} -2.13011 q^{95} -4.71129 q^{96} +13.8789 q^{97} -6.30611 q^{98} -1.46345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 15q^{2} - 12q^{3} + 89q^{4} - 33q^{5} - 28q^{6} - 14q^{7} - 45q^{8} + 60q^{9} + O(q^{10}) \) \( 100q - 15q^{2} - 12q^{3} + 89q^{4} - 33q^{5} - 28q^{6} - 14q^{7} - 45q^{8} + 60q^{9} - 18q^{10} - 47q^{11} - 27q^{12} - 29q^{13} - 51q^{14} - 36q^{15} + 71q^{16} - 99q^{17} - 27q^{18} - 45q^{19} - 75q^{20} - 79q^{21} - 2q^{22} - 25q^{23} - 66q^{24} + 67q^{25} - 73q^{26} - 42q^{27} - 31q^{28} - 78q^{29} - 29q^{30} - 41q^{31} - 95q^{32} - 83q^{33} - 44q^{34} - 45q^{35} + 23q^{36} - 16q^{37} - 29q^{38} - 42q^{39} - 37q^{40} - 235q^{41} + 16q^{42} - 6q^{43} - 122q^{44} - 79q^{45} - 17q^{46} - 67q^{47} - 25q^{48} + 30q^{49} - 68q^{50} - 18q^{51} - 41q^{52} - 69q^{53} - 63q^{54} - 32q^{55} - 120q^{56} - 63q^{57} - 7q^{58} - 118q^{59} - 49q^{60} - 60q^{61} - 23q^{62} - 43q^{63} + 43q^{64} - 181q^{65} - 4q^{66} - 18q^{67} - 130q^{68} - 80q^{69} + 12q^{70} - 77q^{71} - 40q^{72} - 64q^{73} - 48q^{74} - 18q^{75} - 134q^{76} - 87q^{77} + 65q^{78} - 48q^{79} - 95q^{80} - 20q^{81} + 45q^{82} - 108q^{83} - 97q^{84} - 21q^{85} - 73q^{86} - 3q^{87} + 23q^{88} - 325q^{89} + 6q^{90} - 17q^{91} - 19q^{92} + 2q^{93} - 5q^{94} - 54q^{95} - 105q^{96} - 81q^{97} - 61q^{98} - 76q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34805 −1.66032 −0.830162 0.557523i \(-0.811752\pi\)
−0.830162 + 0.557523i \(0.811752\pi\)
\(3\) −1.17352 −0.677534 −0.338767 0.940870i \(-0.610010\pi\)
−0.338767 + 0.940870i \(0.610010\pi\)
\(4\) 3.51335 1.75667
\(5\) 0.325575 0.145601 0.0728007 0.997347i \(-0.476806\pi\)
0.0728007 + 0.997347i \(0.476806\pi\)
\(6\) 2.75549 1.12493
\(7\) −3.11218 −1.17629 −0.588147 0.808754i \(-0.700142\pi\)
−0.588147 + 0.808754i \(0.700142\pi\)
\(8\) −3.55342 −1.25632
\(9\) −1.62284 −0.540948
\(10\) −0.764466 −0.241745
\(11\) 0.901782 0.271898 0.135949 0.990716i \(-0.456592\pi\)
0.135949 + 0.990716i \(0.456592\pi\)
\(12\) −4.12299 −1.19021
\(13\) 0.278911 0.0773561 0.0386781 0.999252i \(-0.487685\pi\)
0.0386781 + 0.999252i \(0.487685\pi\)
\(14\) 7.30756 1.95303
\(15\) −0.382069 −0.0986499
\(16\) 1.31691 0.329228
\(17\) 4.78193 1.15979 0.579894 0.814692i \(-0.303094\pi\)
0.579894 + 0.814692i \(0.303094\pi\)
\(18\) 3.81052 0.898148
\(19\) −6.54262 −1.50098 −0.750490 0.660881i \(-0.770183\pi\)
−0.750490 + 0.660881i \(0.770183\pi\)
\(20\) 1.14386 0.255774
\(21\) 3.65222 0.796979
\(22\) −2.11743 −0.451438
\(23\) 0.624344 0.130185 0.0650924 0.997879i \(-0.479266\pi\)
0.0650924 + 0.997879i \(0.479266\pi\)
\(24\) 4.17002 0.851201
\(25\) −4.89400 −0.978800
\(26\) −0.654898 −0.128436
\(27\) 5.42501 1.04404
\(28\) −10.9342 −2.06637
\(29\) 4.53032 0.841260 0.420630 0.907232i \(-0.361809\pi\)
0.420630 + 0.907232i \(0.361809\pi\)
\(30\) 0.897119 0.163791
\(31\) 10.5723 1.89884 0.949419 0.314013i \(-0.101674\pi\)
0.949419 + 0.314013i \(0.101674\pi\)
\(32\) 4.01465 0.709697
\(33\) −1.05826 −0.184220
\(34\) −11.2282 −1.92562
\(35\) −1.01325 −0.171270
\(36\) −5.70161 −0.950268
\(37\) 2.02104 0.332257 0.166128 0.986104i \(-0.446873\pi\)
0.166128 + 0.986104i \(0.446873\pi\)
\(38\) 15.3624 2.49211
\(39\) −0.327309 −0.0524114
\(40\) −1.15690 −0.182922
\(41\) −5.23071 −0.816900 −0.408450 0.912781i \(-0.633931\pi\)
−0.408450 + 0.912781i \(0.633931\pi\)
\(42\) −8.57560 −1.32324
\(43\) 7.56540 1.15371 0.576856 0.816846i \(-0.304279\pi\)
0.576856 + 0.816846i \(0.304279\pi\)
\(44\) 3.16827 0.477635
\(45\) −0.528357 −0.0787627
\(46\) −1.46599 −0.216149
\(47\) −10.7040 −1.56134 −0.780669 0.624945i \(-0.785121\pi\)
−0.780669 + 0.624945i \(0.785121\pi\)
\(48\) −1.54543 −0.223063
\(49\) 2.68568 0.383668
\(50\) 11.4914 1.62512
\(51\) −5.61170 −0.785796
\(52\) 0.979913 0.135889
\(53\) 1.60569 0.220558 0.110279 0.993901i \(-0.464825\pi\)
0.110279 + 0.993901i \(0.464825\pi\)
\(54\) −12.7382 −1.73345
\(55\) 0.293597 0.0395887
\(56\) 11.0589 1.47781
\(57\) 7.67792 1.01697
\(58\) −10.6374 −1.39676
\(59\) 8.21823 1.06992 0.534961 0.844876i \(-0.320326\pi\)
0.534961 + 0.844876i \(0.320326\pi\)
\(60\) −1.34234 −0.173296
\(61\) −12.1066 −1.55009 −0.775046 0.631905i \(-0.782273\pi\)
−0.775046 + 0.631905i \(0.782273\pi\)
\(62\) −24.8243 −3.15268
\(63\) 5.05058 0.636314
\(64\) −12.0604 −1.50756
\(65\) 0.0908065 0.0112632
\(66\) 2.48486 0.305865
\(67\) 11.3945 1.39206 0.696030 0.718012i \(-0.254948\pi\)
0.696030 + 0.718012i \(0.254948\pi\)
\(68\) 16.8006 2.03737
\(69\) −0.732683 −0.0882046
\(70\) 2.37916 0.284364
\(71\) −3.12791 −0.371215 −0.185607 0.982624i \(-0.559425\pi\)
−0.185607 + 0.982624i \(0.559425\pi\)
\(72\) 5.76664 0.679605
\(73\) −2.36889 −0.277257 −0.138629 0.990344i \(-0.544269\pi\)
−0.138629 + 0.990344i \(0.544269\pi\)
\(74\) −4.74550 −0.551654
\(75\) 5.74322 0.663170
\(76\) −22.9865 −2.63673
\(77\) −2.80651 −0.319832
\(78\) 0.768539 0.0870199
\(79\) 13.5492 1.52440 0.762202 0.647340i \(-0.224119\pi\)
0.762202 + 0.647340i \(0.224119\pi\)
\(80\) 0.428754 0.0479361
\(81\) −1.49785 −0.166428
\(82\) 12.2820 1.35632
\(83\) −12.4417 −1.36565 −0.682826 0.730581i \(-0.739249\pi\)
−0.682826 + 0.730581i \(0.739249\pi\)
\(84\) 12.8315 1.40003
\(85\) 1.55687 0.168867
\(86\) −17.7640 −1.91554
\(87\) −5.31644 −0.569982
\(88\) −3.20441 −0.341591
\(89\) −4.77624 −0.506281 −0.253140 0.967430i \(-0.581463\pi\)
−0.253140 + 0.967430i \(0.581463\pi\)
\(90\) 1.24061 0.130772
\(91\) −0.868023 −0.0909936
\(92\) 2.19354 0.228692
\(93\) −12.4068 −1.28653
\(94\) 25.1335 2.59233
\(95\) −2.13011 −0.218545
\(96\) −4.71129 −0.480844
\(97\) 13.8789 1.40918 0.704592 0.709612i \(-0.251130\pi\)
0.704592 + 0.709612i \(0.251130\pi\)
\(98\) −6.30611 −0.637013
\(99\) −1.46345 −0.147082
\(100\) −17.1943 −1.71943
\(101\) −12.4264 −1.23647 −0.618237 0.785992i \(-0.712153\pi\)
−0.618237 + 0.785992i \(0.712153\pi\)
\(102\) 13.1766 1.30467
\(103\) 14.4547 1.42427 0.712133 0.702044i \(-0.247729\pi\)
0.712133 + 0.702044i \(0.247729\pi\)
\(104\) −0.991089 −0.0971842
\(105\) 1.18907 0.116041
\(106\) −3.77024 −0.366198
\(107\) −8.28486 −0.800927 −0.400464 0.916313i \(-0.631151\pi\)
−0.400464 + 0.916313i \(0.631151\pi\)
\(108\) 19.0600 1.83405
\(109\) 2.46382 0.235991 0.117996 0.993014i \(-0.462353\pi\)
0.117996 + 0.993014i \(0.462353\pi\)
\(110\) −0.689382 −0.0657300
\(111\) −2.37174 −0.225115
\(112\) −4.09847 −0.387269
\(113\) −5.48211 −0.515713 −0.257857 0.966183i \(-0.583016\pi\)
−0.257857 + 0.966183i \(0.583016\pi\)
\(114\) −18.0282 −1.68849
\(115\) 0.203271 0.0189551
\(116\) 15.9166 1.47782
\(117\) −0.452629 −0.0418456
\(118\) −19.2968 −1.77642
\(119\) −14.8822 −1.36425
\(120\) 1.35765 0.123936
\(121\) −10.1868 −0.926072
\(122\) 28.4269 2.57365
\(123\) 6.13836 0.553477
\(124\) 37.1441 3.33564
\(125\) −3.22124 −0.288116
\(126\) −11.8590 −1.05649
\(127\) 10.8580 0.963489 0.481744 0.876312i \(-0.340003\pi\)
0.481744 + 0.876312i \(0.340003\pi\)
\(128\) 20.2892 1.79333
\(129\) −8.87817 −0.781680
\(130\) −0.213218 −0.0187005
\(131\) 9.97166 0.871228 0.435614 0.900134i \(-0.356531\pi\)
0.435614 + 0.900134i \(0.356531\pi\)
\(132\) −3.71804 −0.323614
\(133\) 20.3618 1.76559
\(134\) −26.7549 −2.31127
\(135\) 1.76625 0.152014
\(136\) −16.9922 −1.45707
\(137\) 20.5105 1.75233 0.876166 0.482009i \(-0.160093\pi\)
0.876166 + 0.482009i \(0.160093\pi\)
\(138\) 1.72038 0.146448
\(139\) 1.58378 0.134334 0.0671671 0.997742i \(-0.478604\pi\)
0.0671671 + 0.997742i \(0.478604\pi\)
\(140\) −3.55989 −0.300866
\(141\) 12.5614 1.05786
\(142\) 7.34450 0.616337
\(143\) 0.251517 0.0210329
\(144\) −2.13714 −0.178095
\(145\) 1.47496 0.122489
\(146\) 5.56227 0.460337
\(147\) −3.15171 −0.259948
\(148\) 7.10061 0.583667
\(149\) 2.07286 0.169816 0.0849078 0.996389i \(-0.472940\pi\)
0.0849078 + 0.996389i \(0.472940\pi\)
\(150\) −13.4854 −1.10108
\(151\) 1.07759 0.0876927 0.0438463 0.999038i \(-0.486039\pi\)
0.0438463 + 0.999038i \(0.486039\pi\)
\(152\) 23.2487 1.88572
\(153\) −7.76032 −0.627384
\(154\) 6.58983 0.531024
\(155\) 3.44207 0.276473
\(156\) −1.14995 −0.0920697
\(157\) −5.99232 −0.478239 −0.239119 0.970990i \(-0.576859\pi\)
−0.239119 + 0.970990i \(0.576859\pi\)
\(158\) −31.8142 −2.53100
\(159\) −1.88431 −0.149436
\(160\) 1.30707 0.103333
\(161\) −1.94307 −0.153136
\(162\) 3.51703 0.276324
\(163\) 5.29279 0.414563 0.207282 0.978281i \(-0.433538\pi\)
0.207282 + 0.978281i \(0.433538\pi\)
\(164\) −18.3773 −1.43503
\(165\) −0.344543 −0.0268227
\(166\) 29.2137 2.26742
\(167\) −0.147895 −0.0114445 −0.00572224 0.999984i \(-0.501821\pi\)
−0.00572224 + 0.999984i \(0.501821\pi\)
\(168\) −12.9779 −1.00126
\(169\) −12.9222 −0.994016
\(170\) −3.65562 −0.280373
\(171\) 10.6176 0.811952
\(172\) 26.5799 2.02670
\(173\) −7.71964 −0.586913 −0.293457 0.955972i \(-0.594806\pi\)
−0.293457 + 0.955972i \(0.594806\pi\)
\(174\) 12.4833 0.946354
\(175\) 15.2310 1.15136
\(176\) 1.18757 0.0895164
\(177\) −9.64429 −0.724909
\(178\) 11.2149 0.840590
\(179\) −8.01095 −0.598766 −0.299383 0.954133i \(-0.596781\pi\)
−0.299383 + 0.954133i \(0.596781\pi\)
\(180\) −1.85630 −0.138360
\(181\) 5.11607 0.380275 0.190137 0.981757i \(-0.439107\pi\)
0.190137 + 0.981757i \(0.439107\pi\)
\(182\) 2.03816 0.151079
\(183\) 14.2074 1.05024
\(184\) −2.21856 −0.163554
\(185\) 0.657999 0.0483770
\(186\) 29.1318 2.13605
\(187\) 4.31226 0.315343
\(188\) −37.6068 −2.74276
\(189\) −16.8836 −1.22810
\(190\) 5.00161 0.362855
\(191\) 2.05663 0.148813 0.0744063 0.997228i \(-0.476294\pi\)
0.0744063 + 0.997228i \(0.476294\pi\)
\(192\) 14.1532 1.02142
\(193\) −1.33651 −0.0962042 −0.0481021 0.998842i \(-0.515317\pi\)
−0.0481021 + 0.998842i \(0.515317\pi\)
\(194\) −32.5883 −2.33970
\(195\) −0.106564 −0.00763117
\(196\) 9.43572 0.673980
\(197\) −27.3001 −1.94505 −0.972525 0.232796i \(-0.925212\pi\)
−0.972525 + 0.232796i \(0.925212\pi\)
\(198\) 3.43626 0.244204
\(199\) 2.87597 0.203872 0.101936 0.994791i \(-0.467496\pi\)
0.101936 + 0.994791i \(0.467496\pi\)
\(200\) 17.3904 1.22969
\(201\) −13.3717 −0.943168
\(202\) 29.1778 2.05295
\(203\) −14.0992 −0.989569
\(204\) −19.7159 −1.38039
\(205\) −1.70299 −0.118942
\(206\) −33.9405 −2.36474
\(207\) −1.01321 −0.0704232
\(208\) 0.367302 0.0254678
\(209\) −5.90002 −0.408113
\(210\) −2.79200 −0.192666
\(211\) −7.27685 −0.500959 −0.250479 0.968122i \(-0.580588\pi\)
−0.250479 + 0.968122i \(0.580588\pi\)
\(212\) 5.64134 0.387449
\(213\) 3.67068 0.251511
\(214\) 19.4533 1.32980
\(215\) 2.46310 0.167982
\(216\) −19.2773 −1.31166
\(217\) −32.9029 −2.23359
\(218\) −5.78518 −0.391822
\(219\) 2.77994 0.187851
\(220\) 1.03151 0.0695444
\(221\) 1.33373 0.0897167
\(222\) 5.56896 0.373764
\(223\) −14.5339 −0.973262 −0.486631 0.873608i \(-0.661774\pi\)
−0.486631 + 0.873608i \(0.661774\pi\)
\(224\) −12.4943 −0.834813
\(225\) 7.94220 0.529480
\(226\) 12.8723 0.856250
\(227\) 12.4510 0.826401 0.413200 0.910640i \(-0.364411\pi\)
0.413200 + 0.910640i \(0.364411\pi\)
\(228\) 26.9752 1.78648
\(229\) −28.0256 −1.85198 −0.925992 0.377543i \(-0.876769\pi\)
−0.925992 + 0.377543i \(0.876769\pi\)
\(230\) −0.477290 −0.0314716
\(231\) 3.29351 0.216697
\(232\) −16.0981 −1.05689
\(233\) −3.74643 −0.245437 −0.122718 0.992442i \(-0.539161\pi\)
−0.122718 + 0.992442i \(0.539161\pi\)
\(234\) 1.06280 0.0694772
\(235\) −3.48495 −0.227333
\(236\) 28.8735 1.87951
\(237\) −15.9003 −1.03283
\(238\) 34.9442 2.26510
\(239\) −9.38154 −0.606842 −0.303421 0.952857i \(-0.598129\pi\)
−0.303421 + 0.952857i \(0.598129\pi\)
\(240\) −0.503152 −0.0324783
\(241\) −27.5267 −1.77315 −0.886576 0.462583i \(-0.846923\pi\)
−0.886576 + 0.462583i \(0.846923\pi\)
\(242\) 23.9191 1.53758
\(243\) −14.5173 −0.931284
\(244\) −42.5347 −2.72301
\(245\) 0.874389 0.0558626
\(246\) −14.4132 −0.918951
\(247\) −1.82481 −0.116110
\(248\) −37.5677 −2.38555
\(249\) 14.6006 0.925275
\(250\) 7.56363 0.478366
\(251\) −23.5481 −1.48634 −0.743170 0.669103i \(-0.766679\pi\)
−0.743170 + 0.669103i \(0.766679\pi\)
\(252\) 17.7445 1.11780
\(253\) 0.563023 0.0353969
\(254\) −25.4951 −1.59970
\(255\) −1.82703 −0.114413
\(256\) −23.5193 −1.46996
\(257\) 6.13326 0.382582 0.191291 0.981533i \(-0.438733\pi\)
0.191291 + 0.981533i \(0.438733\pi\)
\(258\) 20.8464 1.29784
\(259\) −6.28984 −0.390832
\(260\) 0.319035 0.0197857
\(261\) −7.35200 −0.455077
\(262\) −23.4140 −1.44652
\(263\) −4.86356 −0.299900 −0.149950 0.988694i \(-0.547911\pi\)
−0.149950 + 0.988694i \(0.547911\pi\)
\(264\) 3.76045 0.231440
\(265\) 0.522772 0.0321136
\(266\) −47.8106 −2.93146
\(267\) 5.60503 0.343022
\(268\) 40.0329 2.44540
\(269\) −5.96648 −0.363783 −0.181891 0.983319i \(-0.558222\pi\)
−0.181891 + 0.983319i \(0.558222\pi\)
\(270\) −4.14724 −0.252393
\(271\) −23.8283 −1.44747 −0.723735 0.690078i \(-0.757576\pi\)
−0.723735 + 0.690078i \(0.757576\pi\)
\(272\) 6.29738 0.381835
\(273\) 1.01865 0.0616512
\(274\) −48.1598 −2.90944
\(275\) −4.41332 −0.266133
\(276\) −2.57417 −0.154947
\(277\) 6.80659 0.408968 0.204484 0.978870i \(-0.434448\pi\)
0.204484 + 0.978870i \(0.434448\pi\)
\(278\) −3.71879 −0.223038
\(279\) −17.1571 −1.02717
\(280\) 3.60049 0.215171
\(281\) −27.1593 −1.62019 −0.810094 0.586300i \(-0.800584\pi\)
−0.810094 + 0.586300i \(0.800584\pi\)
\(282\) −29.4948 −1.75639
\(283\) 0.271762 0.0161546 0.00807729 0.999967i \(-0.497429\pi\)
0.00807729 + 0.999967i \(0.497429\pi\)
\(284\) −10.9894 −0.652103
\(285\) 2.49974 0.148072
\(286\) −0.590576 −0.0349215
\(287\) 16.2789 0.960914
\(288\) −6.51515 −0.383909
\(289\) 5.86683 0.345107
\(290\) −3.46328 −0.203371
\(291\) −16.2872 −0.954771
\(292\) −8.32272 −0.487050
\(293\) 18.0364 1.05370 0.526849 0.849959i \(-0.323373\pi\)
0.526849 + 0.849959i \(0.323373\pi\)
\(294\) 7.40037 0.431598
\(295\) 2.67565 0.155782
\(296\) −7.18159 −0.417422
\(297\) 4.89218 0.283873
\(298\) −4.86719 −0.281949
\(299\) 0.174137 0.0100706
\(300\) 20.1779 1.16497
\(301\) −23.5449 −1.35711
\(302\) −2.53023 −0.145598
\(303\) 14.5827 0.837753
\(304\) −8.61607 −0.494165
\(305\) −3.94160 −0.225696
\(306\) 18.2216 1.04166
\(307\) 17.4149 0.993921 0.496961 0.867773i \(-0.334449\pi\)
0.496961 + 0.867773i \(0.334449\pi\)
\(308\) −9.86025 −0.561840
\(309\) −16.9630 −0.964989
\(310\) −8.08215 −0.459035
\(311\) −26.0417 −1.47669 −0.738345 0.674424i \(-0.764392\pi\)
−0.738345 + 0.674424i \(0.764392\pi\)
\(312\) 1.16307 0.0658456
\(313\) −3.55307 −0.200832 −0.100416 0.994946i \(-0.532017\pi\)
−0.100416 + 0.994946i \(0.532017\pi\)
\(314\) 14.0703 0.794031
\(315\) 1.64434 0.0926482
\(316\) 47.6030 2.67788
\(317\) −19.1080 −1.07321 −0.536605 0.843834i \(-0.680293\pi\)
−0.536605 + 0.843834i \(0.680293\pi\)
\(318\) 4.42447 0.248112
\(319\) 4.08536 0.228736
\(320\) −3.92657 −0.219502
\(321\) 9.72247 0.542656
\(322\) 4.56244 0.254255
\(323\) −31.2863 −1.74082
\(324\) −5.26247 −0.292360
\(325\) −1.36499 −0.0757162
\(326\) −12.4277 −0.688309
\(327\) −2.89135 −0.159892
\(328\) 18.5869 1.02629
\(329\) 33.3128 1.83659
\(330\) 0.809006 0.0445343
\(331\) −18.4441 −1.01378 −0.506891 0.862010i \(-0.669205\pi\)
−0.506891 + 0.862010i \(0.669205\pi\)
\(332\) −43.7119 −2.39900
\(333\) −3.27983 −0.179733
\(334\) 0.347266 0.0190015
\(335\) 3.70976 0.202686
\(336\) 4.80966 0.262388
\(337\) −1.17361 −0.0639307 −0.0319653 0.999489i \(-0.510177\pi\)
−0.0319653 + 0.999489i \(0.510177\pi\)
\(338\) 30.3420 1.65039
\(339\) 6.43338 0.349413
\(340\) 5.46984 0.296644
\(341\) 9.53389 0.516289
\(342\) −24.9308 −1.34810
\(343\) 13.4270 0.724987
\(344\) −26.8830 −1.44944
\(345\) −0.238543 −0.0128427
\(346\) 18.1261 0.974466
\(347\) 19.5628 1.05018 0.525092 0.851045i \(-0.324031\pi\)
0.525092 + 0.851045i \(0.324031\pi\)
\(348\) −18.6785 −1.00127
\(349\) −5.17091 −0.276792 −0.138396 0.990377i \(-0.544195\pi\)
−0.138396 + 0.990377i \(0.544195\pi\)
\(350\) −35.7632 −1.91163
\(351\) 1.51310 0.0807632
\(352\) 3.62034 0.192965
\(353\) −9.92715 −0.528369 −0.264185 0.964472i \(-0.585103\pi\)
−0.264185 + 0.964472i \(0.585103\pi\)
\(354\) 22.6453 1.20358
\(355\) −1.01837 −0.0540494
\(356\) −16.7806 −0.889370
\(357\) 17.4646 0.924327
\(358\) 18.8101 0.994146
\(359\) 36.6829 1.93605 0.968026 0.250851i \(-0.0807104\pi\)
0.968026 + 0.250851i \(0.0807104\pi\)
\(360\) 1.87747 0.0989514
\(361\) 23.8059 1.25294
\(362\) −12.0128 −0.631379
\(363\) 11.9544 0.627445
\(364\) −3.04967 −0.159846
\(365\) −0.771249 −0.0403690
\(366\) −33.3597 −1.74374
\(367\) −26.5453 −1.38565 −0.692827 0.721103i \(-0.743635\pi\)
−0.692827 + 0.721103i \(0.743635\pi\)
\(368\) 0.822208 0.0428605
\(369\) 8.48862 0.441900
\(370\) −1.54502 −0.0803215
\(371\) −4.99720 −0.259442
\(372\) −43.5895 −2.26001
\(373\) 7.71020 0.399219 0.199610 0.979876i \(-0.436033\pi\)
0.199610 + 0.979876i \(0.436033\pi\)
\(374\) −10.1254 −0.523572
\(375\) 3.78020 0.195208
\(376\) 38.0358 1.96154
\(377\) 1.26356 0.0650766
\(378\) 39.6436 2.03905
\(379\) 6.38638 0.328046 0.164023 0.986457i \(-0.447553\pi\)
0.164023 + 0.986457i \(0.447553\pi\)
\(380\) −7.48382 −0.383912
\(381\) −12.7421 −0.652796
\(382\) −4.82907 −0.247077
\(383\) −38.6132 −1.97304 −0.986522 0.163630i \(-0.947680\pi\)
−0.986522 + 0.163630i \(0.947680\pi\)
\(384\) −23.8099 −1.21504
\(385\) −0.913729 −0.0465679
\(386\) 3.13820 0.159730
\(387\) −12.2775 −0.624098
\(388\) 48.7613 2.47548
\(389\) 7.80422 0.395690 0.197845 0.980233i \(-0.436606\pi\)
0.197845 + 0.980233i \(0.436606\pi\)
\(390\) 0.250217 0.0126702
\(391\) 2.98557 0.150987
\(392\) −9.54334 −0.482011
\(393\) −11.7020 −0.590287
\(394\) 64.1020 3.22941
\(395\) 4.41127 0.221955
\(396\) −5.14161 −0.258376
\(397\) −34.1848 −1.71568 −0.857842 0.513913i \(-0.828195\pi\)
−0.857842 + 0.513913i \(0.828195\pi\)
\(398\) −6.75293 −0.338494
\(399\) −23.8951 −1.19625
\(400\) −6.44498 −0.322249
\(401\) −29.4431 −1.47032 −0.735159 0.677894i \(-0.762893\pi\)
−0.735159 + 0.677894i \(0.762893\pi\)
\(402\) 31.3975 1.56596
\(403\) 2.94873 0.146887
\(404\) −43.6583 −2.17208
\(405\) −0.487663 −0.0242321
\(406\) 33.1056 1.64300
\(407\) 1.82254 0.0903398
\(408\) 19.9407 0.987213
\(409\) 5.74323 0.283985 0.141992 0.989868i \(-0.454649\pi\)
0.141992 + 0.989868i \(0.454649\pi\)
\(410\) 3.99870 0.197482
\(411\) −24.0696 −1.18726
\(412\) 50.7845 2.50197
\(413\) −25.5766 −1.25854
\(414\) 2.37908 0.116925
\(415\) −4.05069 −0.198841
\(416\) 1.11973 0.0548994
\(417\) −1.85860 −0.0910161
\(418\) 13.8536 0.677599
\(419\) 34.8874 1.70436 0.852181 0.523247i \(-0.175280\pi\)
0.852181 + 0.523247i \(0.175280\pi\)
\(420\) 4.17761 0.203847
\(421\) 25.5550 1.24547 0.622737 0.782432i \(-0.286021\pi\)
0.622737 + 0.782432i \(0.286021\pi\)
\(422\) 17.0864 0.831754
\(423\) 17.3709 0.844602
\(424\) −5.70568 −0.277093
\(425\) −23.4028 −1.13520
\(426\) −8.61894 −0.417589
\(427\) 37.6780 1.82336
\(428\) −29.1076 −1.40697
\(429\) −0.295162 −0.0142505
\(430\) −5.78349 −0.278905
\(431\) −33.3519 −1.60650 −0.803251 0.595640i \(-0.796898\pi\)
−0.803251 + 0.595640i \(0.796898\pi\)
\(432\) 7.14427 0.343729
\(433\) 7.09935 0.341173 0.170586 0.985343i \(-0.445434\pi\)
0.170586 + 0.985343i \(0.445434\pi\)
\(434\) 77.2576 3.70848
\(435\) −1.73090 −0.0829902
\(436\) 8.65626 0.414560
\(437\) −4.08485 −0.195405
\(438\) −6.52745 −0.311894
\(439\) 24.6379 1.17591 0.587953 0.808895i \(-0.299934\pi\)
0.587953 + 0.808895i \(0.299934\pi\)
\(440\) −1.04327 −0.0497361
\(441\) −4.35843 −0.207544
\(442\) −3.13168 −0.148959
\(443\) 13.5680 0.644635 0.322318 0.946632i \(-0.395538\pi\)
0.322318 + 0.946632i \(0.395538\pi\)
\(444\) −8.33273 −0.395454
\(445\) −1.55502 −0.0737152
\(446\) 34.1264 1.61593
\(447\) −2.43255 −0.115056
\(448\) 37.5343 1.77333
\(449\) 20.3828 0.961922 0.480961 0.876742i \(-0.340288\pi\)
0.480961 + 0.876742i \(0.340288\pi\)
\(450\) −18.6487 −0.879107
\(451\) −4.71696 −0.222113
\(452\) −19.2605 −0.905940
\(453\) −1.26457 −0.0594148
\(454\) −29.2356 −1.37209
\(455\) −0.282606 −0.0132488
\(456\) −27.2829 −1.27764
\(457\) 0.759564 0.0355309 0.0177654 0.999842i \(-0.494345\pi\)
0.0177654 + 0.999842i \(0.494345\pi\)
\(458\) 65.8056 3.07489
\(459\) 25.9420 1.21087
\(460\) 0.714161 0.0332979
\(461\) −17.9079 −0.834055 −0.417028 0.908894i \(-0.636928\pi\)
−0.417028 + 0.908894i \(0.636928\pi\)
\(462\) −7.73332 −0.359787
\(463\) 14.5297 0.675253 0.337626 0.941280i \(-0.390376\pi\)
0.337626 + 0.941280i \(0.390376\pi\)
\(464\) 5.96604 0.276966
\(465\) −4.03934 −0.187320
\(466\) 8.79681 0.407504
\(467\) 17.9017 0.828391 0.414196 0.910188i \(-0.364063\pi\)
0.414196 + 0.910188i \(0.364063\pi\)
\(468\) −1.59024 −0.0735091
\(469\) −35.4618 −1.63747
\(470\) 8.18284 0.377446
\(471\) 7.03212 0.324023
\(472\) −29.2028 −1.34417
\(473\) 6.82234 0.313692
\(474\) 37.3347 1.71484
\(475\) 32.0196 1.46916
\(476\) −52.2864 −2.39654
\(477\) −2.60578 −0.119311
\(478\) 22.0283 1.00755
\(479\) −35.7490 −1.63341 −0.816706 0.577053i \(-0.804202\pi\)
−0.816706 + 0.577053i \(0.804202\pi\)
\(480\) −1.53388 −0.0700116
\(481\) 0.563691 0.0257021
\(482\) 64.6342 2.94401
\(483\) 2.28024 0.103755
\(484\) −35.7897 −1.62681
\(485\) 4.51861 0.205179
\(486\) 34.0873 1.54623
\(487\) −36.3886 −1.64893 −0.824463 0.565915i \(-0.808523\pi\)
−0.824463 + 0.565915i \(0.808523\pi\)
\(488\) 43.0198 1.94742
\(489\) −6.21121 −0.280881
\(490\) −2.05311 −0.0927501
\(491\) −23.0643 −1.04088 −0.520439 0.853899i \(-0.674232\pi\)
−0.520439 + 0.853899i \(0.674232\pi\)
\(492\) 21.5662 0.972279
\(493\) 21.6637 0.975682
\(494\) 4.28475 0.192780
\(495\) −0.476463 −0.0214154
\(496\) 13.9228 0.625151
\(497\) 9.73463 0.436658
\(498\) −34.2830 −1.53626
\(499\) −37.3057 −1.67003 −0.835015 0.550227i \(-0.814541\pi\)
−0.835015 + 0.550227i \(0.814541\pi\)
\(500\) −11.3173 −0.506126
\(501\) 0.173559 0.00775403
\(502\) 55.2920 2.46780
\(503\) 15.4181 0.687461 0.343730 0.939068i \(-0.388309\pi\)
0.343730 + 0.939068i \(0.388309\pi\)
\(504\) −17.9468 −0.799415
\(505\) −4.04572 −0.180032
\(506\) −1.32201 −0.0587704
\(507\) 15.1645 0.673480
\(508\) 38.1478 1.69254
\(509\) 3.86699 0.171401 0.0857006 0.996321i \(-0.472687\pi\)
0.0857006 + 0.996321i \(0.472687\pi\)
\(510\) 4.28996 0.189962
\(511\) 7.37241 0.326136
\(512\) 14.6460 0.647270
\(513\) −35.4938 −1.56709
\(514\) −14.4012 −0.635211
\(515\) 4.70609 0.207375
\(516\) −31.1921 −1.37316
\(517\) −9.65267 −0.424524
\(518\) 14.7689 0.648907
\(519\) 9.05917 0.397654
\(520\) −0.322673 −0.0141502
\(521\) 1.18885 0.0520844 0.0260422 0.999661i \(-0.491710\pi\)
0.0260422 + 0.999661i \(0.491710\pi\)
\(522\) 17.2629 0.755576
\(523\) −32.9351 −1.44015 −0.720075 0.693896i \(-0.755893\pi\)
−0.720075 + 0.693896i \(0.755893\pi\)
\(524\) 35.0339 1.53046
\(525\) −17.8740 −0.780084
\(526\) 11.4199 0.497931
\(527\) 50.5559 2.20225
\(528\) −1.39364 −0.0606504
\(529\) −22.6102 −0.983052
\(530\) −1.22750 −0.0533190
\(531\) −13.3369 −0.578772
\(532\) 71.5382 3.10157
\(533\) −1.45890 −0.0631922
\(534\) −13.1609 −0.569528
\(535\) −2.69734 −0.116616
\(536\) −40.4894 −1.74888
\(537\) 9.40104 0.405685
\(538\) 14.0096 0.603997
\(539\) 2.42190 0.104318
\(540\) 6.20544 0.267040
\(541\) −25.3091 −1.08812 −0.544062 0.839045i \(-0.683114\pi\)
−0.544062 + 0.839045i \(0.683114\pi\)
\(542\) 55.9502 2.40327
\(543\) −6.00383 −0.257649
\(544\) 19.1978 0.823098
\(545\) 0.802158 0.0343607
\(546\) −2.39183 −0.102361
\(547\) −21.1335 −0.903604 −0.451802 0.892118i \(-0.649219\pi\)
−0.451802 + 0.892118i \(0.649219\pi\)
\(548\) 72.0606 3.07828
\(549\) 19.6471 0.838519
\(550\) 10.3627 0.441867
\(551\) −29.6402 −1.26271
\(552\) 2.60353 0.110813
\(553\) −42.1676 −1.79315
\(554\) −15.9822 −0.679020
\(555\) −0.772177 −0.0327771
\(556\) 5.56436 0.235981
\(557\) −43.0616 −1.82458 −0.912290 0.409546i \(-0.865687\pi\)
−0.912290 + 0.409546i \(0.865687\pi\)
\(558\) 40.2859 1.70544
\(559\) 2.11008 0.0892467
\(560\) −1.33436 −0.0563870
\(561\) −5.06053 −0.213656
\(562\) 63.7714 2.69003
\(563\) 16.5865 0.699039 0.349520 0.936929i \(-0.386345\pi\)
0.349520 + 0.936929i \(0.386345\pi\)
\(564\) 44.1325 1.85831
\(565\) −1.78483 −0.0750886
\(566\) −0.638112 −0.0268218
\(567\) 4.66159 0.195768
\(568\) 11.1148 0.466366
\(569\) 28.8352 1.20884 0.604418 0.796667i \(-0.293406\pi\)
0.604418 + 0.796667i \(0.293406\pi\)
\(570\) −5.86951 −0.245847
\(571\) −35.5671 −1.48844 −0.744218 0.667937i \(-0.767178\pi\)
−0.744218 + 0.667937i \(0.767178\pi\)
\(572\) 0.883668 0.0369480
\(573\) −2.41350 −0.100826
\(574\) −38.2238 −1.59543
\(575\) −3.05554 −0.127425
\(576\) 19.5722 0.815508
\(577\) 12.2153 0.508531 0.254266 0.967134i \(-0.418166\pi\)
0.254266 + 0.967134i \(0.418166\pi\)
\(578\) −13.7756 −0.572990
\(579\) 1.56843 0.0651816
\(580\) 5.18204 0.215172
\(581\) 38.7208 1.60641
\(582\) 38.2431 1.58523
\(583\) 1.44798 0.0599693
\(584\) 8.41764 0.348324
\(585\) −0.147365 −0.00609278
\(586\) −42.3504 −1.74948
\(587\) 15.0470 0.621055 0.310528 0.950564i \(-0.399494\pi\)
0.310528 + 0.950564i \(0.399494\pi\)
\(588\) −11.0730 −0.456644
\(589\) −69.1704 −2.85012
\(590\) −6.28256 −0.258649
\(591\) 32.0373 1.31784
\(592\) 2.66153 0.109388
\(593\) 32.5019 1.33469 0.667347 0.744747i \(-0.267430\pi\)
0.667347 + 0.744747i \(0.267430\pi\)
\(594\) −11.4871 −0.471321
\(595\) −4.84528 −0.198637
\(596\) 7.28269 0.298311
\(597\) −3.37502 −0.138130
\(598\) −0.408882 −0.0167204
\(599\) 6.73077 0.275012 0.137506 0.990501i \(-0.456091\pi\)
0.137506 + 0.990501i \(0.456091\pi\)
\(600\) −20.4081 −0.833156
\(601\) 42.1103 1.71772 0.858858 0.512213i \(-0.171174\pi\)
0.858858 + 0.512213i \(0.171174\pi\)
\(602\) 55.2847 2.25323
\(603\) −18.4915 −0.753032
\(604\) 3.78593 0.154047
\(605\) −3.31656 −0.134837
\(606\) −34.2409 −1.39094
\(607\) 27.2151 1.10463 0.552314 0.833636i \(-0.313745\pi\)
0.552314 + 0.833636i \(0.313745\pi\)
\(608\) −26.2664 −1.06524
\(609\) 16.5457 0.670467
\(610\) 9.25509 0.374728
\(611\) −2.98547 −0.120779
\(612\) −27.2647 −1.10211
\(613\) 16.9023 0.682676 0.341338 0.939941i \(-0.389120\pi\)
0.341338 + 0.939941i \(0.389120\pi\)
\(614\) −40.8911 −1.65023
\(615\) 1.99849 0.0805871
\(616\) 9.97270 0.401812
\(617\) 6.68079 0.268958 0.134479 0.990916i \(-0.457064\pi\)
0.134479 + 0.990916i \(0.457064\pi\)
\(618\) 39.8299 1.60219
\(619\) 30.2690 1.21661 0.608307 0.793702i \(-0.291849\pi\)
0.608307 + 0.793702i \(0.291849\pi\)
\(620\) 12.0932 0.485674
\(621\) 3.38708 0.135919
\(622\) 61.1473 2.45178
\(623\) 14.8645 0.595535
\(624\) −0.431038 −0.0172553
\(625\) 23.4213 0.936850
\(626\) 8.34280 0.333445
\(627\) 6.92381 0.276510
\(628\) −21.0531 −0.840110
\(629\) 9.66446 0.385347
\(630\) −3.86100 −0.153826
\(631\) 17.3959 0.692518 0.346259 0.938139i \(-0.387452\pi\)
0.346259 + 0.938139i \(0.387452\pi\)
\(632\) −48.1459 −1.91514
\(633\) 8.53955 0.339417
\(634\) 44.8665 1.78188
\(635\) 3.53508 0.140285
\(636\) −6.62025 −0.262510
\(637\) 0.749066 0.0296791
\(638\) −9.59264 −0.379776
\(639\) 5.07611 0.200808
\(640\) 6.60566 0.261112
\(641\) 17.7232 0.700023 0.350012 0.936745i \(-0.386178\pi\)
0.350012 + 0.936745i \(0.386178\pi\)
\(642\) −22.8289 −0.900984
\(643\) 29.0692 1.14638 0.573189 0.819423i \(-0.305706\pi\)
0.573189 + 0.819423i \(0.305706\pi\)
\(644\) −6.82669 −0.269009
\(645\) −2.89051 −0.113814
\(646\) 73.4620 2.89032
\(647\) −38.8368 −1.52683 −0.763416 0.645908i \(-0.776479\pi\)
−0.763416 + 0.645908i \(0.776479\pi\)
\(648\) 5.32249 0.209087
\(649\) 7.41106 0.290909
\(650\) 3.20507 0.125713
\(651\) 38.6123 1.51333
\(652\) 18.5954 0.728252
\(653\) 7.84953 0.307176 0.153588 0.988135i \(-0.450917\pi\)
0.153588 + 0.988135i \(0.450917\pi\)
\(654\) 6.78905 0.265473
\(655\) 3.24652 0.126852
\(656\) −6.88839 −0.268947
\(657\) 3.84433 0.149982
\(658\) −78.2201 −3.04934
\(659\) −27.6785 −1.07820 −0.539100 0.842242i \(-0.681236\pi\)
−0.539100 + 0.842242i \(0.681236\pi\)
\(660\) −1.21050 −0.0471187
\(661\) 13.3687 0.519983 0.259992 0.965611i \(-0.416280\pi\)
0.259992 + 0.965611i \(0.416280\pi\)
\(662\) 43.3078 1.68320
\(663\) −1.56517 −0.0607861
\(664\) 44.2105 1.71570
\(665\) 6.62930 0.257073
\(666\) 7.70121 0.298416
\(667\) 2.82848 0.109519
\(668\) −0.519608 −0.0201042
\(669\) 17.0559 0.659418
\(670\) −8.71071 −0.336524
\(671\) −10.9175 −0.421466
\(672\) 14.6624 0.565614
\(673\) 20.5707 0.792944 0.396472 0.918047i \(-0.370234\pi\)
0.396472 + 0.918047i \(0.370234\pi\)
\(674\) 2.75570 0.106146
\(675\) −26.5500 −1.02191
\(676\) −45.4002 −1.74616
\(677\) −41.3070 −1.58756 −0.793778 0.608207i \(-0.791889\pi\)
−0.793778 + 0.608207i \(0.791889\pi\)
\(678\) −15.1059 −0.580139
\(679\) −43.1935 −1.65762
\(680\) −5.53222 −0.212151
\(681\) −14.6115 −0.559915
\(682\) −22.3861 −0.857207
\(683\) −46.8947 −1.79438 −0.897188 0.441648i \(-0.854394\pi\)
−0.897188 + 0.441648i \(0.854394\pi\)
\(684\) 37.3035 1.42633
\(685\) 6.67771 0.255142
\(686\) −31.5272 −1.20371
\(687\) 32.8887 1.25478
\(688\) 9.96298 0.379835
\(689\) 0.447845 0.0170615
\(690\) 0.560111 0.0213231
\(691\) −47.2198 −1.79633 −0.898163 0.439662i \(-0.855098\pi\)
−0.898163 + 0.439662i \(0.855098\pi\)
\(692\) −27.1218 −1.03101
\(693\) 4.55453 0.173012
\(694\) −45.9344 −1.74365
\(695\) 0.515638 0.0195593
\(696\) 18.8915 0.716081
\(697\) −25.0129 −0.947430
\(698\) 12.1416 0.459565
\(699\) 4.39652 0.166292
\(700\) 53.5119 2.02256
\(701\) −3.96292 −0.149678 −0.0748388 0.997196i \(-0.523844\pi\)
−0.0748388 + 0.997196i \(0.523844\pi\)
\(702\) −3.55283 −0.134093
\(703\) −13.2229 −0.498711
\(704\) −10.8759 −0.409901
\(705\) 4.08967 0.154026
\(706\) 23.3095 0.877264
\(707\) 38.6732 1.45446
\(708\) −33.8837 −1.27343
\(709\) 42.5890 1.59946 0.799731 0.600358i \(-0.204975\pi\)
0.799731 + 0.600358i \(0.204975\pi\)
\(710\) 2.39118 0.0897395
\(711\) −21.9882 −0.824622
\(712\) 16.9720 0.636052
\(713\) 6.60074 0.247200
\(714\) −41.0079 −1.53468
\(715\) 0.0818877 0.00306243
\(716\) −28.1452 −1.05184
\(717\) 11.0095 0.411156
\(718\) −86.1334 −3.21447
\(719\) 26.7342 0.997017 0.498508 0.866885i \(-0.333881\pi\)
0.498508 + 0.866885i \(0.333881\pi\)
\(720\) −0.695800 −0.0259309
\(721\) −44.9857 −1.67536
\(722\) −55.8975 −2.08029
\(723\) 32.3032 1.20137
\(724\) 17.9745 0.668019
\(725\) −22.1714 −0.823425
\(726\) −28.0696 −1.04176
\(727\) 27.3724 1.01519 0.507594 0.861597i \(-0.330535\pi\)
0.507594 + 0.861597i \(0.330535\pi\)
\(728\) 3.08445 0.114317
\(729\) 21.5299 0.797404
\(730\) 1.81093 0.0670257
\(731\) 36.1772 1.33806
\(732\) 49.9155 1.84493
\(733\) 28.0429 1.03579 0.517895 0.855444i \(-0.326716\pi\)
0.517895 + 0.855444i \(0.326716\pi\)
\(734\) 62.3298 2.30063
\(735\) −1.02612 −0.0378488
\(736\) 2.50653 0.0923918
\(737\) 10.2754 0.378498
\(738\) −19.9317 −0.733697
\(739\) 8.35865 0.307478 0.153739 0.988111i \(-0.450868\pi\)
0.153739 + 0.988111i \(0.450868\pi\)
\(740\) 2.31178 0.0849827
\(741\) 2.14146 0.0786685
\(742\) 11.7337 0.430757
\(743\) 25.6522 0.941086 0.470543 0.882377i \(-0.344058\pi\)
0.470543 + 0.882377i \(0.344058\pi\)
\(744\) 44.0866 1.61629
\(745\) 0.674872 0.0247254
\(746\) −18.1040 −0.662833
\(747\) 20.1909 0.738746
\(748\) 15.1505 0.553955
\(749\) 25.7840 0.942126
\(750\) −8.87609 −0.324109
\(751\) −15.6703 −0.571817 −0.285908 0.958257i \(-0.592295\pi\)
−0.285908 + 0.958257i \(0.592295\pi\)
\(752\) −14.0962 −0.514037
\(753\) 27.6342 1.00705
\(754\) −2.96690 −0.108048
\(755\) 0.350835 0.0127682
\(756\) −59.3181 −2.15738
\(757\) 1.03102 0.0374729 0.0187364 0.999824i \(-0.494036\pi\)
0.0187364 + 0.999824i \(0.494036\pi\)
\(758\) −14.9955 −0.544663
\(759\) −0.660720 −0.0239826
\(760\) 7.56918 0.274563
\(761\) −2.42703 −0.0879798 −0.0439899 0.999032i \(-0.514007\pi\)
−0.0439899 + 0.999032i \(0.514007\pi\)
\(762\) 29.9191 1.08385
\(763\) −7.66786 −0.277595
\(764\) 7.22566 0.261415
\(765\) −2.52656 −0.0913481
\(766\) 90.6658 3.27589
\(767\) 2.29216 0.0827651
\(768\) 27.6004 0.995945
\(769\) −8.01305 −0.288958 −0.144479 0.989508i \(-0.546151\pi\)
−0.144479 + 0.989508i \(0.546151\pi\)
\(770\) 2.14548 0.0773178
\(771\) −7.19753 −0.259213
\(772\) −4.69563 −0.168999
\(773\) 25.4058 0.913784 0.456892 0.889522i \(-0.348963\pi\)
0.456892 + 0.889522i \(0.348963\pi\)
\(774\) 28.8281 1.03620
\(775\) −51.7407 −1.85858
\(776\) −49.3174 −1.77039
\(777\) 7.38127 0.264802
\(778\) −18.3247 −0.656973
\(779\) 34.2226 1.22615
\(780\) −0.374395 −0.0134055
\(781\) −2.82070 −0.100932
\(782\) −7.01027 −0.250687
\(783\) 24.5771 0.878312
\(784\) 3.53681 0.126314
\(785\) −1.95095 −0.0696323
\(786\) 27.4768 0.980067
\(787\) −14.9432 −0.532667 −0.266333 0.963881i \(-0.585812\pi\)
−0.266333 + 0.963881i \(0.585812\pi\)
\(788\) −95.9147 −3.41682
\(789\) 5.70750 0.203192
\(790\) −10.3579 −0.368517
\(791\) 17.0613 0.606630
\(792\) 5.20025 0.184783
\(793\) −3.37667 −0.119909
\(794\) 80.2676 2.84859
\(795\) −0.613485 −0.0217581
\(796\) 10.1043 0.358137
\(797\) −19.5066 −0.690961 −0.345480 0.938426i \(-0.612284\pi\)
−0.345480 + 0.938426i \(0.612284\pi\)
\(798\) 56.1069 1.98616
\(799\) −51.1857 −1.81082
\(800\) −19.6477 −0.694652
\(801\) 7.75109 0.273871
\(802\) 69.1340 2.44120
\(803\) −2.13622 −0.0753856
\(804\) −46.9795 −1.65684
\(805\) −0.632615 −0.0222968
\(806\) −6.92377 −0.243879
\(807\) 7.00180 0.246475
\(808\) 44.1562 1.55341
\(809\) −50.5381 −1.77683 −0.888413 0.459046i \(-0.848191\pi\)
−0.888413 + 0.459046i \(0.848191\pi\)
\(810\) 1.14506 0.0402332
\(811\) −0.446678 −0.0156850 −0.00784249 0.999969i \(-0.502496\pi\)
−0.00784249 + 0.999969i \(0.502496\pi\)
\(812\) −49.5353 −1.73835
\(813\) 27.9631 0.980710
\(814\) −4.27941 −0.149993
\(815\) 1.72320 0.0603610
\(816\) −7.39013 −0.258706
\(817\) −49.4976 −1.73170
\(818\) −13.4854 −0.471506
\(819\) 1.40867 0.0492228
\(820\) −5.98318 −0.208942
\(821\) 1.74179 0.0607887 0.0303944 0.999538i \(-0.490324\pi\)
0.0303944 + 0.999538i \(0.490324\pi\)
\(822\) 56.5166 1.97124
\(823\) 0.906348 0.0315933 0.0157966 0.999875i \(-0.494972\pi\)
0.0157966 + 0.999875i \(0.494972\pi\)
\(824\) −51.3637 −1.78934
\(825\) 5.17914 0.180314
\(826\) 60.0553 2.08959
\(827\) −33.4505 −1.16319 −0.581593 0.813480i \(-0.697570\pi\)
−0.581593 + 0.813480i \(0.697570\pi\)
\(828\) −3.55977 −0.123711
\(829\) −11.8970 −0.413199 −0.206600 0.978426i \(-0.566240\pi\)
−0.206600 + 0.978426i \(0.566240\pi\)
\(830\) 9.51124 0.330140
\(831\) −7.98769 −0.277090
\(832\) −3.36380 −0.116619
\(833\) 12.8427 0.444974
\(834\) 4.36409 0.151116
\(835\) −0.0481510 −0.00166633
\(836\) −20.7288 −0.716921
\(837\) 57.3548 1.98247
\(838\) −81.9175 −2.82979
\(839\) −0.0212549 −0.000733802 0 −0.000366901 1.00000i \(-0.500117\pi\)
−0.000366901 1.00000i \(0.500117\pi\)
\(840\) −4.22526 −0.145785
\(841\) −8.47619 −0.292282
\(842\) −60.0044 −2.06789
\(843\) 31.8721 1.09773
\(844\) −25.5661 −0.880021
\(845\) −4.20714 −0.144730
\(846\) −40.7878 −1.40231
\(847\) 31.7031 1.08933
\(848\) 2.11455 0.0726141
\(849\) −0.318919 −0.0109453
\(850\) 54.9509 1.88480
\(851\) 1.26182 0.0432548
\(852\) 12.8964 0.441822
\(853\) −3.98662 −0.136499 −0.0682496 0.997668i \(-0.521741\pi\)
−0.0682496 + 0.997668i \(0.521741\pi\)
\(854\) −88.4698 −3.02738
\(855\) 3.45684 0.118221
\(856\) 29.4396 1.00622
\(857\) −51.6879 −1.76563 −0.882813 0.469725i \(-0.844353\pi\)
−0.882813 + 0.469725i \(0.844353\pi\)
\(858\) 0.693054 0.0236605
\(859\) 16.2703 0.555135 0.277568 0.960706i \(-0.410472\pi\)
0.277568 + 0.960706i \(0.410472\pi\)
\(860\) 8.65373 0.295090
\(861\) −19.1037 −0.651052
\(862\) 78.3119 2.66731
\(863\) −21.2682 −0.723977 −0.361989 0.932183i \(-0.617902\pi\)
−0.361989 + 0.932183i \(0.617902\pi\)
\(864\) 21.7796 0.740955
\(865\) −2.51332 −0.0854554
\(866\) −16.6696 −0.566457
\(867\) −6.88486 −0.233822
\(868\) −115.599 −3.92369
\(869\) 12.2184 0.414481
\(870\) 4.06424 0.137791
\(871\) 3.17806 0.107684
\(872\) −8.75499 −0.296481
\(873\) −22.5232 −0.762295
\(874\) 9.59144 0.324435
\(875\) 10.0251 0.338909
\(876\) 9.76691 0.329993
\(877\) −30.9034 −1.04353 −0.521767 0.853088i \(-0.674727\pi\)
−0.521767 + 0.853088i \(0.674727\pi\)
\(878\) −57.8512 −1.95238
\(879\) −21.1661 −0.713916
\(880\) 0.386642 0.0130337
\(881\) −2.04031 −0.0687400 −0.0343700 0.999409i \(-0.510942\pi\)
−0.0343700 + 0.999409i \(0.510942\pi\)
\(882\) 10.2338 0.344591
\(883\) −29.3945 −0.989204 −0.494602 0.869119i \(-0.664686\pi\)
−0.494602 + 0.869119i \(0.664686\pi\)
\(884\) 4.68587 0.157603
\(885\) −3.13994 −0.105548
\(886\) −31.8584 −1.07030
\(887\) −15.2813 −0.513095 −0.256548 0.966532i \(-0.582585\pi\)
−0.256548 + 0.966532i \(0.582585\pi\)
\(888\) 8.42777 0.282817
\(889\) −33.7920 −1.13335
\(890\) 3.65128 0.122391
\(891\) −1.35074 −0.0452514
\(892\) −51.0627 −1.70970
\(893\) 70.0322 2.34354
\(894\) 5.71176 0.191030
\(895\) −2.60816 −0.0871812
\(896\) −63.1438 −2.10949
\(897\) −0.204354 −0.00682317
\(898\) −47.8598 −1.59710
\(899\) 47.8958 1.59742
\(900\) 27.9037 0.930123
\(901\) 7.67829 0.255801
\(902\) 11.0757 0.368779
\(903\) 27.6305 0.919485
\(904\) 19.4802 0.647902
\(905\) 1.66566 0.0553685
\(906\) 2.96928 0.0986477
\(907\) 23.9857 0.796432 0.398216 0.917292i \(-0.369629\pi\)
0.398216 + 0.917292i \(0.369629\pi\)
\(908\) 43.7446 1.45172
\(909\) 20.1661 0.668867
\(910\) 0.663574 0.0219973
\(911\) 35.7417 1.18418 0.592088 0.805873i \(-0.298304\pi\)
0.592088 + 0.805873i \(0.298304\pi\)
\(912\) 10.1112 0.334814
\(913\) −11.2197 −0.371317
\(914\) −1.78350 −0.0589928
\(915\) 4.62557 0.152916
\(916\) −98.4637 −3.25333
\(917\) −31.0336 −1.02482
\(918\) −60.9132 −2.01044
\(919\) 52.8337 1.74282 0.871411 0.490553i \(-0.163205\pi\)
0.871411 + 0.490553i \(0.163205\pi\)
\(920\) −0.722306 −0.0238137
\(921\) −20.4368 −0.673416
\(922\) 42.0487 1.38480
\(923\) −0.872411 −0.0287157
\(924\) 11.5712 0.380665
\(925\) −9.89097 −0.325213
\(926\) −34.1165 −1.12114
\(927\) −23.4578 −0.770454
\(928\) 18.1877 0.597039
\(929\) 2.84065 0.0931987 0.0465994 0.998914i \(-0.485162\pi\)
0.0465994 + 0.998914i \(0.485162\pi\)
\(930\) 9.48459 0.311012
\(931\) −17.5714 −0.575879
\(932\) −13.1625 −0.431152
\(933\) 30.5605 1.00051
\(934\) −42.0341 −1.37540
\(935\) 1.40396 0.0459144
\(936\) 1.60838 0.0525716
\(937\) −32.7325 −1.06933 −0.534663 0.845066i \(-0.679561\pi\)
−0.534663 + 0.845066i \(0.679561\pi\)
\(938\) 83.2661 2.71873
\(939\) 4.16961 0.136070
\(940\) −12.2438 −0.399350
\(941\) −44.1617 −1.43963 −0.719815 0.694166i \(-0.755773\pi\)
−0.719815 + 0.694166i \(0.755773\pi\)
\(942\) −16.5118 −0.537983
\(943\) −3.26576 −0.106348
\(944\) 10.8227 0.352249
\(945\) −5.49688 −0.178814
\(946\) −16.0192 −0.520830
\(947\) 16.5346 0.537303 0.268652 0.963237i \(-0.413422\pi\)
0.268652 + 0.963237i \(0.413422\pi\)
\(948\) −55.8632 −1.81435
\(949\) −0.660710 −0.0214475
\(950\) −75.1837 −2.43928
\(951\) 22.4236 0.727136
\(952\) 52.8828 1.71394
\(953\) −42.5360 −1.37788 −0.688939 0.724820i \(-0.741923\pi\)
−0.688939 + 0.724820i \(0.741923\pi\)
\(954\) 6.11851 0.198094
\(955\) 0.669587 0.0216673
\(956\) −32.9606 −1.06602
\(957\) −4.79427 −0.154977
\(958\) 83.9405 2.71199
\(959\) −63.8325 −2.06126
\(960\) 4.60793 0.148720
\(961\) 80.7731 2.60558
\(962\) −1.32358 −0.0426738
\(963\) 13.4450 0.433260
\(964\) −96.7109 −3.11485
\(965\) −0.435134 −0.0140075
\(966\) −5.35413 −0.172266
\(967\) 1.77649 0.0571280 0.0285640 0.999592i \(-0.490907\pi\)
0.0285640 + 0.999592i \(0.490907\pi\)
\(968\) 36.1979 1.16344
\(969\) 36.7153 1.17946
\(970\) −10.6099 −0.340664
\(971\) 17.6973 0.567933 0.283966 0.958834i \(-0.408350\pi\)
0.283966 + 0.958834i \(0.408350\pi\)
\(972\) −51.0042 −1.63596
\(973\) −4.92901 −0.158017
\(974\) 85.4424 2.73775
\(975\) 1.60185 0.0513003
\(976\) −15.9434 −0.510334
\(977\) 9.86596 0.315640 0.157820 0.987468i \(-0.449553\pi\)
0.157820 + 0.987468i \(0.449553\pi\)
\(978\) 14.5842 0.466353
\(979\) −4.30713 −0.137657
\(980\) 3.07203 0.0981324
\(981\) −3.99840 −0.127659
\(982\) 54.1562 1.72819
\(983\) −36.7320 −1.17157 −0.585785 0.810467i \(-0.699214\pi\)
−0.585785 + 0.810467i \(0.699214\pi\)
\(984\) −21.8122 −0.695346
\(985\) −8.88822 −0.283202
\(986\) −50.8674 −1.61995
\(987\) −39.0933 −1.24435
\(988\) −6.41120 −0.203967
\(989\) 4.72342 0.150196
\(990\) 1.11876 0.0355565
\(991\) 16.2178 0.515177 0.257588 0.966255i \(-0.417072\pi\)
0.257588 + 0.966255i \(0.417072\pi\)
\(992\) 42.4440 1.34760
\(993\) 21.6446 0.686871
\(994\) −22.8574 −0.724993
\(995\) 0.936343 0.0296841
\(996\) 51.2970 1.62541
\(997\) 41.8714 1.32608 0.663040 0.748584i \(-0.269266\pi\)
0.663040 + 0.748584i \(0.269266\pi\)
\(998\) 87.5956 2.77279
\(999\) 10.9642 0.346891
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 2671.2.a.a.1.13 100
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2671.2.a.a.1.13 100 1.1 even 1 trivial